CN108362493B - A kind of numerically-controlled machine tool linear axis angular errors rapid detection method - Google Patents
A kind of numerically-controlled machine tool linear axis angular errors rapid detection method Download PDFInfo
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Abstract
A kind of numerically-controlled machine tool linear axis angular errors rapid detection method, numerically-controlled machine tool detection technique field.Measuring device is installed on linear axis first by this, and determines the initial angular errors that installation generates by accelerometer；Then, for linear axis with three kinds of friction speed uniform motion, upper layer measuring system carries out multichannel collecting, storage movement measuring point measurement data automatically；Then, accelerometer is merged to obtain the angular error measured under three kinds of speed with gyroscope measurement corner information using Kalman filter theory；It can be analyzed to different frequency component subsequently, based on identical geometric error signal, the difference lower measurement angle error that tests the speed be filtered；Finally, the measurement angle error under testing the speed to filtered three kinds is overlapped, lathe linear axis angular error rapid survey is completed.Measurement efficiency of the present invention is high, data-handling capacity is strong, it can be achieved that lathe linear motion axis angular errors rapid survey, easy to operate, device integration is high, is easy to implement automation.
Description
Technical field
The invention belongs to numerical control machine tool technique field, in particular to a kind of numerically-controlled machine tool linear axis angular errors quickly detect
Method.
Background technique
Characterization of the angular errors of lathe linear axis as kinematic pair operation deflection angle is assessment geometric precision of machine tool weight
Index is wanted, size directly affects the processing quality of workpiece, and is gradually increased during lathe is on active service.Therefore, linear axis turns
The acquisition of angle error safeguards the assessment of geometric precision of machine tool in time with lathe and is of great significance.For this purpose, to straight line Shaft angle
The detection of error is put into all kinds of machine tool accuracy test stones.In actual production, lathe producer and Subscriber Unit use laser
The detecting instruments such as interferometer, ball bar carry out periodic detection to the angular errors of lathe linear axis.However, due to detection device
Large volume, high cost, debugging is cumbersome, time-consuming for measurement, serious to restrict machine tool accuracy detection efficiency, influences normal production process.
Especially for production line, frequent shutdown is firmly avoided.Therefore, seek a kind of numerically-controlled machine tool linear axis angular errors quickly to detect
Method is extremely urgent.
Studies have shown that the quick detection of numerically-controlled machine tool linear axis angular errors, should meet measurement efficiency height, data processing energy
Power is strong, device volume is small, cheap, the convenient and fast primary condition of installation and debugging, has great engineering challenges.By to top
Spiral shell instrument obtains the angular speed of kinematic pair during exercise, and integral obtains movement deflection angle, in conjunction with the deflection angle of accelerometer measures
It is modified, completes the quick obtaining of linear axis angular errors, provided for the quick detection of numerically-controlled machine tool linear axis angular errors
Possibility.
Harbin Institute of Technology Li Li, Xia Hong in 2013 are big etc. to disclose one kind three in patented invention CN103234512A
Axis air floating table table high-precision attitude angle and angular velocity measurement device, this method and are swashed using intelligent gauge head, gyro, kaleidoscope prism
Optical tracker system obtains angle and angular velocity information by Kalman filtering algorithm, realizes Dynamic High-accuracy measurement.However, this method
Measuring device is more, debugging is complicated, measurement and its time-consuming.2010, Beijing Sanchi Technoogy Development Co., Ltd. was in patented invention
A kind of method of precision compensation of inertial measurement unit is disclosed in CN102135431A, this method uses the angle of optical fibre gyro output
Velocity information, and attitude angle is calculated according to the angular velocity information by aviation attitude system.However, this method uses apparatus cost pole
It is high and vulnerable to external interferences such as temperature, it is unable to satisfy the detection demand of operating under complex working conditions of numerically-controlled machine tool straight line Shaft angle.
Summary of the invention
Present invention aims to overcome that existing method is insufficient, quickly detects and ask for numerically-controlled machine tool linear axis angular errors
Topic, has invented a kind of lathe linear axis angular errors rapid detection method.The device that this method uses is accelerometer and gyro
Instrument has the advantages such as strong antijamming capability, detection efficiency height；The component of device is few, and each component is small in size, at low cost, structure is tight
It gathers simply, convenient for assembling.This method detects gravity vector components using accelerometer, determines installation error, misses for measurement angle
The correction of difference provides foundation；Based on Kalman filtering, gyroscope measurement result is carried out using accelerometer measures angular error
Amendment increases measurement accuracy；Using noise profile rule of the identical angular errors under difference tests the speed, high letter is retained by filtering
It makes an uproar than ingredient, is based on the continuously distributed principle of spatial frequency, merge the measurement data for the middle high s/n ratio bandwidth that respectively tests the speed, increase measurement
Bandwidth；Measuring system is installed on lathe linear axis, it can be achieved that lathe linear axis angular errors quick detection, it is easy to operate,
Device integration is high, is easy to implement automation.
Technical solution of the present invention:
A kind of numerically-controlled machine tool linear axis angular errors rapid detection method, using gyroscope and accelerometer measures linear axis
Deflection angle when uniform motion, and then the pitching angle error, beat angle error and rolling angle error of linear axis is calculated；It is first
First, measuring device is installed on linear axis, and the initial angular errors that installation generates is determined by accelerometer；Then, directly
For spool with three kinds of friction speed uniform motion, data collecting card carries out multichannel collecting and storage movement measuring point measurement number automatically
According to；Then, accelerometer is merged using Kalman filter theory with gyroscope measurement corner information, obtains three kinds of speed
The angular error of lower measurement；It is different frequency component subsequently, based on identical geometric error signal decomposition, tests the speed lower measurement to difference
Angular error is filtered；Finally, being overlapped to the measurement angle error under filtered three kinds of speed, lathe straight line is completed
Axis angular error rapid survey；
Specific step is as follows:
The first step assembles numerically-controlled machine tool linear axis angular errors device for fast detecting
Using three single-axis accelerometers: 1#Single-axis accelerometer 1,2#Single-axis accelerometer 2 and 3#Single-axis accelerometer 3
The three-dimensional accelerometer group of composition；Three gyroscopes: 4#Single axis gyroscope 4,5#Single axis gyroscope 5 and 6#Single axis gyroscope 6 forms
Three-dimensional gyroscope；Guarantee 1#1 measurement direction of single-axis accelerometer be the direction I, 2#2 measurement direction of single-axis accelerometer is the side n
To 3#Single-axis accelerometer measurement direction is the direction t；Guarantee the measurement of 4# single axis gyroscope 4 around the direction n coordinate Shaft angle, angle
Initial line is I reference axis, rotates clockwise and is positive；5#For the measurement of single axis gyroscope 5 around the direction t coordinate Shaft angle, angle initial line is I seat
Parameter, rotation is positive counterclockwise；6#For the measurement of single axis gyroscope 6 around the direction I coordinate Shaft angle, angle initial line is t reference axis, up time
Needle rotation is positive；Three single-axis accelerometers and three single axis gyroscopes pass through nut respectively and are fixed in detection box 7；Detect box
7 are fixed on numerically-controlled machine tool linear axis 8 by side flanges, complete the clamping of measuring device and numerically-controlled machine tool linear axis 8；
Second step, measuring device are measured in machine installation error
Firstly, controlling numerically-controlled machine tool linear axis I and moving to its any end；Then, the data collection system of host computer
Store each 1#Single-axis accelerometer 1,2#Single-axis accelerometer 2 and 3#The measurement data of single-axis accelerometer 3 is respectivelyObtain measuring device installation pitch angle error alphacWith rolling angle error γc,
Wherein, g is the acceleration of gravity of measurement position；Adjustment detection box flange nut, until installation pitch angle error alphac
With rolling angle error γcWithin 0.1 °；
Third step, the measurement of numerically-controlled machine tool linear axis angular errors
Firstly, setting val (val=max, mid, min) is the measuring speed of measuring device, three kinds of measuring speeds are respectively
High speed vmax, middling speed vmidOr low speed vmin；Then, by measuring device along the direction I respectively with high speed vmax, middling speed vmid, low speed vmin
The other side is moved to from any side of linear axis, while the data collection system high frequency of host computer stores each measuring point coordinate and defeated
Digital signal data out；Wherein movement velocity are as follows:
Wherein, VmaxFor the maximum feed speed of kinematic axis；Accelerometer under the corresponding linear axis high-speed motion of three kinds of speed
Sample frequency fmax, the sample frequency f of accelerometer under linear axis middling speed movesmidWith accelerometer under linear axis low-speed motion
Sample frequency fminIt is respectively as follows:
Measurement obtains measurement acceleration subset of the linear axis under three kinds of measuring speedsWith angular speed subset For k#Accelerometer
Under the conditions of measuring speed is val, in the i-th measuring point output signal,For k#Accelerometer is val condition in measuring speed
Under, in the i-th measuring point output signal, r is the measuring point number in the track of section, and k is accelerometer label,For k#Accelerometer exists
Measuring speed be val under the conditions of in the time of measuring of the i-th measuring point,
Wherein,For k#Accelerometer under high-speed condition in the time of measuring of the i-th measuring point,For k#Accelerometer
In the time of measuring of the i-th measuring point under the conditions of middling speed,For k#Accelerometer is at low speeds when the measurement of the i-th measuring point
Between；
4th step, the linear axis measurement corner amendment based on Kalman filtering
In this method, settingIt is measured under the conditions of measuring speed is val, in the i-th measuring point for accelerometer inclined
Corner, wherein k=1,2,3 respectively represent the pitch angle that measurement obtainsDeflection angleWith roll angleIt calculates first and measures deflection angle in the difference lower each measuring point that tests the speed by three-dimensional accelerometer,
Then, initial value, k are set#Accelerometer measures deflection angle under the conditions of measuring speed is val, in the 1st measuring pointRespectively as 4#Single axis gyroscope 4,5#Single axis gyroscope 5,6#Single axis gyroscope 6 measuring speed be val under the conditions of,
In the amendment deflection angle of the 1st measuring pointWherein k=1,2,3；Set k#Single axis gyroscope is val condition in measuring speed
Under, the measured value covariance of the amendment deflection angle of the 1st measuring pointFor the arbitrary value of non-zero, wherein k=4,5,6；
Then, calculating is iterated to each measuring point of linear axis measurement deflection angle
Wherein, [2, r] i ∈,For k#Single axis gyroscope is under the conditions of measuring speed is val, the survey of the i-th measuring point
Deflection angle is measured, wherein k=4,5,6；For k#Single axis gyroscope is under the conditions of measuring speed is val, the (i-1)-th measuring point
Amendment deflection angle, wherein k=4,5,6；
The value of amendment deflection angle is found out according to measured value,
Wherein, k=4,5,6,For k#Single axis gyroscope is under the conditions of measuring speed is val in the i-th measuring point Kalman
Filtering gain,
Wherein,For k#Single axis gyroscope is under the conditions of measuring speed is val, the association of the measurement deflection angle of the i-th measuring point
Variance；For k#Single axis gyroscope is under the conditions of measuring speed is val, the measured value association side of the amendment deflection angle of the i-th measuring point
Difference；For k#Single axis gyroscope is under the conditions of measuring speed is val, the measurement noise variance of the i-th measuring point, wherein k=4,5,
6；For k#Single-axis accelerometer is under the conditions of measuring speed is val, the measurement noise variance of the i-th measuring point, wherein k=1,2,
3；
Formula (6)~(10) are constantly computed repeatedly, calculates and obtains measurement amendment of the linear axis under three kinds of measuring speeds partially
Corner subsetWherein,
It is i measuring point along the measurement distance in the direction I,
Wherein,For along the high speed in the direction I,For the sample frequency of the accelerometer under the high-speed motion in the direction I；
5th step, filtering and data fusion based on the spatial frequency condition of continuity
Firstly, measurement obtains the direction I kinematic axis in high speedMiddling speedLow speedMeasurement under measuring condition is repaired
Positive deflection angle subset Θk,max、Θk,midWith Θk,min；Measurement Subset is filtered respectively, filters upper limiting frequency fu,valWith lower limit
Frequency fd,valFor
Wherein,Upper limiting frequency is filtered for the direction I high speed is lower,Lower frequency limit is filtered for the direction I high speed is lower；To filter upper limiting frequency under the middling speed of the direction I,To filter lower frequency limit under the middling speed of the direction I；It is low for the direction I
Speed is lower to filter upper limiting frequency,To filter lower frequency limit under the middling speed of the direction I；
By aforesaid operations, filtering measurement amendment deflection angle subset is obtainedWhereinFor k#Uniaxial gyro
Instrument is under the conditions of measurement direction speed is val, the filtered measurement amendment deflection angle signal of the i-th measuring point；liFor the measurement of i measuring point
Distance；
Then, the measurement under low speed, middling speed, high speed measuring condition, measured each element in subset is displaced to be added, it is complete
At data fusion, i.e.,
Wherein,For k#Single axis gyroscope is in the case where measurement direction speed is high-speed condition, the filtered measurement of the i-th measuring point
Amendment deflection angle signal；For k#Single axis gyroscope is under the conditions of measurement direction speed is middling speed, the filtered survey of the i-th measuring point
Amount amendment deflection angle signal；For k#Single axis gyroscope is in the case where measurement direction speed is low-speed conditions, after the filtering of the i-th measuring point
Measurement amendment deflection angle signal；ElementCollection be combined into measurement corner always collect,
Finally, linear axis pitch angle α, deflection angle β and roll angle γ be calculated being
Beneficial effects of the present invention: using accelerometer and gyroscope is measured during moving along a straight line secondary uniform motion and hung down
In the deflection angle of the direction of motion, and then the method for obtaining the deflection angle error of linear motion axis, it realizes to numerically-controlled machine tool
Linear motion axis angular errors rapid survey.
Detailed description of the invention
Fig. 1 is geometric accuracy device for fast detecting composition figure.
Fig. 2 is geometric accuracy device for fast detecting detection figure.
Fig. 3 be linear axis under three kinds of speed in the measurement acceleration subset distribution schematic diagram in the direction n.
Fig. 4 be linear axis under three kinds of speed in the measurement acceleration subset distribution schematic diagram in the direction I.
Fig. 5 be linear axis under three kinds of speed around the measurement angular speed subset distribution schematic diagram in the direction t.
Fig. 6 be accelerometer under three kinds of measuring speeds around the direction t measurement deflection angle subset schematic diagram.
Fig. 7 is that deflection angle subset schematic diagram is corrected in measurement of the linear axis under three kinds of measuring speeds around the direction t.
Fig. 8 is that amendment deflection angle subset schematic diagram is measured around t trend pass filtering.
Fig. 9 is always to collect schematic diagram around t orientation measurement corner.
In figure: 1-1# accelerometer；2-2# single-axis accelerometer；3-3# single-axis accelerometer；4-4# single axis gyroscope meter；
5-5# single axis gyroscope, 6-6# single axis gyroscope；7- detects box；8- numerically-controlled machine tool linear axis；
I, n, t are the direction I, the direction n and the direction t.
Specific embodiment
Below in conjunction with attached drawing and the technical solution specific embodiment that the present invention will be described in detail.
The first step assembles numerically-controlled machine tool linear axis angular errors device for fast detecting
Using three single-axis accelerometers: 1#Single-axis accelerometer 1,2#Single-axis accelerometer 2,3#3 groups of single-axis accelerometer
At three-dimensional accelerometer group；Three gyroscopes: 4#Single axis gyroscope 4,5#Single axis gyroscope 5,6#What single axis gyroscope 6 formed
Three-dimensional gyroscope.Guarantee 1#1 measurement direction of single-axis accelerometer is the direction I；2#2 measurement direction of single-axis accelerometer is the direction n；
3#Single-axis accelerometer measurement direction is the direction t；Guarantee the measurement of 4# single axis gyroscope 4 around the direction n coordinate Shaft angle, angle initial line
For I reference axis, rotates clockwise and be positive；5#For the measurement of single axis gyroscope 5 around the direction t coordinate Shaft angle, angle initial line is I coordinate
Axis, rotation is positive counterclockwise；6#The measurement of single axis gyroscope 6 is around the direction I coordinate Shaft angle, and angle initial line is t reference axis, clockwise
Rotation is positive；Three single-axis accelerometers and three single axis gyroscopes pass through nut respectively and are fixed in detection box 7；Detect box 7
It is fixed on linear axis by side flanges, completes the clamping of measuring device and numerically-controlled machine tool linear axis 8.
Second step, measuring device are measured in machine installation error
Firstly, controlling numerically-controlled machine tool linear axis I and moving to its any end.Then, the data collection system of host computer
Store each 1#、2#、3#The measurement data of single-axis accelerometer 1,2,3 is respectively 0.00045g, 0.00095g, 0.9999g, is obtained
Measuring device installs pitch angle error alphac=arcsin (0.00045g/g)=0.025 ° and rolling angle error βc=arcsin
(0.00095g/cos (0.025) g)=0.054 °.
Third step, the measurement of numerically-controlled machine tool linear axis angular errors
For measuring linear axis deflection angle, by measuring device along the direction I with high speed vmax=500mm/s, middling speed vmid=
500/5=100mm/s, low speed vmin=500/25=20mm/s moves to the other side respectively, while the data of host computer acquire system
High frequency of uniting stores each measuring point coordinate and output digit signals data.Wherein, the maximum feed speed of kinematic axis is 500mm/s.Directly
The sample frequency of accelerometer is f under spool high-speed motionmax=500/0.5 × 4=4000Hz, the movement of linear axis middling speed is lower to be added
The sample frequency of speedometer is fmid=4000/500 × 100=1000Hz, the sampling frequency of accelerometer under linear axis low-speed motion
Rate is fmin=4000/500 × 20=160Hz.Obtain by aforesaid operations: attached drawing 3- linear axis is under three kinds of speed in the direction n
The distribution of acceleration subset is measured, attached drawing 4- linear axis is under three kinds of speed in the measurement acceleration subset distribution in the direction I, attached drawing 5-
Linear axis is distributed under three kinds of speed around the measurement angular speed subset in the direction t.
4th step, the linear axis measurement corner amendment based on Kalman filtering
It is calculated by formula (5) and is measured by what 1# single-axis accelerometer 1,2# single-axis accelerometer 2 measured in three kinds first
Each measuring point measures deflection angle under speed, obtain attached drawing 6- accelerometer under three kinds of measuring speeds around the direction t measurement beat
Silver coin collection.
Then, initial value is set, accelerometer is under the conditions of measuring speed is 500mm/s, 100mm/s, 20mm/s in the 1st
0.024 ° of the measurement deflection angle of measuring point, 0.025 °, 0.024 ° be used as 5#Single axis gyroscope 5 measuring speed be 500mm/s,
The amendment deflection angle of 1st measuring point under the conditions of 100mm/s, 20mm/s.Setting 5#Single axis gyroscope measuring speed be 500mm/s,
The measured value covariance of the amendment deflection angle of the 1st measuring point is 1 under the conditions of 100mm/s, 20mm/s.Setting 5#Single axis gyroscope
It is 0.001 in the measurement noise variance for the lower each measuring point that respectively tests the speed.Each single-axis accelerometer is set in the lower each measuring point that respectively tests the speed
Measuring noise variance is 1.
Then, it by calculation formula (6)~(10), calculates measurement of the linear axis under three kinds of measuring speeds and corrects deflection angle
Subset.Obtain by aforesaid operations: attached drawing 7- linear axis corrects deflection angle subset around the measurement in the direction t under three kinds of measuring speeds.
5th step, filtering and data fusion based on the spatial frequency condition of continuity
Firstly, being filtered respectively to measurement Subset, measurement obtains measurement amendment deflection angle subset under high speed measuring condition
The filtering upper limit beLower limit isMeasurement obtains to be measured under middling speed measuring condition
Amendment deflection angle subset the filtering upper limit beLower limit isIt surveys
The filtering upper limit of measurement amendment deflection angle subset is under amount acquisition low speed measuring conditionLower limit
ForObtain by aforesaid operations: attached drawing 8- measures amendment deflection angle subset around t trend pass filtering.
It is added finally, the measurement measured under low speed, middling speed and high speed measuring condition is displaced each element in subset, it is complete
At data fusion.Obtain by aforesaid operations: attached drawing 9- always collects around t orientation measurement corner.Finally obtaining deflection angle is 0.039 °.
A kind of numerically-controlled machine tool linear axis angular errors rapid detection method of the present invention, it passes through accelerometer, top
The deflection angle of the direction of motion is fallen in when spiral shell instrument measurement linear motion pair uniform motion, it is logical that linear motion axis is calculated in turn
Angular errors provide possibility for the quick detection of numerically-controlled machine tool angular errors.
A kind of numerically-controlled machine tool linear axis angular errors rapid detection method described above only preferred approach of the invention, thus it is all
It include present patent application according to the equivalent change or modification that feature described in present patent application range and principle are done
In range.
Claims (1)
1. a kind of numerically-controlled machine tool linear axis angular errors rapid detection method, even using gyroscope and accelerometer measures linear axis
Deflection angle when speed movement, and then the pitching angle error, beat angle error and rolling angle error of linear axis is calculated；It is first
First, measuring device is installed on linear axis, and the initial angular errors that installation generates is determined by accelerometer；Then, directly
For spool with three kinds of friction speed uniform motion, data collecting card carries out multichannel collecting and storage movement measuring point measurement number automatically
According to；Then, accelerometer is merged using Kalman filter theory with gyroscope measurement corner information, obtains three kinds of speed
The angular error of lower measurement；It is different frequency component subsequently, based on identical geometric error signal decomposition, tests the speed lower measurement to difference
Angular error is filtered；Finally, being overlapped to the measurement angle error under filtered three kinds of speed, lathe straight line is completed
Axis angular error rapid survey；
It is characterized in that, steps are as follows:
The first step assembles numerically-controlled machine tool linear axis angular errors rapid measurement device
Using three single-axis accelerometers: 1#Single-axis accelerometer 1,2#Single-axis accelerometer 2 and 3#Single-axis accelerometer 3 forms
Three-dimensional accelerometer group；Three gyroscopes: 4#Single axis gyroscope 4,5#Single axis gyroscope 5 and 6#The three of the composition of single axis gyroscope 6
To gyroscope；Guarantee 1#1 measurement direction of single-axis accelerometer be the direction I, 2#2 measurement direction of single-axis accelerometer be the direction n, 3#
Single-axis accelerometer measurement direction is the direction t；Guarantee the measurement of 4# single axis gyroscope 4 around the direction n coordinate Shaft angle, angle initial line is
I reference axis, rotates clockwise and is positive；5#For the measurement of single axis gyroscope 5 around the direction t coordinate Shaft angle, angle initial line is I reference axis,
Rotation is positive counterclockwise；6#For the measurement of single axis gyroscope 6 around the direction I coordinate Shaft angle, angle initial line is t reference axis, is revolved clockwise
Switch to just；Three single-axis accelerometers and three single axis gyroscopes pass through nut respectively and are fixed in detection box 7；It is logical to detect box 7
It crosses side flanges to be fixed on numerically-controlled machine tool linear axis 8, completes the clamping of measuring device and numerically-controlled machine tool linear axis 8；
Second step, measuring device are measured in machine installation error
Firstly, controlling numerically-controlled machine tool linear axis I and moving to its any end；Then, the data collection system storage of host computer
Each 1#Single-axis accelerometer 1,2#Single-axis accelerometer 2 and 3#The measurement data of single-axis accelerometer 3 is respectivelyObtain measuring device installation pitch angle error alphacWith rolling angle error γc,
Wherein, g is the acceleration of gravity of measurement position；Adjustment detection box flange nut, until installation pitch angle error alphacWith rolling
Angle error γcWithin 0.1 °；
Third step, the measurement of numerically-controlled machine tool linear axis angular errors
Firstly, setting val as the measuring speed of measuring device, three kinds of measuring speeds are respectively high speed vmax, middling speed vmidOr low speed
vmin；Then, by measuring device along the direction I respectively with high speed vmax, middling speed vmid, low speed vminIt is moved from any side of linear axis
To the other side, while the data collection system high frequency of host computer stores each measuring point coordinate and output digit signals data；Wherein transport
Dynamic speed are as follows:
Wherein, VmaxFor the maximum feed speed of kinematic axis；Accelerometer adopts under the corresponding linear axis high-speed motion of three kinds of speed
Sample frequency fmax, the sample frequency f of accelerometer under linear axis middling speed movesmidIt is adopted with accelerometer under linear axis low-speed motion
Sample frequency fminIt is respectively as follows:
Measurement obtains measurement acceleration subset of the linear axis under three kinds of measuring speedsWith angular speed subset For k#Accelerometer
Under the conditions of measuring speed is val, in the i-th measuring point output signal,For w#Single axis gyroscope is val condition in measuring speed
Under, in the i-th measuring point output signal, r is the measuring point number in the track of section, and k is accelerometer label, and w is single axis gyroscope label,For k#Accelerometer under the conditions of measuring speed is val in the time of measuring of the i-th measuring point,For w#Gyroscope is measuring
Speed be val under the conditions of in the time of measuring of the i-th measuring point；
Wherein,For k#Accelerometer under high-speed condition in the time of measuring of the i-th measuring point,For k#Accelerometer is in
In the time of measuring of the i-th measuring point under the conditions of speed,For k#Accelerometer is at low speeds in the time of measuring of the i-th measuring point；
4th step, the linear axis measurement corner amendment based on Kalman filtering
SettingThe deflection angle measured for accelerometer under the conditions of measuring speed is val, in the i-th measuring point, wherein k=
1,2,3 respectively represents the pitch angle that measurement obtainsDeflection angleWith roll angleIt calculates first
It is tested the speed lower each measuring point measurement deflection angle by three-dimensional accelerometer in difference,
Then, initial value, k are set#Accelerometer measures deflection angle under the conditions of measuring speed is val, in the 1st measuring pointRespectively as 4#Single axis gyroscope 4,5#Single axis gyroscope 5,6#Single axis gyroscope 6 is val condition in measuring speed
Under, in the amendment deflection angle of the 1st measuring pointWherein k=1,2,3；Set w#Single axis gyroscope is val in measuring speed
Under the conditions of, the measured value covariance of the amendment deflection angle of the 1st measuring pointFor the arbitrary value of non-zero, wherein w=4,5,6；
Then, calculating is iterated to each measuring point of linear axis measurement deflection angle
Wherein, [2, r] i ∈,For w#For single axis gyroscope under the conditions of measuring speed is val, the measurement of the i-th measuring point is inclined
Corner, wherein w=4,5,6；For w#Single axis gyroscope under the conditions of measuring speed is val, repair by the (i-1)-th measuring point
Positive deflection angle, w=4,5,6；
The value of amendment deflection angle is found out according to measured value,
Wherein, w=4,5,6,For w#Single axis gyroscope is under the conditions of measuring speed is val in the i-th measuring point Kalman filtering
Gain,
Wherein,For w#Single axis gyroscope is under the conditions of measuring speed is val, the covariance of the measurement deflection angle of the i-th measuring point；For w#Single axis gyroscope is under the conditions of measuring speed is val, the measured value covariance of the amendment deflection angle of the i-th measuring point；For w#Single axis gyroscope is under the conditions of measuring speed is val, the measurement noise variance of the i-th measuring point, wherein w=4,5,6；For k#Single-axis accelerometer is under the conditions of measuring speed is val, the measurement noise variance of the i-th measuring point, wherein k=1,2,3；
Formula (6)~(10) are constantly computed repeatedly, the measurement amendment deflection angle for obtaining linear axis under three kinds of measuring speeds is calculated
SubsetWherein,For i
Measuring point along the direction I measurement distance,
Wherein,For along the high speed in the direction I,For the sample frequency of the accelerometer under the high-speed motion in the direction I；
5th step, filtering and data fusion based on the spatial frequency condition of continuity
Firstly, measurement obtains the direction I kinematic axis in high speedMiddling speedLow speedMeasurement amendment under measuring condition
Deflection angle subset Θw,max、Θw,midWith Θw,min；Measurement Subset is filtered respectively, filters upper limiting frequency fu,valWith lower frequency limit
Rate fd,valFor
Wherein,Upper limiting frequency is filtered for the direction I high speed is lower,Lower frequency limit is filtered for the direction I high speed is lower；
To filter upper limiting frequency under the middling speed of the direction I,To filter lower frequency limit under the middling speed of the direction I；To be filtered under the low speed of the direction I
Wave upper limiting frequency,To filter lower frequency limit under the middling speed of the direction I；
By aforesaid operations, filtering measurement amendment deflection angle subset is obtainedWhereinFor w#Uniaxial top
Spiral shell instrument is under the conditions of measurement direction speed is val, the filtered measurement amendment deflection angle signal of the i-th measuring point；liFor the survey of i measuring point
Span from；
Then, the measurement under low speed, middling speed, high speed measuring condition, measured is displaced each element in subset to be added, completes number
According to fusion, i.e.,
Wherein,For w#Single axis gyroscope is in the case where measurement direction speed is low-speed conditions, the filtered measurement amendment of the i-th measuring point
Deflect angle signal；For w#Single axis gyroscope under the conditions of measurement direction speed is middling speed, repair by the filtered measurement of the i-th measuring point
Positively biased angular signal；For w#Single axis gyroscope is in the case where measurement direction speed is high-speed condition, the filtered survey of the i-th measuring point
Amount amendment deflection angle signal；Element θi wCollection be combined into measurement corner always collect,
Finally, linear axis pitch angle α, deflection angle β and roll angle γ be calculated being
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