CN112432625B - Roundness measuring method based on two sensors - Google Patents
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Abstract
The invention discloses a roundness measuring method based on two sensors, which utilizes the two sensors to detect and detect a radial runout signal of a measured workpiece, adopts a rollover method algorithm and a two-point method algorithm to combine an estimated value based on the radial runout signal, and performs quantification and further ensures the estimated value through frequency domain hybridization, thereby ensuring the accuracy and precision of a measuring result.
Description
Technical Field
The invention relates to the technical field of roundness measurement, in particular to a roundness measurement method based on two sensors.
Background
Rotary parts can be finished with nanometer-scale surface finish quality by means of a single-point diamond lathe, and therefore, are widely used as core parts such as bearings, plungers/cylinders, optical mirrors, and the like. The roundness error of a standard rod configured by the main shaft measuring instrument of the American lion is less than 50 nanometers. The surface processing precision of the hydrostatic bearing is related to the static rigidity, the load capacity, the service life and the rotation precision of the main shaft; along with the reduction of the roundness error of the bearing, the revolution precision of the main shaft can reach the nanometer level, and the main shaft is hardly subjected to damping force. The surface topology of the optical lens determines its focusing power, image resolution, and imaging quality. Because of the large output pressure, the high-pressure plunger pump is used in various heavy-load machines such as tanks, armored cars, forging presses and the like; in the plunger pump, the roundness of the plunger and the cylinder is improved, which contributes to the improvement of the output pressure limit of the pump.
In order to machine these rotary parts, roundness measurement techniques are indispensable in addition to ultra-precision diamond turning machines, and thus, attention is paid to academia and industry. The roundness measuring instrument Talyrond 595H can be used for measuring the roundness of the workpiece at present, and the detection result can be obtained by the detection of the roundness measuring instrument. However, the accuracy and precision of the measurement result obtained by the currently adopted measurement method cannot be guaranteed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a roundness measuring method based on two sensors. The roundness measuring method based on the two sensors can reduce the system error and the random error in the measuring process and improve the accuracy and precision of the measuring result.
The purpose of the invention is realized by the following technical scheme: the roundness measuring method based on the two sensors comprises the following steps,
s1, fixing the workpiece to be measured on a three-jaw chuck in the measuring device, and aligning a first sensor and a second sensor in the measuring device with the measured section of the workpiece to be measured; adjusting the relative angle between a second rotary table and a first rotary table in the measuring device to enable the relative angle between the second rotary table and the first rotary table to be 0; then, in the rotating process of the first rotating platform, a first sensor and a second sensor in the measuring device synchronously acquire radial runout signals of the surface of the workpiece to be measured, wherein the radial runout signals acquired by the first sensor are m11(theta), and recording the radial run-out signal collected by the second sensor as m12(θ)；
S2, adjusting the relative angle between the second rotary table and the first rotary table in the measuring device again to enable the relative angle between the second rotary table and the first rotary table to be 180 degrees; then, in the process of rotating the first rotating platform, a first sensor and a second sensor in the measuring device synchronously acquire radial runout signals of the surface of the workpiece to be measured, wherein the radial runout signals acquired by the first sensor are recorded as m21(theta), and recording the radial run-out signal collected by the second sensor as m22(θ)；
S3, based on the collected radial runout signal m11(θ)、m12(θ)、m21(theta) and m22(theta), estimating the estimated value of the roundness profile of the measured workpiece by adopting a turnover algorithm;
S4based on the collected radial run-out signal m11(θ)、m12(θ)、m21(theta) and m22(theta), estimating the estimated value of the roundness profile of the measured workpiece by adopting a two-point method algorithm;
s5, carrying out frequency domain hybridization on the estimated values obtained in S3 and S4 to obtain a Fourier coefficient estimated value of the roundness error;
and S6, calculating the roundness profile of the measured workpiece through inverse Fourier transform based on the Fourier coefficient estimated value of the roundness error.
Preferably, in step S3, the estimation value obtained by the flipping algorithm includes the following steps,
s3-1, mixing11(theta) and m22(theta) first adding and then dividing by 2 to calculate a first estimate r of the roundness profiler,1(θ)；
S3-2, mixing12(theta) and m21(theta) adding the two, then dividing by 2 to calculate a second estimate r of the roundness profiler,2(θ)。
Preferably, in step S4, the estimation value obtained by the two-point method algorithm includes the steps of,
s4-1, mixing11(theta) and m12(θ) add to yield:
m(θ)＝m11(θ)+m12(θ)＝r(θ)+r(θ-180°)+noise11(θ)+noise12(θ), which is equation (1), Laplace transform of equation (1) is:
M(s)＝(1+e-πs)R(s)+Noise11(s)+Noise12(s), which is equation (2), a third estimate of the roundness profile is calculated from equation (2)
Further, in the present invention,
s4-2, mixing21(theta) and m22(θ) add to yield:
m(θ)＝r(θ)+r(θ-180°)+noise21(θ)+noise22(theta), which is formula (3),
laplace transform of equation (3) becomes:
M(s)＝(1+e-πs)R(s)+Noise21(s)+Noise22(s), which is equation (4), a fourth estimate of the roundness profile is calculated from equation (4)
Further, in the present invention,
preferably, in step S5, the frequency domain hybridization is based on the following principle:
Rhybrid(jk)＝Rt,1(jk) or Rt,2(jk), if k mod2 is 0, which is formula (5),
Rhybrid(jk)＝Rr,1(jk) or Rr,2(jk), if k mod2 is 1, which is formula (6);
wherein k is ═ infinity … -2,2 … ∞.
Preferably, the measuring device comprises a base, a first rotary table, a second rotary table, a chuck, a first displacement sensor and a second displacement sensor, wherein the first rotary table is arranged on the base; the second rotary table is arranged on the first rotary table through a magnetic suction seat; the chuck is arranged on the second rotary table; the central axis of the first rotary table, the central axis of the second rotary table and the central axis of the chuck are all positioned on the same straight line; the first displacement sensor and the second displacement sensor are respectively installed on the base through the first height adjusting mechanism and the second height adjusting mechanism, and the first displacement sensor and the second displacement sensor are located on the same straight line.
Preferably, the first height adjusting mechanism comprises a first guide rail and a first sliding table; the lower end of the first guide rail is arranged on the base, the first sliding table is connected with the first guide rail, and one end of the first displacement sensor is arranged on the first sliding table;
the second height adjusting mechanism comprises a second guide rail and a second sliding table; the lower extreme of second guide rail is installed on the base, the second slip table is connected with the guide rail, the one end of second displacement sensor is installed in the second slip table.
Preferably, the first rotating platform and the second rotating platform are both provided with a rotation angle measuring unit.
Compared with the prior art, the invention has the following advantages:
1. the invention utilizes two sensors to detect a workpiece to obtain two radial runout signals, and combines a roll-over method algorithm and a two-point method algorithm based on the two radial runout signals to realize self calibration and eliminate random measurement uncertainty caused by asynchronous errors of a turntable, thereby improving the accuracy and precision of a measurement result.
2. The measuring method can overcome the defect of the precision of the turntable and provide important basis for the research and development of the ultra-precise roundness measuring instrument with the self-calibration function.
3. Compared with the existing two-step method, the method can effectively solve the problem of odd harmonic suppression; compared with the existing three-point method, the measuring method reduces the use of parts and reduces the cost of the measuring device; compared with the existing multi-step method, the measuring method of the invention reduces the operation steps and avoids the verbose measuring process.
4. The method combines a turning method and a two-point method to evaluate the uncertainty of the roundness measurement result, and then further quantitatively evaluates the uncertainty of the roundness measurement result by adopting a frequency domain hybridization principle, thereby ensuring the accuracy and precision of the measurement result.
Drawings
Fig. 1 is a schematic structural diagram of a measuring apparatus according to the present invention.
FIG. 2 is a block diagram of a system for flip-flop roundness measurement.
FIG. 3 is a block diagram of a two-point method roundness measurement system.
FIG. 4 is a block diagram of the principle of frequency domain hybridization between the inversion method and the two-point method.
Fig. 5 is a polar plot of roundness profile measurements.
The device comprises a base 1, a first rotary table 2, a second rotary table 3, a chuck 4, a first displacement sensor 5, a second displacement sensor 6, a first height adjusting mechanism 7, a first guide rail 701, a first sliding table 702, a second height adjusting mechanism 8, a second guide rail 801, a second sliding table 802 and a workpiece to be measured 9.
Detailed Description
The invention is further illustrated by the following figures and examples.
The measuring device adopted in the measurement process of the present application as shown in fig. 1 comprises a base, a first rotary table, a second rotary table, a chuck, a first displacement sensor and a second displacement sensor, wherein the first rotary table is mounted on the base; the second rotary table is arranged on the first rotary table through a magnetic suction seat; the chuck is arranged on the second rotary table; the central axis of the first rotary table, the central axis of the second rotary table and the central axis of the chuck are all positioned on the same straight line; the first displacement sensor and the second displacement sensor are respectively installed on the base through the first height adjusting mechanism and the second height adjusting mechanism, and the first displacement sensor and the second displacement sensor are located on the same straight line. Specifically, when the magnetic suction seat is released, the second rotary table can rotate relative to the first rotary table to adjust the relative angle between the first rotary table and the second rotary table; when the relative angle is adjusted and the magnetic suction seat is sucked to fix the second rotary table on the first rotary table, the second rotary table rotates synchronously with the first rotary table and does not move relatively.
The first height adjusting mechanism comprises a first guide rail and a first sliding table; the lower end of the first guide rail is arranged on the base, the first sliding table is connected with the first guide rail, and one end of the first displacement sensor is arranged on the first sliding table; the second height adjusting mechanism comprises a second guide rail and a second sliding table; the lower extreme of second guide rail is installed on the base, the second slip table is connected with the guide rail, the one end of second displacement sensor is installed in the second slip table. The first height adjusting mechanism and the second height adjusting mechanism are identical in structure and respectively adjust the heights of the first sensor and the second sensor so as to meet the requirements of workpieces to be measured in different sizes.
And the first rotary table and the second rotary table are both provided with a corner measuring unit. The rotation angle measuring unit arranged on the first rotary table is a first rotation angle measuring unit and used for detecting the absolute rotation angle of the first rotary table; the rotation angle measuring unit mounted on the second turntable is a second rotation angle measuring unit for determining a relative angle between the second turntable and the first turntable. The structure is simple, and the measuring accuracy is ensured. Specifically, the first rotation angle measuring unit and the second rotation angle measuring unit in this embodiment both use circular encoders.
The roundness measuring method based on the two sensors comprises the following steps,
s1, fixing the workpiece to be measured on a three-jaw chuck in the measuring device, and aligning a first sensor and a second sensor in the measuring device with the measured section of the workpiece to be measured; adjusting the relative angle between a second rotary table and a first rotary table in the measuring device to enable the relative angle between the second rotary table and the first rotary table to be 0; then, in the rotating process of the first rotating platform, a first sensor and a second sensor in the measuring device synchronously acquire radial runout signals of the surface of the workpiece to be measured, wherein the radial runout signals acquired by the first sensor are m11(theta), and recording the radial run-out signal collected by the second sensor as m12(θ)；
Wherein m is11(θ)＝xs(θ)+xas,1(θ)+r(θ)+noise11(theta), which is formula (7),
m12(θ)＝-xs(θ)-xas,1(θ)+r(θ-180°)+noise12(theta) of the formula (8)
In the above formulae (7) and (8), xs(theta) represents the synchronous radial rotation error of the first rotary table, r (theta) represents the section roundness error of the measured workpiece, and xas,1(theta) represents the asynchronous radial gyration error, x, of the first turntable at the 1 st measurementas,2(θ)，noise11(theta) and noise12(θ) each represents sensor noise;
s2, readjusting the testMeasuring the relative angle between a second rotary table and a first rotary table in the device, wherein the relative angle between the second rotary table and the first rotary table is 180 degrees; then, in the process of rotating the first rotating platform, a first sensor and a second sensor in the measuring device synchronously acquire radial runout signals of the surface of the workpiece to be measured, wherein the radial runout signals acquired by the first sensor are recorded as m21(theta), and recording the radial run-out signal collected by the second sensor as m22(θ)；
Wherein m is21(θ)＝xs(θ)+xas,2(θ)+r(θ-180°)+noise21(theta), which is formula (9),
m22(θ)＝-xs(θ)-xas,2(θ)+r(θ)+noise22(theta) of the formula (10)
In the above formulae (9) and (10), xas,2(theta) represents the asynchronous radial gyration error, noise, of the first turntable at the 2 nd measurement21(theta) and noise22(θ) each represents sensor noise;
s3, based on the collected radial runout signal m11(θ)、m12(θ)、m21(theta) and m22(theta), estimating the estimated value of the roundness profile of the measured workpiece by adopting a turnover algorithm; as shown in the block diagram of the measurement system of the flipping method in fig. 2, the specific steps are as follows:
s3-1, mixing11(theta) and m22(theta) first adding and then dividing by 2 to calculate a first estimate r of the roundness profiler,1(θ); wherein the content of the first and second substances,
And then Fourier transform is carried out on the first estimation value to obtain a harmonic system estimation value:
let the total noise energy of the two sensors be
The distribution of energy in the frequency domain is pp(k) The total energy of asynchronous errors of the two turntables is
The distribution of energy in the frequency domain is px(k) Then the total variance of the roundness estimate is:
this is represented by the formula (13),
and the harmonic variance is:
this is the formula (14),
from a mathematical point of view, pp(k) And px(k) The power spectral densities of the sensor noise and the turntable asynchronous error respectively can be calculated by referring to the following formula:
s3-2, mixing12(theta) and m21(theta) adding the two, then dividing by 2 to calculate a second estimate r of the roundness profiler,2(theta). Wherein the content of the first and second substances,
Also by means of laplace transform
This is formula (18);
in the above formulae (17) and (18), R(s) is rr,1(θ) is a Laplace transform, s is a complex number.
From the phase shift, the second estimated value rr,2Uncertainty of (theta) and first estimated value rr,1Uncertainty of (θ) equals:
total variance of
And the variance of the harmonics is
S4, based on the collected radial runout signal m11(θ)、m12(θ)、m21(theta) and m22(theta), estimating the estimated value of the roundness profile of the measured workpiece by adopting a two-point method algorithm; as shown in fig. 4, the two-point method comprises the following steps:
s4-1, mixing11(theta) and m12(θ) add to yield:
m(θ)＝m11(θ)+m12(θ)＝r(θ)+r(θ-180°)+noise11(θ)+noise12(θ), which is equation (1), Laplace transform of equation (1) is:
M(s)＝(1+e-πs)R(s)+Noise11(s)+Noise12(s), which is equation (2), a third estimate R of the roundness profile is calculated from equation (2)t,1(s)；
That is to say that the first and second electrodes,
this is represented by the formula (19),
in the above formulae (2) and (19), M(s) and Noise11(s) and Noise12(s) is m (theta) and noise respectively11(theta) and noise12(θ) is a Laplace transform, s is a complex number.
Substituting s-jk into equation (19) to obtain a fourier coefficient of the roundness profile:
the third estimate also contains uncertainty, caused by sensor noise, whose harmonic variance is:
1+ e when the harmonic order k is an even number-jkπWith roundness harmonic variance equal to that of the sensor 2
When k is an odd number, 1+ e-jkπThe roundness harmonic variance becomes infinite at 0. The harmonic variance of the roundness is equal to:
pr,t(k) k is an odd number, which is formula (22),
S4-2, mixing21(theta) and m22(θ) add to yield:
m(θ)＝r(θ)+r(θ-180°)+noise21(θ)+noise22(theta), which is formula (3),
laplace transform of equation (3) becomes:
M(s)＝(1+e-πs)R(s)+Noise21(s)+Noise22(s) which is the formula (4), and the roundness profile is calculated from the formula (4)Fourth estimated value R oft,2(s) that is
in the above formulae (4) and (22), Noise21(s) and Noise22(s) are each noise21(theta) and noise22(θ) is a Laplace transform, s is a complex number.
From the above, the fourth estimated value Rt,2(s) and a third estimated value Rt,1(s) have the same uncertainty: when the harmonic order k is an odd number, the roundness harmonic variance is infinite; when k is an even number, the roundness harmonic variance is
S5, carrying out frequency domain hybridization on the estimated values obtained in S3 and S4 to obtain a Fourier coefficient estimated value of the roundness error; as can be seen from the steps (3) and (4), for odd harmonics, the harmonic coefficient of the roundness cannot be estimated by the two-point method (or the uncertainty of the harmonic is infinite), so that the harmonic coefficient can be estimated only by the overturning method; for even harmonics, the harmonic coefficient of roundness can be estimated by both the flip method and the two-point method, but the variance of the harmonic estimation by the two-point method is smaller than that of the flip estimation:
therefore, by appropriate frequency domain hybridization, uncertainty of the roundness estimation value can be reduced; as shown in fig. 4, the frequency domain hybridization is based on the following principle:
Rhybrid(jk)＝Rt,1(jk) or Rt,2(jk), if k mod2 is 0, which is formula (5),
Rhybrid(jk)＝Rr,1(jk) or Rr,2(jk), if k mod2 is 1, which is formula (6),
wherein k is ═ infinity … -2,2 … ∞.
Therefore, the fourier coefficient estimation value of the roundness error odd harmonic is obtained by the flip method, and the fourier coefficient estimation value of the even harmonic is obtained by the two-point method. The harmonic variance of circularity after frequency domain hybridization is
S6, obtaining the roundness profile r of the measured workpiece after Fourier inverse transformation calculation based on the Fourier coefficient estimated value of the roundness errorhybrid(theta), i.e.
The above-mentioned embodiments are preferred embodiments of the present invention, and the present invention is not limited thereto, and any other modifications or equivalent substitutions that do not depart from the technical spirit of the present invention are included in the scope of the present invention.
Claims (6)
1. The roundness measuring method based on the two sensors is characterized in that: comprises the following steps of (a) carrying out,
s1, fixing the workpiece to be measured on a three-jaw chuck in the measuring device, and aligning a first sensor and a second sensor in the measuring device with the measured section of the workpiece to be measured; adjusting the relative angle between a second rotary table and a first rotary table in the measuring device to enable the relative angle between the second rotary table and the first rotary table to be 0; then, in the rotating process of the first rotating platform, a first sensor and a second sensor in the measuring device synchronously acquire radial runout signals of the surface of the workpiece to be measured, wherein the radial runout signals acquired by the first sensor are m11(theta), and recording the radial run-out signal collected by the second sensor as m12(θ)；
S2, adjusting the relative angle between the second rotary table and the first rotary table in the measuring device again to enable the second rotary table and the first rotary table to rotateThe relative angle of the stages is 180 °; then, in the process of rotating the first rotating platform, a first sensor and a second sensor in the measuring device synchronously acquire radial runout signals of the surface of the workpiece to be measured, wherein the radial runout signals acquired by the first sensor are recorded as m21(theta), and recording the radial run-out signal collected by the second sensor as m22(θ)；
S3, based on the collected radial runout signal m11(θ)、m12(θ)、m21(theta) and m22(theta), estimating the Fourier coefficient of the estimated value of the roundness profile of the measured workpiece by adopting a flip algorithm: rr，1(jk) and Rr，2(jk), wherein k represents a harmonic order and j represents an imaginary unit;
s4, based on the collected radial runout signal m11(θ)、m12(θ)、m21(theta) and m22(θ), estimating a fourier coefficient of the estimated value of the roundness profile of the measured workpiece by using a two-point algorithm: rt，1(jk) and Rt，2(jk)；
S5, carrying out frequency domain hybridization on the estimated values obtained in S3 and S4 to obtain an estimated Fourier coefficient value R of the roundness errorhybrid(jk)；
And S6, calculating the roundness profile of the measured workpiece through inverse Fourier transform based on the Fourier coefficient estimated value of the roundness error.
2. The two-sensor based roundness measurement method of claim 1, wherein: in step S3, the estimation value obtained by the flip algorithm includes the steps of,
s3-1, mixing11(theta) and m22(theta) first adding and then dividing by 2 to calculate a first estimate r of the roundness profiler，1(θ)；
S3-2, mixing12(theta) and m21(theta) adding the two, then dividing by 2 to calculate a second estimate r of the roundness profiler，2(θ)。
3. The two-sensor based roundness measurement method of claim 1, wherein: in step S4, the estimated value obtained by the two-point method algorithm includes the steps of,
s4-1, mixing11(theta) and m12(θ) add to yield:
m(θ)＝m11(θ)+m12(θ)＝r(θ)+r(θ-180°)+noise11(θ)+noise12(θ), which is equation (1), Laplace transform of equation (1) is:
M(s)＝(1+e-πs)R(s)+Noise11(s)+Noise12(s), which is equation (2), a third estimate of the roundness profile is calculated from equation (2)
Further, in the present invention,
s4-2, mixing21(theta) and m22(θ) add to yield:
m(θ)＝r(θ)+r(θ-180°)+noise21(θ)+noise22(theta), which is formula (3),
laplace transform of equation (3) becomes:
M(s)＝(1+e-πs)R(s)+Noise21(s)+Noise22(s), which is equation (4), a fourth estimate of the roundness profile is calculated from equation (4)
Further, in the present invention,
wherein r (theta) and r (theta-180 DEG) both represent section roundness errors of the measured workpiece, noise11(θ)、noise12(θ)、noise21(theta) and noise22(θ) represents the Noise of the sensor, M(s), Noise11(s)、Noise12(s)、Noise21(s) and Noise22(s) is m (theta) and noise respectively11(θ)、noise12(θ)、noise21(theta) and noise22(theta) Laplace transform, R(s) being rr，1The laplace transform s of (θ) is a complex number, k denotes the harmonic order, and j denotes the imaginary unit.
4. The two-sensor based roundness measurement method of claim 1, wherein: in step S5, frequency domain hybridization is based on the following principle:
Rhybrid(jk)＝Rt，1(jk) or Rt，2(jk), if k mod2 is 0, which is formula (5),
Rhybrid(jk)＝Rr，1(jk) or Rr，2(jk), if k mod2 ═ 1, which is formula (6);
wherein k is ═ infinity … -2,2 … ∞; rr，1(jk) and Rr，2(jk) all represent Fourier coefficients for estimating the estimated value of the roundness profile of the measured workpiece by adopting a rollover algorithm; rt，1(jk) and Rt，2(jk) each represents a Fourier coefficient of an estimated value of the roundness profile of the measured workpiece estimated by a two-point algorithm; rhybrid(jk) a fourier coefficient estimate representing the roundness error; k denotes the harmonic order and j denotes the imaginary unit.
5. The two-sensor based roundness measurement method of claim 1, wherein: the measuring device comprises a base, a first rotary table, a second rotary table, a chuck, a first displacement sensor and a second displacement sensor, wherein the first rotary table is arranged on the base; the second rotary table is arranged on the first rotary table through a magnetic suction seat; the chuck is arranged on the second rotary table; the central axis of the first rotary table, the central axis of the second rotary table and the central axis of the chuck are all positioned on the same straight line; the first displacement sensor and the second displacement sensor are respectively installed on the base through the first height adjusting mechanism and the second height adjusting mechanism, and the first displacement sensor and the second displacement sensor are located on the same straight line.
6. The two-sensor based roundness measurement method of claim 5, wherein: the first height adjusting mechanism comprises a first guide rail and a first sliding table; the lower end of the first guide rail is arranged on the base, the first sliding table is connected with the first guide rail, and one end of the first displacement sensor is arranged on the first sliding table;
the second height adjusting mechanism comprises a second guide rail and a second sliding table; the lower extreme of second guide rail is installed on the base, the second slip table is connected with the guide rail, the one end of second displacement sensor is installed in the second slip table.
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