CN107122333A - It is a kind of to reduce the data processing method of measurement data uncertainty - Google Patents
It is a kind of to reduce the data processing method of measurement data uncertainty Download PDFInfo
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- CN107122333A CN107122333A CN201710137703.2A CN201710137703A CN107122333A CN 107122333 A CN107122333 A CN 107122333A CN 201710137703 A CN201710137703 A CN 201710137703A CN 107122333 A CN107122333 A CN 107122333A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
- G06F17/153—Multidimensional correlation or convolution
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/045—Correction of measurements
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/30—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring roughness or irregularity of surfaces
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
Abstract
The data processing method of measurement data uncertainty is reduced the invention discloses a kind of, it is finally that synthesis is embodied in measurement data that this method, which fully takes into account various influence factors, so having carried out the analysis and compensation of statistical law to measurement data, systematic error is employed and repeatedly measures the method being averaged and compensates, filtered out for the random error remained after systematic error compensation with wavelet filteration method, it is combined the data more approaching to reality data after compensation, reduce the uncertainty of measurement data, processing procedure is succinctly effective, the present invention is by taking the Measurement and Data Processing of three coordinate measuring machine as an example, but it is not limited to the data processing of three coordinates, it is a kind of data processing method of universality, with higher engineering application value.
Description
Technical field
The invention belongs to technical field of measurement and test, and in particular to a kind of data processing side of reduction measurement data uncertainty
Method.
Background technology
Digitized measurement is the first stage towards the geometrical error modeling of precision assembly, high efficiency and high-precision data
Collection is the basis of later data processing and Model Reconstruction.Therefore suitable digitized measurement equipment and measuring method are used, is obtained
It is most basic, most critical link in geometrical error modeling to obtain accurate measurement data.
In actual measurement process, the measurement cost of high precision measuring instrument is higher, by being surveyed to low precision measure instrument
Amount data carry out error analysis and measurement error are compensated, and realize that low accurate facility realizes the work(of equivalent high-acruracy survey
Can, with very high economic value and engineering application value, such as three coordinate measuring machine.And uncertainty of measurement is used for characterizing survey
The credibility of amount, is the index of measurement result quality.Uncertainty is smaller, affiliated result and measured true value closer to,
Show that measurement result is more reliable, its use value is higher；Uncertainty is bigger, and the reliability of measurement result is poorer, and it uses valency
Value is also lower.All measurements can all be influenceed by uncertainty, may be from measuring instrument, measured object, survey crew or survey
Environment etc. is measured, wherein measuring instrument is to cause the key factor of uncertainty of measurement, and uncertain degree and source are because of measuring instrument
Device is different and different from measuring method, and no matter uncertainty of measurement is caused by which kind of factor, finally can all be embodied in measurement
The accuracy of data and the influence of degree of certainty.So to find a kind of data processing method of universality, data are made more to approach very
Truth condition, reduces the uncertainty of data.
By taking three coordinate measuring machine as an example, because its measurement accuracy is high, measurement range is big, can easily carry out space three-dimensional size
Measurement, so typically choose Contacting three coordinates measurement machine carries out data acquisition to the surface topography of fine structure body.At present
To three-dimensional coordinates measurement result more approaching to reality value, most of is to improve three-dimensional coordinates measurement precision aspect, that is, finds three-dimensional coordinates measurement
Every error source of machine, and error correcting method is proposed, mainly there are two kinds of basic skills：Error preventive treatment and error compensation method.
Error preventive treatment is to eliminate or reduce possible error source by design and manufacture approach, by raising three-dimensional coordinates measurement mechanism
Measurement accuracy requirement is met as precision, such as Jianghan University improves and set by changing measuring system to three coordinate measuring machine
The mechanical part that meter matches with measuring system, improves the precision of measuring machine, but error prevention method have significant limitation,
And financial cost is high；And error compensation method is to use software engineering, artificially produces a kind of new error and go to offset current original
Beginning error, this method financial cost is low, the quasi- rigid-body error correction model based on 21 geometric errors that such as University Of Tianjin proposes,
This 21 errors are measured and controlled, and are accordingly compensated, but this method process is complicated, unsuitable engineer applied, and it is main
What is corrected is the influence of every systematic error, and various influence factors are not taken into full account, and the processing to random element is less.
With the difference of measuring instrument, measuring method, measuring environment etc., the uncertainty of measurement result all can not
Together, so research at present rests on and theoretical analysis and evaluation is carried out to uncertainty mostly, subtract only for certain measuring instrument
The uncertainty of small measurement data, is handled measurement data without a kind of method with universality.
The content of the invention
In view of this, the data processing method of measurement data uncertainty is reduced the invention provides a kind of, this method is not
The function that equivalent high-acruracy survey is realized using low accurate facility can be only reached, while data handling procedure is simple, or one
Plant the stronger data processing method of universality.
That implements the present invention has scheme as follows：
A kind of to reduce the data processing method of measurement data uncertainty, this method includes：
Step one：The plane that flatness is prepared less than setting flatness S is used as standard flat；
Step 2：Sample frequency and sampling length are set to standard flat and actual processing plane to be compensated；
Step 3：According to the sample frequency and sampling length in step 2, any angle point using standard flat is origin, z
Axle points to the normal direction of standard flat, sets up rectangular coordinate system, standard flat is sampled using measuring instrument, surveyed
The measurement data X1 of the z-axis of measuring appratus, the measurement data of standard flat is measurement error；
Step 4：Measurement data to the measuring instrument of acquisition carries out best fit positioning, and the positioning for removing coordinate system is missed
Difference, obtains the measurement data X2 for the position error for removing coordinate system；
Step 5：According to the metering system of step 3, multiple measurement standard plane, pin under the same rectangular coordinate system
The measurement error that step 3 is obtained is handled according to the removal position error mode of step 4, multigroup removal coordinate system is obtained
Position error measurement data X2, the measurement data X2 is analyzed, if the measurement data X2 has identical change rule
Rule, then take average, the average is designated as systematic error X3, and systematic error is compensated, after being compensated to measurement data X2
Measurement data X4, i.e. X4=X2-X3；If measurement data X2 does not have rule, ignore shadow of the systematic error to measurement result
Ring；
Step 6：Measurement data X4 is filtered using optional filtering method, the best filtering side of filter effect is selected
Method；
Step 7：When being measured to actual processing plane, using the sample frequency and sampling length determined in step 2,
In actual processing plane, set up and rectangular coordinate system identical coordinate system described in step 3, the measurement used using step 3
Instrument is sampled to actual processing plane, obtains the measurement data Y1 of actual processing plane；Measurement to actual processing plane
Data Y1 is handled in the way of the removal position error of step 4, obtains the measurement data Y2 for removing position error, profit
The systematic error X3 obtained with step 5 is compensated to measurement data Y2, the measurement data Y3 after being compensated, and utilizes step
Six selected filtering methods, are filtered out, the measurement data Y4 after being filtered out to the random error in measurement data Y3.
Further, the filtering method selected to step 6, using spectrum analysis filter effect, if filter effect meets
Sets requirement, then complete the determination of filtering method, otherwise, and filtering method is selected again.
Further, S=0.3 μm.
Beneficial effect：
The present invention starts with from the angle to measurement data post-processing, proposes a kind of number of reduction measurement data uncertainty
According to processing method, it is result affected by various factors to have fully taken into account measurement data, so being united to measurement data
The analysis and compensation of rule are counted, repeatedly measuring the method being averaged to systematic error use compensates, and is mended for systematic error
The random error remained after repaying is filtered out with wavelet filteration method, is combined the data more approaching to reality number after compensation
According to reducing the uncertainty of measurement data, processing procedure is succinctly effective；Realize low accurate facility and carry out high-acruracy survey
Function, with very high engineering application value.
Brief description of the drawings
Fig. 1 is " CMM Data error compensation " method and step figure；
Fig. 2 is error in geometrical form schematic diagram；
Fig. 3 is systematic error distribution map；
Fig. 4 is random error probability distribution graph；
Fig. 5 is two-dimentional amplitude frequency diagram before standard flat filtering；
Fig. 6 is two-dimentional amplitude frequency diagram after standard flat filtering；
Fig. 7 is two-dimentional amplitude frequency diagram before finished surface filtering；
Fig. 8 is two-dimentional amplitude frequency diagram after finished surface filtering.
Embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
Present specification is started with from the angle to measurement data post-processing, proposes a kind of reduction CMM Data not
The data processing method of degree of certainty, it is finally that synthesis is embodied in measurement data that this method, which has fully taken into account various influence factors,
, so having carried out the analysis and compensation of statistical law to measurement data, employ what repeatedly measurement was averaged to systematic error
Method is compensated, and is filtered out for the random error remained after systematic error compensation with wavelet filteration method, carry out group
The data more approaching to reality data after compensation are closed, the uncertainty of measurement data are reduced, processing procedure is succinctly effective, the application
File is not limited to the data processing of three coordinates by taking the Measurement and Data Processing of three coordinate measuring machine as an example, is a kind of universality
Data processing method, with higher engineering application value.
Measurement accuracy is considered as low precision three-dimensional coordinates measurement by the present invention for 3-5 μm of three coordinate measuring machine；Measurement accuracy is 1
Three coordinate measuring machine below μm is considered as high precision three-dimensional coordinates measurement；Random error is separated with systematic error, to systematic error
Compensate, random error is filtered, the final accuracy for improving measurement data, as shown in figure 1, concrete scheme is as follows：
Step one：The plane that flatness is prepared less than setting flatness S is used as standard flat；
Step 2：Sample frequency and sampling length are set to standard flat and actual processing plane to be compensated；Setting is adopted
Sample frequency and sampling length are specially：It is twice of sample frequency at least above highest frequency in signal according to sampling principle, this
To choose sample frequency and sampling length for the purpose of controlling the data accuracy of macroshape error scale in embodiment, for example,
If the macroshape error pitch of waves is λ=15mm, sampling length is at least below 7.5mm, and sample frequency is at least to enter at interval of 7.5mm
Row sampling is once.
Wherein, Fig. 2 is error in geometrical form schematic diagram；Three kinds of scale calibrations of form error are as follows：Surface roughness
Pitch of waves λ：λ≤1mm；The surface waviness pitch of waves：1mm<λ≤10mm；The macroshape error pitch of waves：λ>10mm.
Step 3：According to the sample frequency and sampling length in step 2, any angle point using standard flat is origin, z
Axle points to the normal direction of standard flat, sets up rectangular coordinate system, standard flat is adopted using the measuring instrument of low precision
Sample, obtains the measurement data X1 of the z-axis of measuring instrument, the measurement data of standard flat is measurement data；
Step 4：Measurement data to the measuring instrument of acquisition carries out best fit positioning, and the positioning for removing coordinate system is missed
Difference, obtains the measurement data X2 for the position error for removing coordinate system；
Due to measurement original point position and measurement coordinate system and the position error of the misaligned generation of workpiece coordinate system, with optimization
Position and attitude error parameter in algorithm reverse measuring data, be for example iterated using LM algorithms can obtain it is inclined in position and attitude error
Distance and deflection angle are put, finally overlaps measurement coordinate system and workpiece coordinate system, directly in imageware in present specification
Middle input measurement coordinate system is the rectangular coordinate system, and measurement coordinate just can be realized using imageware positioning fitting function
The best fit of system and workpiece coordinate system is positioned.
Step 5：According to the metering system of step 3, multiple measurement standard plane, pin under the same rectangular coordinate system
The measurement error that step 3 is obtained is handled according to the removal position error mode of step 4, multigroup removal coordinate system is obtained
Position error measurement data X2, the measurement data X2 is analyzed, if the measurement data X2 has identical change rule
Rule, so-called identical changing rule refers to that the rule that the change of multigroup measurement data is presented is same or similar, is such as repeated several times and surveys
Measure corresponding multi-group data show it is stepped；Average then is taken to measurement data X2, the average is designated as systematic error X3, and right
Systematic error is compensated, the measurement data X4 after being compensated, i.e. X4=X2-X3；If measurement data X2 does not have rule,
Ignore influence of the systematic error to measurement result；
Step 6：Measurement data X4 is filtered using optional filtering method, the best filtering side of filter effect is selected
Method；
Measurement data X4 after the systematic error compensation obtained to step 5 can select mean filter, medium filtering, Gauss
Filtering or wavelet filtering etc. are handled, and are analyzed by the MATLAB filter effects obtained to each method, using frequency spectrum point
Filter effect is analysed, if filter effect meets sets requirement, the determination of filtering method is completed, otherwise, filtering side is selected again
Method.Present invention determine that filtering method be wavelet filtering, by measurement data X4 carry out probability density analysis, know measurement number
According to X4 Normal Distribution rules, the signal of Normal Distribution is filtered out using wavelet filtering, it is then front and rear to filtering
Data carry out two-dimensional Fourier transform, obtain two-dimentional amplitude frequency diagram, amplitude frequency diagram center correspondence low frequency signal, surrounding correspondence high frequency letter
Number, low frequency signal correspondence useful signal, so can obtain the useful frequency range of data by two-dimentional amplitude frequency diagram, is set according to useful frequency range
The number of plies of wavelet filtering is put, wherein, the important parameter of wavelet filtering is basic function and the number of plies of filtering.
Step 7：Actual processing plane is measured, using the sample frequency and sampling length determined in step 2,
In actual processing plane, set up and rectangular coordinate system identical coordinate system described in step 3, using measuring instrument to actual processing
Plane is sampled, and obtains the measurement data Y1 of actual processing plane；To the measurement data Y1 of actual processing plane according to step
The mode of four removal position error is handled, and is obtained the measurement data Y2 for removing position error, is obtained using step 5
Systematic error X3 is compensated to measurement data Y2, the measurement data Y3 after being compensated, the filtering side selected using step 6
Method, is filtered out to the random error in measurement data Y3, the measurement data Y4 after being filtered out.
Step 8：Actual processing plane is measured using high precision measuring instrument, measurement data Y5 is obtained；
Step 9：Calculate measurement data Y1 respectively, filter out after measurement data Y4 and measurement data Y5 flatness, will survey
Amount data Y1 flatness, filter out after measurement data Y4 flatness of the flatness with measurement data Y5 contrast, filtered
The flatness of measurement data Y4 after removing more approaches measurement data Y5 flatness, reduces the uncertainty of measurement data.
Embodiment：The detailed process of embodiment is as follows：
Error in geometrical form schematic diagram according to Fig. 2, one block size of selection is made for 80 × 60 × 10mm level crossing
For standard flat, the laser interferometer for being 60nm or so with measurement accuracy is measured to plane, is with uncertainty of measurement
3.5um three coordinate machine is measured, and sampling step length is 2.5mm, and duplicate measurements 4 times gathers 441 sample points, obtained every time
Measurement error discrete point cloud with topological rectangular mesh feature.
In reverse engineering software, the ideal plane under measurement point and the same coordinate system is subjected to best fit, removes and sits
Mark system position error, the arithmetic average for taking four measurement data is systematic error, and Fig. 3 is systematic error distribution map.
Raw measurement data is subtracted into systematic error, random error is obtained, Statistical Analysis is carried out to random error, such as
Shown in Fig. 4, random error Normal Distribution.As shown in figure 5, carrying out two-dimensional frequency analysis to random error, random noise is
A kind of signal with higher frequency components, the method for selection wavelet filtering is filtered out to random error.Fig. 5,6 are put down for standard
Two-dimentional amplitude frequency diagram before and after the filtering of face.Table 1 lists the measurement result and low precision three-dimensional coordinates measurement number of high-precision laser interferometer
According to the comparing result before and after Error processing.
Table 1 is the comparing result of the measurement result and the coordinate data of low precision three of high-precision laser interferometer before and after the processing
It can be seen that from the result of table 1：Data process effects are notable, to CMM Data before processing, low precision three
The uncertainty of measurement of coordinate is in 3.5um, after handling measurement data, and uncertainty of measurement is reduced into 1um by 3.5um
Hereinafter, measurement data accuracy is substantially increased, makes measurement data more approaching to reality value.
Selection 10 pieces of 60 × 60 × 10mm milling plane verified, respectively uncertainty of measurement be 0.6um with
Measured under 3.5um three coordinate machine.Identical is used for the measurement result under 3.5um three coordinate machine to uncertainty of measurement
Data processing method handled, systematic error is identical with the systematic error that above-mentioned standard plane reference is good, select identical
Wavelet filtering threshold value is filtered out to random error, as a result as shown in table 2.
Table 2 is the contrast knot before and after the high accuracy three coordinate machine of physical plane and low precision three coordinate machine Measurement and Data Processing
Really
It can be seen that from the result of table 2：At a kind of data for reducing measurement data uncertainty proposed by the present invention
Reason method, makes measurement data more approaching to reality value, reduces measurement data uncertainty；As Figure 7-8, finished surface is filtered
Front and rear two-dimentional amplitude frequency diagram.
In summary, presently preferred embodiments of the present invention is these are only, is not intended to limit the scope of the present invention.
Within the spirit and principles of the invention, any modification, equivalent substitution and improvements made etc., should be included in the present invention's
Within protection domain.
Claims (3)
1. a kind of reduce the data processing method of measurement data uncertainty, it is characterised in that this method includes：
Step one：The plane that flatness is prepared less than setting flatness S is used as standard flat；
Step 2：Sample frequency and sampling length are set to standard flat and actual processing plane to be compensated；
Step 3：According to the sample frequency and sampling length in step 2, any angle point using standard flat is origin, and z-axis refers to
To the normal direction of standard flat, rectangular coordinate system is set up, standard flat is sampled using measuring instrument, measuring instrument is obtained
The measurement data X1 of the z-axis of device, the measurement data of standard flat is measurement error；
Step 4：Measurement data to the measuring instrument of acquisition carries out best fit positioning, removes the position error of coordinate system, obtains
The measurement data X2 of the position error of coordinate system must be removed；
Step 5：According to the metering system of step 3, the multiple measurement standard plane under the same rectangular coordinate system, for step
Rapid three measurement errors obtained are handled according to the removal position error mode of step 4, obtain determining for multigroup removal coordinate system
The measurement data X2 of position error, analyzes the measurement data X2, if the measurement data X2 has identical changing rule,
Average is taken to measurement data X2, the average is designated as systematic error X3, and systematic error is compensated, the measurement after being compensated
Data X4, i.e. X4=X2-X3；If measurement data X2 does not have rule, ignore influence of the systematic error to measurement result；
Step 6：Measurement data X4 is filtered using optional filtering method, the best filtering method of filter effect is selected；
Step 7：When being measured to actual processing plane, using the sample frequency and sampling length determined in step 2, in reality
In border processing plane, set up and rectangular coordinate system identical coordinate system described in step 3, the measuring instrument used using step 3
Actual processing plane is sampled, the measurement data Y1 of actual processing plane is obtained；To the measurement data of actual processing plane
Y1 is handled in the way of the removal position error of step 4, is obtained the measurement data Y2 for removing position error, is utilized step
The rapid five systematic error X3 obtained are compensated to measurement data Y2, and the measurement data Y3 after being compensated is selected using step 6
Fixed filtering method, is filtered out to the random error in measurement data Y3, the measurement data Y4 after being filtered out.
2. a kind of as claimed in claim 1 reduce the data processing method of measurement data uncertainty, it is characterised in that to step
Six selected filtering methods, using spectrum analysis filter effect, if filter effect meets sets requirement, complete filtering method
Determination, otherwise, again select filtering method.
3. a kind of as claimed in claim 1 reduce the data processing method of measurement data uncertainty, it is characterised in that S=0.3
μm。
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108180831A (en) * | 2017-12-30 | 2018-06-19 | 北京工业大学 | The CMM error of coordinate update the system uncertainty analysis methods measured based on LT multi-court positions |
| CN109696665A (en) * | 2018-12-28 | 2019-04-30 | 百度在线网络技术（北京）有限公司 | Processing method, device and the equipment of ultrasonic sensor measurement data |
| CN110411380A (en) * | 2019-08-01 | 2019-11-05 | 合肥工业大学 | Non-contact Surface Roughness Measurement method based on wavelet package texture analysis |
| CN110793482A (en) * | 2019-11-13 | 2020-02-14 | 佛山科学技术学院 | Vehicle sample data acquisition system for collecting data conforming to normal distribution |
| CN111982052A (en) * | 2020-08-04 | 2020-11-24 | 广西科技大学 | Shape error decomposition method for circle feature measurement |
| CN117681037A (en) * | 2024-01-26 | 2024-03-12 | 江西佳时特精密机械有限责任公司 | High-precision main shaft thermal elongation closed-loop compensation method based on displacement sensor |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108180831A (en) * | 2017-12-30 | 2018-06-19 | 北京工业大学 | The CMM error of coordinate update the system uncertainty analysis methods measured based on LT multi-court positions |
| CN109696665A (en) * | 2018-12-28 | 2019-04-30 | 百度在线网络技术（北京）有限公司 | Processing method, device and the equipment of ultrasonic sensor measurement data |
| CN110411380A (en) * | 2019-08-01 | 2019-11-05 | 合肥工业大学 | Non-contact Surface Roughness Measurement method based on wavelet package texture analysis |
| CN110411380B (en) * | 2019-08-01 | 2021-01-22 | 合肥工业大学 | Non-contact surface roughness measurement method based on wavelet packet texture analysis |
| CN110793482A (en) * | 2019-11-13 | 2020-02-14 | 佛山科学技术学院 | Vehicle sample data acquisition system for collecting data conforming to normal distribution |
| CN111982052A (en) * | 2020-08-04 | 2020-11-24 | 广西科技大学 | Shape error decomposition method for circle feature measurement |
| CN111982052B (en) * | 2020-08-04 | 2021-03-02 | 广西科技大学 | Shape error decomposition method for circle feature measurement |
| CN117681037A (en) * | 2024-01-26 | 2024-03-12 | 江西佳时特精密机械有限责任公司 | High-precision main shaft thermal elongation closed-loop compensation method based on displacement sensor |
| CN117681037B (en) * | 2024-01-26 | 2024-04-16 | 江西佳时特精密机械有限责任公司 | High-precision main shaft thermal elongation closed-loop compensation method based on displacement sensor |
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Application publication date: 20170901 |