CN117848722A - Ultra-precise spindle measurement method and measurement support based on three-point method error separation technology - Google Patents
Ultra-precise spindle measurement method and measurement support based on three-point method error separation technology Download PDFInfo
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Abstract
The invention discloses an ultra-precise main shaft measuring method and a measuring support based on a three-point method error separation technology, wherein the measuring method comprises the following steps: s1, installing a check rod so that the axis of the check rod is coaxial with the axis of the main shaft; s2, checking the roundness profile of the check rod by adopting a three-point method error separation technology; s3, installing three displacement sensors along three directions of XYZ, and measuring radial runout signals and axial runout signals of the main shaft; s4, subtracting the checked roundness profile signal of the rod from the radial runout signal of the main shaft to eliminate the influence of the roundness profile of the rod on the measurement result of the main shaft, thereby more accurately evaluating the radial rotation error of the main shaft; s5, calculating the axial rotation error of the main shaft based on the axial runout signal detected in the step S3. The three-point method error separation technology provided by the invention can eliminate the influence of the roundness profile of the rod on the measurement result of the main shaft, is simple and convenient to operate for measuring the roundness profile of the rod, can finish the checking of the roundness profile of the rod through one-time installation, does not need to reinstall the rod in the measuring process, reduces the operation steps and avoids the tedious measuring process.
Description
Technical Field
The invention relates to a measurement technology, in particular to an ultra-precise spindle measurement method based on a three-point method error separation technology.
Background
Spindle is one of the most critical core features of a machine tool, and is found in almost all types of machine tools, with accuracy decisive for the machining accuracy of the machine tool. In a lathe, the topography errors of the machined part are mapped directly from the spindle errors. Single-point diamond lathe developed by Precitick company of AmericaX, the configured spindle error is less than 15 nanometers.
In other electromechanical systems, spindle accuracy often has a decisive influence on system performance as well. For example, the storage density of the hard disk is calculated by the track width, but in order to ensure the read/write accuracy of the hard disk, the spindle error of the hard disk needs to be an order of magnitude lower than the track width; in 2006, a typical magnetic ring width was about 200 nm, which means that the hard disk spindle error was below 20 nm. The measurement accuracy of the roundness measuring instrument mainly depends on the rotation accuracy of the turntable; currently, the spindle error of Talyrond 595H is only 10 nanometers for the most accurate roundness measuring instrument. In the manufacturing industry, major axes with 10 nanometer precision have been commercialized and are advancing to nanometer scale.
In 2006, the international standards for spindle measurements were first published by the international committee for standardization, ISO/TC 39/SC 2: ISO 230-7,Geometric accuracy of axes of rotation; in 2016, ISO 230-7:2006 was translated and national standard GB/T17421.7-2016 was established. According to ISO 230-7, currently, there are only two brands of spindle gauges on the market: lionprecision (lion) and API, both from the United states. In particular, the male lion spindle gauge is in monopoly in the market. In order to ensure the measurement precision, on one hand, the male lion spindle measuring instrument is provided with a high-precision check rod, and the roundness of the check rod is less than 50 nanometers; on the other hand, a high-precision capacitive sensor is configured, and the resolution thereof can reach the nanometer level. However, the male lion spindle measuring instrument is expensive, which restricts the popularization of the precise spindle measuring instrument in domestic machine tools and spindle enterprises to a great extent.
Currently, most machine tools and spindle enterprises still adopt dial indicators to measure spindle accuracy based on cost consideration: when the spindle rotates, the dial indicator is aligned with the cylindrical dipstick surface, and the peak-to-peak value of the reading is defined as the runout value, which is used to assess spindle accuracy. The evaluation method is simple to operate and the measuring instrument is inexpensive, however, it should be pointed out that this method is in principle erroneous. When the spindle is measured, the reading of the dial indicator actually comprises components of spindle errors and first harmonic components introduced by eccentric installation of the check rod. Also, typically, the magnitude of the installation eccentricity is much greater than the magnitude of the spindle error. Therefore, the academia generally considers that the jump value index is not the main shaft error of evaluation, but the installation eccentricity of the test rod is evaluated. In addition, the spindle measurement method based on the dial indicator has the following problems: the dial indicator has low resolution, and dynamic measurement cannot be performed.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides an ultraprecise spindle measurement method based on a three-point method error separation technology. The ultra-precise spindle measurement method based on the three-point method error separation technology has the advantages of high accuracy of measurement results and low cost.
Meanwhile, another object of the invention is to provide a measuring support for realizing the ultra-precise spindle measuring method based on the three-point method error separation technology.
The aim of the invention is achieved by the following technical scheme: the ultra-precise spindle measurement method based on the three-point method error separation technology comprises the following steps:
s1, mounting a test rod at the tail end of a main shaft, so that the axis of the test rod is coaxial with the axis of the main shaft;
s2, checking the roundness profile of the check rod by adopting a three-point method:
s21, by means of a measuring support, radially surrounding the dipstick3 displacement sensors are installed, wherein a first displacement sensor is installed along the X direction, an included angle between a second displacement sensor and the first displacement sensor is phi, and an included angle between a third displacement sensor and the first displacement sensor is phi
S22, driving the main shaft to rotate, acquiring displacement signals in real time by 3 displacement sensors, and respectively marking the displacement signals acquired by the 3 displacement sensors as m 1 (θ)、m 2 (θ) and m 3 (θ), wherein:
m 1 (θ) =r (θ) +x (θ), which is formula (1);
m 2 (θ) =r (θ - Φ) +x (θ) cos Φ+y (θ) sin Φ, which is formula (2);
this is formula (3);
wherein r (theta) represents a roundness profile of the test rod, X (theta) represents a radial dynamic rotation error of the spindle in the X direction, and Y (theta) represents a radial dynamic rotation error of the spindle in the Y direction;
s23, pair m 1 (θ)、m 2 (θ) and m 3 (θ) to construct a weighting function m (θ), the construction principle is as follows:
this is formula (4), wherein a and b are weight coefficients;
s24, carrying out Laplacian transformation on the weight function to obtain:
this is formula (5), wherein s represents a Laplacian;
s25, calculating a Laplacian equation of the roundness profile of the dipstick according to the formula (5):
this is formula (6);
s26, substituting s=jk into (6), the fourier coefficient R (jk) of the rod roundness profile can be obtained:
this is equation (7), where s represents a Laplacian operator, j represents an imaginary operator, and k represents a Fourier order;
s27, performing inverse Fourier transform on the Fourier coefficient R (jk) to estimate the roundness profile R of the rod measured (θ) as follows:
this is formula (8);
s3, installing three displacement sensors along three directions of XYZ, wherein the X direction and the Y direction are along the radial direction of a main shaft, and the Z direction is the axial direction of the main shaft; the main shaft rotates, three displacement sensors collect a plurality of circles of displacement signals at the same time in an equal angle, and the three groups of displacement signals obtained by collection are respectively recorded as m x (θ)、m y (θ) and m z (θ)；
S4, roundness profile r estimated in step S2 measured (θ) and the radial sensor signal m measured in step S3 x (θ) and m y (θ) calculating a spindle radial error signal and its magnitude;
s5, the axial displacement signal m obtained by measuring in the step S3 z (θ), an axial error signal of the spindle and its amplitude are calculated.
Preferably, step S4 comprises the following specific steps:
s4-1: will radial displacement signal m x (θ) and m y Filtering out the first harmonic and DC component in (theta) to obtain residual signalAnd->
S4-2: from residual signalsAnd->In (1) subtracting the rod roundness profile component r measured (θ) to calculate a spindle radial total error signal: />And-> The peak-to-peak value of the radial total error signal is the radial total error value: x is X total And Y total ；
S4-3: calculating an average curve of the radial total error signal to obtain a radial synchronous error signal: x is x syn (θ) and y syn (θ); the peak-to-peak value of the radial synchronization error signal is the radial synchronization error value: x is X syn And Y syn ；
S4-4: subtracting the radial synchronous error signal from the radial total error signal to obtain a radial asynchronous error signal: x is x asyn (θ) and y asyn (θ); the radial asynchronous error signal has a maximum width at a certain angle, and the maximum width value is the radial asynchronous error value: x is X asyn And Y asyn 。
Preferably, step S5 comprises the following specific steps:
s5-1: axial displacement signal m z And (theta) is the total error signal of the axial direction of the spindle: z total (θ); the peak-to-peak value of the axial total error signal is the axial total error value: z is Z total ；
S5-2: calculating an average curve of the axial total error signal to obtain an axial synchronous error signal: z syn (θ); the peak-to-peak value of the axial synchronization error signal is the axial synchronization error value: z is Z syn ；
S5-3: subtracting the axial synchronous error signal from the axial total error signal to obtain an axial asynchronous error signal: z asyn (θ)；The axial asynchronous error signal has a maximum width at a certain angle, and the maximum width value is the axial asynchronous error value Z asyn ；
S5-4: in the axial synchronous error signal, the first harmonic component is the axial basic error motion signal: z fund (θ); the peak-to-peak value of the axial basic error motion signal is the axial basic error value: z is Z fund ；
S5-5: filtering out the first harmonic wave in the axial synchronous error signal to obtain an axial residual synchronous error signal: z residual (θ); the peak-to-peak value of the axis residual synchronization error signal is the axis residual synchronization error value: z is Z residual 。
Preferably, the measuring support comprises a bottom, a middle and a top, wherein the bottom, the middle and the top are sequentially connected and fixed by bolts; a plurality of first fixing grooves are formed in the lower surface of the top, a plurality of second fixing grooves and a plurality of third fixing grooves are respectively formed in the upper surface and the lower surface of the middle part, and a plurality of fourth fixing grooves are formed in the upper surface of the bottom; the first fixing grooves and the corresponding second fixing grooves form a plurality of first radial fixing holes; the third fixing groove and the corresponding fourth fixing groove form a second radial fixing hole; the middle parts of the bottom, the middle part and the top are provided with detection holes into which the rod to be detected extends; when the bottom, the middle and the top are connected together, the axes of all the detection holes are positioned on the same straight line; the bottom is provided with an axial fixing hole for installing the Z-direction sensor; the axis of the axial fixing hole and the axis of the detection hole are positioned on the same straight line; the first radial fixing hole, the second radial fixing hole and the axial fixing hole are communicated with the detection hole.
Preferably, all the first radial fixing holes are positioned on the same plane, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole; all the second radial fixing holes are positioned on the same plane, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole.
Preferably, a base is arranged at the lower end of the bottom; the base is provided with a U-shaped groove, and a step is arranged above the U-shaped groove.
The measuring support for realizing the ultra-precise spindle measuring method based on the three-point method error separation technology comprises a bottom part, a middle part and a top part, wherein the bottom part, the middle part and the top part are sequentially connected and fixed by bolts; a plurality of first fixing grooves are formed in the lower surface of the top, a plurality of second fixing grooves and a plurality of third fixing grooves are respectively formed in the upper surface and the lower surface of the middle part, and a plurality of fourth fixing grooves are formed in the upper surface of the bottom; the first fixing groove and the corresponding second fixing groove form a plurality of first radial fixing holes; the third fixing groove and the corresponding fourth fixing groove form a second radial fixing hole; the middle parts of the bottom, the middle part and the top are provided with detection holes into which the rod to be detected extends; when the bottom, the middle and the top are connected together, the axes of all the detection holes are positioned on the same straight line; the bottom is provided with an axial fixing hole; the axis of the axial fixing hole and the axis of the detection hole are positioned on the same straight line; the first radial fixing hole, the second radial fixing hole and the axial fixing hole are communicated with the detection hole.
Preferably, all the first radial fixing holes are positioned on the same plane, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole; all the second radial fixing holes are positioned on the same plane, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole.
Preferably, a base is arranged at the lower end of the bottom; the base is provided with a U-shaped groove, and a step is arranged above the U-shaped groove.
Compared with the prior art, the invention has the following advantages:
1. according to the invention, a capacitive sensor is adopted to replace a traditional dial indicator to measure the rotation error of the main shaft, and the measurement accuracy of the sensor is improved from a micron level to a nano level; in addition, compared with a dial indicator, the frequency response of the capacitance sensor is greatly improved, so that the dynamic rotation error measurement at the working rotation speed can be realized.
2. Through subsequent filtering treatment, the method provided by the invention can remove the first harmonic component introduced by eccentric installation of the test rod.
3. The main shaft measuring instrument based on the error separation technology firstly checks the roundness profile of the detecting rod, further thoroughly eliminates the influence of the roundness of the detecting rod on the main shaft test result, can theoretically realize zero system deviation measurement, exceeds the precision limit of the existing instrument, and provides an ideal means for the measurement of the ultra-precise main shaft. The measurement pairs based on the error separation technique and the measurement pairs that have not conventionally employed the error separation technique are shown in table 1. In addition, the spindle measuring instrument based on the error separation technology does not depend on an ultra-precise test rod any more, so that the problem that the spindle measuring instrument does not have a neck clamping part for processing a ten-nanometer-level precision test rod in China can be solved; moreover, the cost of the instrument can be reduced.
Table 1 measurement results of spindle radial error amplitude
4. The method adopts the three-point error separation technology to measure the roundness profile of the detecting rod, is simple and convenient to operate, can finish checking the roundness profile of the detecting rod through one-time installation, does not need to reinstall the detecting rod in the measuring process, reduces operation steps and avoids tedious measuring process compared with the existing turnover method and multi-step method.
5. The measuring method and the instrument provided by the invention can not only check the roundness profile of the inspection rod, but also measure the dynamic rotation error of the spindle in the three directions of XYZ, and can also measure the average rotation axis drift in the three directions of XYZ, such as the axial drift caused by heat and the axis drift caused by rotation speed variation.
Drawings
Fig. 1 is a schematic installation diagram of the ultra-precise spindle measurement method based on the three-point method error separation technology of the invention.
Fig. 2 is a schematic diagram of the principle of the ultra-precise spindle measurement method based on the three-point method error separation technology of the present invention.
FIG. 3 is a bar roundness profile verified by the ultra-precise spindle measurement method based on the three-point error separation technique of the present invention.
Fig. 4 is a graph of radial error measurement results in the X direction of the main axis obtained by the measurement method of the present invention.
Fig. 5 is a graph of radial error measurement results in the Y direction of the spindle obtained by the measurement method of the present invention.
Fig. 6 is a schematic view of the structure of the measuring support of the present invention.
Fig. 7 is a side view of the measuring support of the present invention.
Fig. 8 is a front view of the measuring support of the present invention.
Fig. 9 is a cross-sectional view taken along the direction A-A in fig. 8.
Fig. 10 is a sectional view in the direction B-B of fig. 8.
Wherein 1 is the main shaft, 2 is examining the stick, 3 is the measurement support, 4 is displacement sensor, 5 is the bottom, 6 is the middle part, 7 is the top, 8 is first fixed slot, 9 is the second fixed slot, 10 is the third fixed slot, 11 is the fourth fixed slot, 12 is first radial fixed hole, 13 is the radial fixed hole of second, 14 is the axial fixed hole, 15 is the base, 16U type groove, 17 is the ladder, 18 is the detection hole.
Detailed Description
The invention is further described below with reference to the drawings and examples.
The ultra-precise spindle measurement method based on the three-point method error separation technology comprises the following steps of:
s1, mounting a test rod at the tail end of a main shaft, so that the axis of the test rod is coaxial with the axis of the main shaft; as shown in fig. 1, the dipstick is fixed at the lower end of the main shaft, and the lower end of the dipstick extends into the detection hole of the measurement support;
s2, determining the roundness profile of the rod by adopting a three-point method error separation technology:
s21, as shown in fig. 2, by means of a measuring support, 3 displacement sensors are arranged around the test rod along the radial direction, wherein a first displacement sensor is arranged along the X direction, an included angle between a second displacement sensor and the first displacement sensor is phi=90 DEG, and an included angle between a third displacement sensor and the first displacement sensor is phi=90 DEG
S22, driving the main shaft to rotate, acquiring displacement signals in real time by 3 displacement sensors, and acquiring the positions by 3 displacement sensorsThe shift signals are respectively recorded as m 1 (θ)、m 2 (θ) and m 3 (θ), wherein:
m 1 (θ) =r (θ) +x (θ), which is formula (1);
m 2 (θ) =r (θ - Φ) +x (θ) cos Φ+y (θ) sin Φ, which is formula (2);
this is formula (3);
wherein r (theta) represents a roundness profile of the test rod, X (theta) represents a radial dynamic rotation error of the spindle in the X direction, and Y (theta) represents a radial dynamic rotation error of the spindle in the Y direction;
s23, pair m 1 (θ)、m 2 (θ) and m 3 (θ) to construct a weighting function m (θ), the construction principle is as follows:
this is formula (4), wherein a and b are weight coefficients;
s24, carrying out Laplacian transformation on the weight function to obtain:
this is formula (5), wherein s represents a Laplacian;
s25, calculating a Laplacian equation of the roundness profile of the dipstick according to the formula (5):
this is formula (6);
s26, substituting s=jk into (6), the fourier coefficient R (jk) of the rod roundness profile can be obtained:
this is equation (7), where s represents a Laplacian operator, j represents an imaginary operator, and k represents a Fourier order;
s27, as shown in FIG. 3The roundness profile R of the dipstick is estimated by performing inverse fourier transform on the fourier coefficient R (jk) measured (θ) as follows:
this is formula (8);
s3, installing three displacement sensors along three directions of XYZ, wherein the X direction and the Y direction are along the radial direction of a main shaft, and the Z direction is the axial direction of the main shaft; the main shaft rotates, three displacement sensors collect a plurality of circles of displacement signals at the same time in an equal angle, and the three groups of displacement signals obtained by collection are respectively recorded as m x (θ)、m y (θ) and m z (θ)；
S4, roundness profile r estimated in step S2 measured (θ) and the radial sensor signal m measured in step S3 x (θ) and m y (θ) calculating a spindle radial error signal and its magnitude; step S4 comprises the following specific steps:
s4-1: will radial displacement signal m x (θ) and m y Filtering out the first harmonic and DC component in (theta) to obtain residual signalAnd->
S4-2: from residual signalsAnd->In (1) subtracting the rod roundness profile component r measured (θ) to calculate a spindle radial total error signal: />And-> The peak-to-peak value of the radial total error signal is the radial total error value: x is X total And Y total ；
S4-3: calculating an average curve of the radial total error signal to obtain a radial synchronous error signal: x is x syn (θ) and y syn (θ); the peak-to-peak value of the radial synchronization error signal is the radial synchronization error value: x is X syn And Y syn ；
S4-4: subtracting the radial synchronous error signal from the radial total error signal to obtain a radial asynchronous error signal: x is x asyn (θ) and y asyn (θ); the radial asynchronous error signal has a maximum width at a certain angle, and the maximum width value is the radial asynchronous error value: x is X asyn And Y asyn . As can be seen from fig. 4, fig. 5 and table 1, after the three-point method error separation is adopted in the present application, each radial error of the spindle is significantly reduced, which means that the error separation technique can effectively eliminate the influence of the roundness of the dipstick on the measurement result of the spindle error, and improve the accuracy of the measurement system.
S5, the axial displacement signal m obtained by measuring in the step S3 z (θ), an axial error signal of the spindle and its amplitude are calculated. Step S5 comprises the following specific steps:
s5-1: axial displacement signal m z And (theta) is the total error signal of the axial direction of the spindle: z total (θ); the peak-to-peak value of the axial total error signal is the axial total error value: z is Z total ；
S5-2: calculating an average curve of the axial total error signal to obtain an axial synchronous error signal: z syn (θ); the peak-to-peak value of the axial synchronization error signal is the axial synchronization error value: z is Z syn ；
S5-3: subtracting the axial synchronous error signal from the axial total error signal to obtain an axial asynchronous error signal: z asyn (θ); the axial asynchronous error signal has a maximum width at a certain angle, and the maximum width value is the axial asynchronous error value Z asyn ；
S5-4: in the axial synchronous error signal, the first harmonic component is the axial basic error motion signal: z fnnd (θ); axial basic errorThe peak-to-peak value of the differential motion signal is the axial basic error value: z is Z fund ；
S5-5: filtering out the first harmonic wave in the axial synchronous error signal to obtain an axial residual synchronous error signal: z residual (θ); the peak-to-peak value of the axis residual synchronization error signal is the axis residual synchronization error value: z is Z residual 。
As can be seen from fig. 4, fig. 5 and table 1, the three-point method error separation technique can effectively eliminate the influence of the roundness of the test rod on the spindle error measurement result, obtain a more accurate spindle radial error, and greatly improve the accuracy of the measurement system. In addition, the measuring method is simple and convenient to operate, the roundness profile of the detecting rod can be checked through one-time installation, the detecting rod is not required to be installed again in the measuring process, and compared with the existing turnover method and multi-step method, the operating steps are reduced, and the tedious measuring process is avoided.
As shown in fig. 6 to 10, the measuring support comprises a bottom, a middle and a top, wherein the bottom, the middle and the top are sequentially connected and fixed by bolts; a plurality of first fixing grooves are formed in the lower surface of the top, a plurality of second fixing grooves and a plurality of third fixing grooves are respectively formed in the upper surface and the lower surface of the middle part, and a plurality of fourth fixing grooves are formed in the upper surface of the bottom; the first fixing grooves and the corresponding second fixing grooves form a plurality of first radial fixing holes for mounting the radial displacement sensor in the X direction; the third fixing groove and the corresponding fourth fixing groove form a second radial fixing hole for installing a Y-direction radial displacement sensor; the middle parts of the bottom, the middle part and the top are provided with detection holes into which the rod to be detected extends; when the bottom, the middle and the top are connected together, the axes of all the detection holes are positioned on the same straight line; the bottom is provided with an axial fixing hole for installing the Z-direction sensor; the axis of the axial fixing hole and the axis of the detection hole are positioned on the same straight line; the first radial fixing hole, the second radial fixing hole and the axial fixing hole are communicated with the detection hole. All the first radial fixing holes are arranged on the same plane in a row, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole; all the second radial fixing holes are arranged on the same plane in a row, and the axes of all the second radial fixing holes are intersected on the axis of the detection hole.
The lower end of the bottom axial fixing hole is provided with a base for fixing the measuring support; the base is provided with a U-shaped groove which is used for facilitating the installation and the disassembly of the axial sensor; the upper part of the U-shaped groove is provided with a step and a threaded hole for fastening the axial displacement sensor.
The measuring support for realizing the ultra-precise spindle measuring method based on the three-point method error separation technology comprises a bottom part, a middle part and a top part, wherein the bottom part, the middle part and the top part are sequentially connected and fixed by bolts; a plurality of first fixing grooves are formed in the lower surface of the top, a plurality of second fixing grooves and a plurality of third fixing grooves are respectively formed in the upper surface and the lower surface of the middle part, and a plurality of fourth fixing grooves are formed in the upper surface of the bottom; the first fixing grooves and the corresponding second fixing grooves form a plurality of first radial fixing holes for mounting the radial displacement sensor in the X direction; the third fixing groove and the corresponding fourth fixing groove form a second radial fixing hole for installing a Y-direction radial displacement sensor; the middle parts of the bottom, the middle part and the top are provided with detection holes into which the rod to be detected extends; when the bottom, the middle and the top are connected together, the axes of all the detection holes are positioned on the same straight line; the bottom is provided with an axial fixing hole for installing the Z-direction sensor; the axis of the axial fixing hole and the axis of the detection hole are positioned on the same straight line; the first radial fixing hole, the second radial fixing hole and the axial fixing hole are communicated with the detection hole. All the first radial fixing holes are arranged on the same plane in a row, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole; all the second radial fixing holes are arranged on the same plane in a row, and the axes of all the second radial fixing holes are intersected on the axis of the detection hole.
The lower end of the bottom is provided with a base; the base is provided with a U-shaped groove, and a step is arranged above the U-shaped groove. The axial displacement sensor can be conveniently installed or detached by adopting the arrangement.
The above embodiments are preferred examples of the present invention, and the present invention is not limited thereto, and any other modifications or equivalent substitutions made without departing from the technical aspects of the present invention are included in the scope of the present invention.
Claims (9)
1. The ultra-precise spindle measurement method based on the three-point method error separation technology is characterized by comprising the following steps of:
s1, mounting a test rod at the tail end of a main shaft, so that the axis of the test rod is coaxial with the axis of the main shaft;
s2, checking the roundness profile of the check rod by adopting a three-point method:
s21, mounting 3 displacement sensors around the detecting rod along the radial direction by means of a measuring support, wherein a first displacement sensor is mounted along the X direction, an included angle between a second displacement sensor and the first displacement sensor is phi, and an included angle between a third displacement sensor and the first displacement sensor is phi
S22, driving the main shaft to rotate, acquiring displacement signals in real time by 3 displacement sensors, and respectively marking the displacement signals acquired by the 3 displacement sensors as m 1 (θ)、m 2 (θ) and m 3 (θ), wherein:
m 1 (θ) =r (θ) +x (θ), which is formula (1);
m 2 (θ) =r (θ - Φ) +x (θ) cos Φ+y (θ) sin Φ, which is formula (2);
this is formula (3);
wherein r (theta) represents a roundness profile of the test rod, X (theta) represents a radial dynamic rotation error of the spindle in the X direction, and Y (theta) represents a radial dynamic rotation error of the spindle in the Y direction;
s23, pair m 1 (θ)、m 2 (θ) and m 3 (θ) to construct a weighting function m (θ), the construction principle is as follows:
this is formula (4), wherein a and b are weight coefficients;
s24, carrying out Laplacian transformation on the weight function to obtain:
this is formula (5), wherein s represents a Laplacian;
s25, calculating a Laplacian equation of the roundness profile of the rod according to the formula (5):
this is formula (6);
s26, substituting s=jk into (6), the fourier coefficient R (jk) of the rod roundness profile can be obtained:
this is equation (7), s represents a Laplains operator, j represents an imaginary operator, and k represents a Fourier order;
s27, performing inverse Fourier transform on the Fourier coefficient R (jk) to estimate the roundness profile R of the rod measured (θ) as follows:
this is formula (8);
s3, installing three displacement sensors along three directions of XYZ, wherein the X and Y directions are radial directions of a main shaft, and the Z direction is axial direction of the main shaft; the main shaft rotates, three displacement sensors collect a plurality of circles of displacement signals at the same time in an equal angle, and the three groups of displacement signals obtained by collection are respectively recorded as m x (θ)、m y (θ) and m z (θ)；
S4, roundness profile r estimated in step S2 measured (θ) and the radial sensor signal m measured in step S3 x (θ) and m y (θ) calculating a spindle radial error signal and its magnitude;
s5, measuring by step S3The obtained axial displacement signal m z (θ), an axial error signal of the spindle and its amplitude are calculated.
2. The ultra-precise spindle measurement method based on the three-point method error separation technology according to claim 1, wherein the method comprises the following steps: step S4 comprises the following specific steps:
s4-1: will radial displacement signal m x (θ) and m y Filtering out the first harmonic and DC component in (theta) to obtain residual signalAnd->
S4-2: from residual signalsAnd->In (1) subtracting the rod roundness profile component r measured (θ) to calculate a spindle radial total error signal: />And-> The peak-to-peak value of the radial total error signal is the radial total error value: x is X total And Y total ；
S4-3: calculating an average curve of the radial total error signal to obtain a radial synchronous error signal: x is x syn (θ) and y syn (θ); the peak-to-peak value of the radial synchronization error signal is the radial synchronization error value: x is X syn And Y syn ；
S4-4: subtracting the radial synchronization error signal from the radial total error signalObtaining a radial asynchronous error signal: x is x asyn (θ) and y asyn (θ); the radial asynchronous error signal has a maximum width at a certain angle, and the maximum width value is the radial asynchronous error value: x is X asyn And Y asyn 。
3. The ultra-precise spindle measurement method based on the three-point method error separation technology according to claim 1, wherein the method comprises the following steps: step S5 comprises the following specific steps:
s5-1: axial displacement signal m z And (theta) is the total error signal of the axial direction of the spindle: z total (θ); the peak-to-peak value of the axial total error signal is the axial total error value: z is Z total ；
S5-2: calculating an average curve of the axial total error signal to obtain an axial synchronous error signal: z syn (θ); the peak-to-peak value of the axial synchronization error signal is the axial synchronization error value: z is Z syn ；
S5-3: subtracting the axial synchronous error signal from the axial total error signal to obtain an axial asynchronous error signal: z asyn (θ); the axial asynchronous error signal has a maximum width at a certain angle, and the maximum width value is the axial asynchronous error value Z asyn ；
S5-4: in the axial synchronous error signal, the first harmonic component is the axial basic error motion signal: z fund (θ); the peak-to-peak value of the axial basic error motion signal is the axial basic error value: z is Z fund ；
S5-5: filtering out the first harmonic wave in the axial synchronous error signal to obtain an axial residual synchronous error signal: z residual (θ); the peak-to-peak value of the axis residual synchronization error signal is the axis residual synchronization error value: z is Z residual 。
4. The ultra-precise spindle measurement method based on the three-point method error separation technology according to claim 1, wherein the method comprises the following steps: the measuring support comprises a bottom, a middle and a top, wherein the bottom, the middle and the top are sequentially connected and fixed by bolts; a plurality of first fixing grooves are formed in the lower surface of the top, a plurality of second fixing grooves and a plurality of third fixing grooves are respectively formed in the upper surface and the lower surface of the middle part, and a plurality of fourth fixing grooves are formed in the upper surface of the bottom; the first fixing groove and the corresponding second fixing groove form a plurality of first radial fixing holes; the third fixing groove and the corresponding fourth fixing groove form a second radial fixing hole; the middle parts of the bottom, the middle part and the top are provided with detection holes into which the rod to be detected extends; when the bottom, the middle and the top are connected together, the axes of all the detection holes are positioned on the same straight line; the bottom is provided with an axial fixing hole; the axis of the axial fixing hole and the axis of the detection hole are positioned on the same straight line; the first radial fixing hole, the second radial fixing hole and the axial fixing hole are communicated with the detection hole.
5. The ultra-precise spindle measurement method based on the three-point method error separation technology according to claim 4, wherein the method comprises the following steps: all the first radial fixing holes are positioned on the same plane, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole; all the second radial fixing holes are positioned on the same plane, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole.
6. The ultra-precise spindle measurement method based on the three-point method error separation technology according to claim 4, wherein the method comprises the following steps: the lower end of the bottom is provided with a base; the base is provided with a U-shaped groove, and a step is arranged above the U-shaped groove.
7. A measurement support for implementing the ultraprecise spindle measurement method based on the three-point method error separation technology according to any one of claims 1 to 3, characterized in that: the measuring support comprises a bottom, a middle and a top, wherein the bottom, the middle and the top are sequentially connected and fixed by bolts; a plurality of first fixing grooves are formed in the lower surface of the top, a plurality of second fixing grooves and a plurality of third fixing grooves are respectively formed in the upper surface and the lower surface of the middle part, and a plurality of fourth fixing grooves are formed in the upper surface of the bottom; the first fixing grooves and the corresponding second fixing grooves form a plurality of first radial fixing holes, the third fixing grooves and the corresponding fourth fixing grooves form a plurality of second radial fixing holes, and detection holes into which the detection bars extend are formed in the middle of the bottom, the middle and the top; when the bottom, the middle and the top are connected together, the axes of all the detection holes are positioned on the same straight line; the bottom is provided with an axial fixing hole, and the axis of the axial fixing hole and the axis of the detection hole are positioned on the same straight line; the first radial fixing hole, the second radial fixing hole and the axial fixing hole are communicated with the detection hole.
8. The measuring support of claim 6, wherein: all the first radial fixing holes are positioned on the same plane, and the axes of all the first radial fixing holes are intersected on the axis of the detection hole; the second radial fixing holes are positioned on the same plane, and the axes of all the second radial fixing holes are intersected on the axis of the detection hole.
9. The measuring support of claim 6, wherein: the lower end of the bottom is provided with a base; the base is provided with a U-shaped groove, and a step is arranged above the U-shaped groove.
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