CN105956383B - The calculation method for the large-scale reflector antenna error in pointing that track unevenness influences - Google Patents
The calculation method for the large-scale reflector antenna error in pointing that track unevenness influences Download PDFInfo
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Abstract
The invention discloses the calculation methods for the large-scale reflector antenna error in pointing for considering the influence of track unevenness, comprising the following steps: Step1, measures to track unevenness, obtains the test data of surface irregularity；Step2, track unevenness mathematical model is constructed using fourier function and fractal function；Step3, amendment track unevenness mathematical model；Orientation frame heeling error and torsional error under the influence of Step4, calculating consideration track unevenness；Step5, it is converted using coordinate, calculates the antenna pointing error considered under the influence of track unevenness.The invention has the beneficial effects that: (1) this method be capable of the macro contours of accurate description track unevenness, and can also embody the microscopic appearance of track, has more been truly reflected the error condition of actual track；(2) track unevenness accurately calculates the quantitative influence to errant unevenness to antenna-point accuracy error, can work Antenna Design and provides theoretical direction, practical application value with higher.
Description
Technical Field
The invention relates to a method for calculating pointing errors of a large reflector antenna, in particular to a method for calculating pointing errors of a large reflector antenna influenced by track unevenness.
Background
With the increasing activity of astronomical observations and space exploration activities, over the last 20 years, countries around the world strive to manufacture large radio antennas, such as Green Bank Telescope in the united states, Effelsberg in germany, and qtt (qi Tai Telescope) that is to be built in new-jiang in china. The common characteristics of these antennas are heavy weight and high pointing accuracy requirements.
The pointing accuracy is an important index in the evaluation of the high-frequency working performance of the large reflector antenna, and is mainly influenced by the structure and the service environment of the antenna, the research on the axis system error of the antenna in the existing antenna pointing error model is more, and the Wufenggao professor divides the axis system error into three conditions: the mechanical axis is not perpendicular to the pitch axis, the pitch axis is not perpendicular to the azimuth axis, and the azimuth axis is not perpendicular to the ground, and each of the cases is analyzed.
But his error model has some disadvantages:
firstly, the considered error condition is single, and the comprehensive influence of a plurality of error sources on the direction cannot be comprehensively considered;
secondly, the pointing error model only considers the pointing error under a special azimuth angle, and is not perfect theoretically.
At present, the wheel-track type antenna base is generally adopted to replace the conventional turntable type antenna base, the weight of the whole structure of the antenna is obviously reduced by the wheel-track type antenna base, but because the diameter of the track of the large-scale antenna structure is very large, the realization of the whole one-step processing forming of the track is unrealistic, only a segmented track splicing mode can be adopted, a small amount of surface errors such as track stress deformation and the inherent surface roughness of the metal surface can be inevitably introduced in the processes of forging and welding, and the errors directly influence the structural error of the azimuth frame and finally influence the pointing accuracy of the whole antenna.
Gawronski.W converts the track unevenness data obtained by the test to the azimuth angle error and the pitch angle error of the antenna directly through the geometric relationship; the Tonino Pisanu considers the pointing error under the comprehensive influence of the deformation of the azimuth frame caused by track unevenness and temperature drift; liyongjiang measures the unevenness of the track and the pointing error of the antenna, analyzes the correlation between the unevenness of the track and the pointing error of the antenna, but the pointing error of the Liyongjiang is obtained by fitting the pointing errors of four fixed directions, and a larger fitting error exists; although the influence of the track unevenness is considered in the model, the track unevenness is not accurately described, so that an accurate calculation method of the antenna pointing error under the influence of the track unevenness is not provided.
Disclosure of Invention
The invention aims to provide a method for calculating the pointing error of a large reflector antenna influenced by track unevenness, which has the following advantages: (1) the total antenna pointing error can be regulated, whether for predictable or unpredictable pointing errors; (2) the error sources in the antenna structure which affect the pointing error can be separated and measured so as to control the error sources respectively; (3) the overall antenna pointing residual can be minimized by reverse compensation of the error source.
In order to achieve the above object, the present invention adopts the following technical solutions:
the method for calculating the pointing error of the large reflector antenna influenced by the track unevenness is characterized by comprising the following steps of:
step 1: measuring the unevenness of the track to obtain test data of the surface unevenness;
step 2: firstly, modeling track unevenness test data by using a Fourier function to obtain a large-scale error model, comparing the large-scale error model with the test data, and then modeling a fitting residual error of the Fourier function by using a fractal function to obtain a track unevenness mathematical model;
step 3: comparing the track unevenness mathematical model with the test data, if the unevenness mathematical model meets the precision requirement, directly jumping to Step4, and if the unevenness mathematical model does not meet the precision requirement, correcting the unevenness mathematical model to enable the unevenness mathematical model to meet the precision requirement;
step 4: calculating the inclination error of the azimuth frame under the influence of the unevenness of the track;
step 5: calculating the torsion error of the azimuth frame under the influence of the unevenness of the track;
step 6: and calculating the antenna pointing error under the influence of track unevenness by using coordinate conversion.
The method for calculating the pointing error of the large reflector antenna affected by the track unevenness is characterized in that in Step1, the method for measuring the track unevenness is as follows:
(11) an inclinometer is arranged on the four groups of roller devices at the bottom of the azimuth frame;
(12) filling a steel sheet under a group of rollers;
(13) when the azimuth frame rotates at a constant speed, the azimuth frame is zoomed according to the proportion between the thickness of the steel sheet and the reading of the inclinometer, the relation between the reading of the inclinometer and the track unevenness value can be obtained, and further the track unevenness data f is obtained0(x)。
The method for calculating the pointing error of the large reflector antenna influenced by the track unevenness is characterized in that in Step2, a method for establishing a track unevenness mathematical model is as follows:
(21) modeling the track unevenness wheel data obtained in the step (13) by using a Fourier function, wherein the mathematical formula of the Fourier function is as follows:
wherein, ansin(nωx)＝Ansin(nωx)cos(θn)，bncos(nωt)＝Ancos(nωt)sin(θn) X denotes the track position, ω is the fundamental frequency, n denotes the sine function sin (n ω x + θ) over the sample lengthn) The repeated occurrence times of the waveform, m is Fourier series expansion order, the value range of m is [1, N/2 ], N is the number of sampling points in the track sampling length, and m is a positive integer;
(22) using fractal function pairs f1(x) And f0(x) The fitting residual of (a) is modeled, and the mathematical formula of the fractal function is as follows:
where A is the fractal function amplitude coefficient, reflecting f2(x) N is the number of sampling points of the fractal function, D is the fractal dimension of the fractal function, and gamma is the fundamental frequency of the fractal function, and the value is 1.5;
(23) the mathematical model for establishing the track unevenness is as follows:
f(x)＝f1(x)+f2(x) (3)。
the method for calculating the pointing error of the large reflector antenna influenced by the track unevenness is characterized in that in Step3, the method for comparing and correcting the unevenness mathematical model is as follows:
(31) according to f obtained in step (13)0(x) Calculating the root mean square RMS of the track unevenness test data;
(32) calculating a root mean square value RMS' of the orbit irregularity mathematical model according to f (x) obtained in the step (23);
(33) if it is not(epsilon is 30%), the established track unevenness mathematical model is considered to meet the precision requirement, the Step is carried out to Step4, and if the precision is not met, the Fourier function f is carried out1(x) The expansion order number m of (1) is increased to m +1, and the fractal function f is obtained2(x) The number n of sampling points is increased to n +10, and the Step2 is skipped, and the loop is continued until the precision requirement is met.
The method for calculating the pointing error of the large reflector antenna due to the track unevenness is characterized in that in Step4, the method for calculating the tilt error of the azimuth frame is as follows:
(41) establishing four coordinate systems of OXXYZ and OaXaYaZa、OeXeYeZeAnd OrXrYrZrWhere OXYZ is the geodetic coordinateThe origin of the system is at the center of an azimuth orbit, the Z axis is vertical to the ground, and the negative direction of the Y axis points to the positive north direction; o isaXaYaZaIs an azimuth axis coordinate system with the origin at the center of the azimuth orbit, ZaThe axis is coincided with the azimuth axis, the integral coordinate system rotates and deflects along with the azimuth axis to move, and when the antenna has no azimuth axis error and the azimuth angle A is 0 degrees, the antenna is coincided with the geodetic coordinate system OXYZ; o iseXeYeZeIs a pitch axis coordinate system with the origin at the midpoint of the pitch axis, XeThe axis is coincident with the pitch axis, the integral coordinate system moves along with the rotation and deflection of the pitch axis, and when the antenna has no shafting error, the pitch angle E is 90 degrees, and the azimuth angle A is 0 degrees, the integral coordinate system and the geodetic coordinate system OXYZ only have a difference of the height value h of the azimuth axis in the Z direction; o isrXrYrZrIs reflector coordinate system, and when the pitch angle E is 90 deg., it is matched with pitch axis coordinate system OeXeYeZeBy a height h in the Z direction1(ii) a Four rollers of the azimuth frame are located in an azimuth axis coordinate system OaXaYaZaWherein the first roller, the second roller, the third roller and the fourth roller have heights of
(42) A small difference in height between the first roller and the third roller will cause the azimuth axis to rotate about the X-axis and the Y-axis by △ X1、△y1：
(43) A small difference in height between the second roller and the fourth roller will cause the azimuth axis to rotate about the X and Y axes by △ ×, respectively2、△y2：
(44) The four rollers act together to make the pitching axis rotate around X according to the right hand ruleaRotation of the shaftAround YaRotation of the shaft
The method for calculating the pointing error of the large reflector antenna influenced by the track unevenness is characterized in that the azimuth error phi of the azimuth frame is calculated in Step5tx、φtyAnd phitzThe following formulas are respectively adopted:
the method for calculating the pointing error of the large reflector antenna due to the track unevenness is characterized in that in Step6, the method for calculating the pointing error of the antenna is as follows:
(61) for a point P in space, the coordinate transformation matrix from the geodetic coordinate system to the azimuth coordinate system is
Wherein A is the azimuth angle of the antenna;
(62) the coordinate transformation matrix from the azimuth frame coordinate system to the pitch axis coordinate system is
Wherein: e is an antenna pitch angle;a translation conversion matrix from the origin of the azimuth coordinate system to the origin of the pitch axis coordinate system;
(63) the coordinate transformation matrix from the pitch axis coordinate system to the reflector coordinate system is
Wherein:a translation conversion matrix from the origin of the pitch axis coordinate system to the origin of the reflector coordinate system;
(64) orientation coordinate system disturbance matrix caused by track unevenness:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(65) the coordinate transformation after considering the track unevenness is shown as follows:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(66) the pointing error amount caused by the track unevenness in the reflector coordinate system is as follows:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(67) the pointing error in the reflector coordinate system is converted into the azimuth and pitch deviation in the geodetic coordinate system, and the antenna pointing error caused by the track unevenness is as follows:
wherein, α ═ △ xr(e) antenna azimuth error, β ═ △ yrIs the antenna pitch angle error.
The invention has the advantages that:
(1) the method can accurately describe the macroscopic contour of the unevenness of the track, can embody the microscopic morphology of the track, and more truly reflects the error condition of the actual track;
(2) the influence of the track unevenness on the antenna pointing accuracy error is quantitatively given through the accurate calculation of the track unevenness, theoretical guidance can be provided for antenna design work, and the method has a high practical application value.
Drawings
FIG. 1 is a general flow chart of a method for calculating pointing error of a large reflector antenna according to the present invention;
FIG. 2 is a comparison graph of the fit residuals of the measured topography of the rail asperities and the Fourier function of the present invention;
FIG. 3(a) is a comparison of measured topography of the rail asperities of the present invention with modeled values of the asperities;
FIG. 3(b) is a plot of the fit error between the measured topography of the rail asperities of FIG. 3(a) and the modeled values of the asperities;
FIG. 4 is a schematic illustration of the azimuth frame inclination caused by track unevenness in the present invention;
FIG. 5(a) is an original geometry of the azimuth mount of the present invention;
FIG. 5(b) is a schematic view of the effect of track unevenness on the orientation frame (torsion) in the present invention;
FIG. 6 is an antenna pointing azimuth error in the present invention that accounts for track irregularity effects;
fig. 7 is an antenna pointing pitch angle error in the present invention taking into account the effects of track unevenness.
Detailed Description
The calculation method of the pointing error of the large reflector antenna considers the influence of the track unevenness, is suitable for analyzing the influence mechanism of the structural error factor of the large antenna with higher requirement on the surface precision on the electrical performance index, and can be widely applied to the fields of error analysis of various large electronic equipment and the like.
The invention is described in detail below with reference to the figures and the embodiments.
Referring to fig. 1, the method for calculating pointing errors of a large reflector antenna affected by track unevenness of the present invention includes the following steps:
first, measuring the unevenness of the track
And measuring the unevenness of the track by using an inclinometer to obtain test data of the surface unevenness. The specific measurement process is as follows:
(11) an inclinometer is arranged on the four groups of roller devices at the bottom of the azimuth frame;
(12) a steel sheet is filled under a group of rollers, and when the rollers of the azimuth frame pass by, the corresponding inclinometer can be inclined;
(13) when the azimuth frame rotates at a constant speed, the azimuth frame is zoomed according to the proportion between the thickness of the steel sheet and the reading of the inclinometer, the relation between the reading of the inclinometer and the track unevenness value can be obtained, and further the track unevenness data f is obtained0(x)。
Second, applying Fourier function and fractal function to establish orbit unevenness mathematical model
The method comprises the steps of firstly, modeling track unevenness test data by using a Fourier function to obtain a large-scale error model, comparing the large-scale error model with the test data, then modeling fitting residual errors of the Fourier function by using a fractal function, and finally obtaining a track unevenness mathematical model. The specific modeling process is as follows:
(21) modeling the track unevenness wheel data obtained in the step (13) by using a Fourier function to obtain a large-scale error model, wherein the mathematical formula of the Fourier function is as follows:
wherein, ansin(nωx)＝Ansin(nωx)cos(θn)，bncos(nωt)＝Ancos(nωt)sin(θn) X denotes the track position, ω is the fundamental frequency, n denotes the sine function sin (n ω x + θ) over the sample lengthn) The repeated occurrence times of the waveform, m is Fourier series expansion order, the value range of m is [1, N/2 ], N is the number of sampling points in the track sampling length, and m is a positive integer.
(22) The large scale error model is compared with the test data and the fractal function is used to compare f shown in FIG. 21(x) And f0(x) The fitting residual of (a) is modeled, and the mathematical formula of the fractal function is as follows:
where A is the fractal function amplitude coefficient, reflecting f2(x) N is the number of sampling points of the fractal function, D is the fractal dimension of the fractal function, and gamma is the fundamental frequency of the fractal function, and the value is 1.5;
(23) the mathematical model for establishing the track unevenness is as follows:
f(x)＝f1(x)+f2(x) (3)。
third, correcting the unevenness mathematical model
And comparing the track unevenness mathematical model with the test data, if the unevenness mathematical model meets the precision requirement, directly jumping to the fourth step, and if the unevenness mathematical model does not meet the precision requirement, correcting the unevenness mathematical model to enable the unevenness mathematical model to meet the precision requirement.
The specific process of comparing and correcting the unevenness mathematical model comprises the following steps:
(31) according to f obtained in step (13)0(x) Calculating the root mean square RMS of the track unevenness test data;
(32) calculating a root mean square value RMS' of the orbit irregularity mathematical model according to f (x) obtained in the step (23);
(33) if it is not(epsilon is 30%), considering that the established track unevenness mathematical model meets the precision requirement, jumping to the fourth step, and if the precision is not met, performing Fourier function f1(x) The expansion order number m of (1) is increased to m +1, and the fractal function f is obtained2(x) The number n of the sampling points is increased to n +10, and the process jumps to the second step and loops until the requirement is met.
Fourthly, calculating the inclination error of the azimuth post
And calculating the inclination error of the azimuth frame under the influence of the unevenness of the track. The specific process is as follows:
(41) establishing four coordinate systems of OXXYZ and OaXaYaZa、OeXeYeZeAnd OrXrYrZrWherein
(a) the OXYZ is a geodetic coordinate system, the origin of the coordinate system is at the center of an azimuth orbit, the Z axis is vertical to the ground, and the negative direction of the Y axis points to the positive north direction;
(b)OaXaYaZais an azimuth axis coordinate system with the origin at the center of the azimuth orbit, ZaThe axis is coincided with the azimuth axis, the integral coordinate system rotates and deflects along with the azimuth axis to move, and when the antenna has no azimuth axis error and the azimuth angle A is 0 degrees, the antenna is coincided with the geodetic coordinate system OXYZ;
(c)OeXeYeZeis a pitch axis coordinate system with the origin at the midpoint of the pitch axis, XeThe axis is coincident with the pitch axis, the integral coordinate system moves along with the rotation and deflection of the pitch axis, and when the antenna has no shafting error, the pitch angle E is 90 degrees, and the azimuth angle A is 0 degrees, the integral coordinate system and the geodetic coordinate system OXYZ only have a difference of the height value h of the azimuth axis in the Z direction;
(d)OrXrYrZris reflector coordinate system, and when the pitch angle E is 90 deg., it is matched with pitch axis coordinate system OeXeYeZeBy a height h in the Z direction1。
Four rollers of the azimuth frame are located in an azimuth axis coordinate system OaXaYaZaWherein the first roller, the second roller, the third roller and the fourth roller have heights of
When there is rail unevenness, the unevenness causes inclination and twisting of the azimuth post, as shown in fig. 4.
(42) A small difference in height between the first roller (at position 1) and the third roller (at position 3) will cause the azimuth axis to rotate about the X and Y axes by △ X1、△y1The expression formula of the two is as follows:
(43) a small difference in height between the second roller (at position 2) and the fourth roller (at position 4) will also cause the azimuth axis to rotate about the X and Y axes by △ X2、△y2The expression formula of the two is as follows:
(44) the four rollers act together to make the pitching axis rotate around X according to the right hand ruleaRotation of the shaftAround YaRotation of the shaft
Fifthly, calculating the azimuth error of the azimuth frame
And calculating the azimuth error of the azimuth frame considering the unevenness of the track. The specific process is as follows:
(51) the unevenness of the wheel track can cause the stress deformation of the azimuth frame, cause the self torsion of the azimuth frame and cause the pitch axis to rotate around the ZaThe axes are rotated, as shown in fig. 5(a) and 5(b), the first and second rollers on the track cause the upper pitch axis end point to translate by δ12The translation amount of the upper pitch axis end point caused by the third roller and the fourth roller on the track is delta34，
Wherein h is the height from the pitching axis to the ground;
(52) the four points act together to make the pitch axis around ZaRotation of the shaft Indicating orientation due to track unevennessesThe rotation amount of the coordinate system around the Z axis, the length l of the pitching axis and r are the track radius, then:
wherein,
therefore, the azimuth error phi of the azimuth axistx、φtyAnd phitzThe following formulas are respectively adopted:
sixthly, calculating the pointing error of the antenna
And calculating the antenna pointing error under the influence of track unevenness by using coordinate conversion. The specific process is as follows:
(61) for a point P in space, the coordinate transformation matrix from the geodetic coordinate system to the azimuth coordinate system is
Wherein A is the azimuth angle of the antenna;
(62) the coordinate transformation matrix from the azimuth frame coordinate system to the pitch axis coordinate system is
Wherein: e is an antenna pitch angle;a translation conversion matrix from the origin of the azimuth coordinate system to the origin of the pitch axis coordinate system;
(63) the coordinate transformation matrix from the pitch axis coordinate system to the reflector coordinate system is
Wherein:a translation conversion matrix from the origin of the pitch axis coordinate system to the origin of the reflector coordinate system;
(64) orientation coordinate system disturbance matrix caused by track unevenness:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(65) the coordinate transformation after considering the track unevenness is shown as follows:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(66) the pointing error amount caused by the track unevenness in the reflector coordinate system is as follows:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(67) the pointing error in the reflector coordinate system is converted into the azimuth and pitch deviation in the geodetic coordinate system, and the antenna pointing error caused by the track unevenness is as follows:
wherein, α ═ △ xr(e) antenna azimuth error, β ═ △ yrIs the antenna pitch angle error.
The advantages of the calculation method of the present invention can be further illustrated by the following simulation experiments.
1. Simulation conditions
A high-precision large-scale wheel-track type radio telescope has 64m track diameter and 48 tracks, the total length of the telescope is about 201 m, and the unevenness RMS0For 0.05286mm, the track adopts the double-deck composite construction that base plate and antifriction plate combine, and the base plate adopts U type groove welding, and the antifriction plate passes through the bolt lock joint with the base plate, and the track adopts high accuracy inclinometer to measure the track surface height value.
2. Simulation result
The track unevenness effect is described by adopting the Fourier series and the fractal function provided by the invention as shown in fig. 3(a) and fig. 3(b), the final description error is that the root mean square value is 0.0107, the Fourier series expansion order m is 18, and the fractal function fitting length l is 60 cm.
The antenna pointing error obtained by the antenna pointing error calculation method provided by the invention is shown in fig. 6 and 7, and the specific numerical value is shown in table 1.
TABLE 1 antenna pointing error taking into account track unevenness
| Index (I) | α | β | △PE |
| Root mean square (second angle) | 0.5218 | 0.2407 | 0.5746 |
| Peak peak value (second angle) | 3.012 | 1.601 | 3.547 |
Wherein α is △ xr(e) antenna azimuth error, β ═ △ yrIn order to account for the antenna pitch angle error,the peak-to-peak value is the difference between the maximum peak value and the minimum peak value.
Simulation results show that: the method is adopted to describe the unevenness of the antenna track, the range of the description error amplitude is controlled to be +/-0.02 mm, the range is reduced by one order of magnitude relative to the track unevenness measured value, the rough appearance of the surface of the track is effectively embodied, and the pointing error of the antenna can be accurately calculated.
In conclusion, by adopting the method of the invention, the antenna pointing error which is influenced by the track unevenness can be accurately calculated, and a foundation is laid for the vibration research of the antenna wheel-track contact.
The method can be used for calculating the antenna pointing error and analyzing the unevenness influence of the annular track of the high-precision annular crane, and has good popularization and application values.
It should be noted that the above-mentioned embodiments do not limit the present invention in any way, and all technical solutions obtained by using equivalent alternatives or equivalent variations fall within the protection scope of the present invention.
Claims (5)
1. The method for calculating the pointing error of the large reflector antenna considering the influence of track unevenness is characterized by comprising the following steps of:
step 1: measuring the unevenness of the track to obtain test data of the surface unevenness;
the method for measuring the unevenness of the track comprises the following steps:
(11) an inclinometer is arranged on the four groups of roller devices at the bottom of the azimuth frame;
(12) filling a steel sheet under a group of rollers;
(13) when in positionWhen the frame rotates at a constant speed, the scale is reduced according to the proportion between the thickness of the steel sheet and the reading of the inclinometer, so that the relation between the reading of the inclinometer and the track unevenness value can be obtained, and further the track unevenness data f can be obtained0(x)；
Step 2: firstly, modeling track unevenness test data by using a Fourier function to obtain a large-scale error model, comparing the large-scale error model with the test data, and then modeling a fitting residual error of the Fourier function by using a fractal function to obtain a track unevenness mathematical model, wherein the method comprises the following specific steps:
(21) modeling the track unevenness wheel data obtained in the step (13) by using a Fourier function, wherein the mathematical formula of the Fourier function is as follows:
wherein, ansin(nωx)＝Ansin(nωx)cos(θn)，bncos(nωt)＝Ancos(nωt)sin(θn) X denotes the track position, ω is the fundamental frequency, n denotes the sine function sin (n ω x + θ) over the sample lengthn) The repeated occurrence times of the waveform, m is Fourier series expansion order, the value range of m is [1, N/2 ], N is the number of sampling points in the track sampling length, and m is a positive integer;
(22) using fractal function pairs f1(x) And f0(x) The fitting residual of (a) is modeled, and the mathematical formula of the fractal function is as follows:
where A is the fractal function amplitude coefficient, reflecting f2(x) N is the number of sampling points of the fractal function, D is the fractal dimension of the fractal function, and gamma is the fundamental frequency of the fractal function, and the value is 1.5;
(23) the mathematical model for establishing the track unevenness is as follows:
f(x)＝f1(x)+f2(x) (3)；
step 3: comparing the track unevenness mathematical model with the test data, if the unevenness mathematical model meets the precision requirement, directly jumping to Step4, and if the unevenness mathematical model does not meet the precision requirement, correcting the unevenness mathematical model to enable the unevenness mathematical model to meet the precision requirement;
step 4: calculating the inclination error of the azimuth frame under the influence of the unevenness of the track;
step 5: calculating the torsion error of the azimuth frame under the influence of the unevenness of the track;
step 6: and calculating the antenna pointing error under the influence of track unevenness by using coordinate conversion.
2. The method of claim 1, wherein the mathematical model of the unevenness is compared and corrected in Step3 as follows:
(31) according to f obtained in step (13)0(x) Calculating the root mean square RMS of the track unevenness test data;
(32) calculating a root mean square value RMS' of the orbit irregularity mathematical model according to f (x) obtained in the step (23);
(33) if it is notIf epsilon is 30%, the established track unevenness mathematical model is considered to meet the precision requirement, the Step is carried out to Step4, and if the precision is not met, the Fourier function f is carried out1(x) The expansion order number m of (1) is increased to m +1, and the fractal function f is obtained2(x) The number n of sampling points is increased to n +10, and the Step2 is skipped, and the loop is continued until the precision requirement is met.
3. The method of claim 2, wherein the method of calculating the azimuth tilt error in Step4 comprises:
(41) establishing four coordinate systems of OXXYZ and OaXaYaZa、OeXeYeZeAnd OrXrYrZrWherein, OXYZ is a geodetic coordinate system, the origin point is at the center of an azimuth orbit, the Z axis is vertical to the ground, and the negative direction of the Y axis points to the positive north direction; o isaXaYaZaIs an azimuth axis coordinate system with the origin at the center of the azimuth orbit, ZaThe axis is coincided with the azimuth axis, the integral coordinate system rotates and deflects along with the azimuth axis to move, and when the antenna has no azimuth axis error and the azimuth angle A is 0 degrees, the antenna is coincided with the geodetic coordinate system OXYZ; o iseXeYeZeIs a pitch axis coordinate system with the origin at the midpoint of the pitch axis, XeThe axis is coincident with the pitch axis, the integral coordinate system moves along with the rotation and deflection of the pitch axis, and when the antenna has no shafting error, the pitch angle E is 90 degrees, and the azimuth angle A is 0 degrees, the integral coordinate system and the geodetic coordinate system OXYZ only have a difference of the height value h of the azimuth axis in the Z direction; o isrXrYrZrIs reflector coordinate system, and when the pitch angle E is 90 deg., it is matched with pitch axis coordinate system OeXeYeZeBy a height h in the Z direction1(ii) a Four rollers of the azimuth frame are located in an azimuth axis coordinate system OaXaYaZaWherein the first roller, the second roller, the third roller and the fourth roller have heights of
(42) A small difference in height between the first roller and the third roller will cause the azimuth axis to rotate about the X and Y axes by △ ×, respectively1、△y1：
(43) A small difference in height between the second and fourth rollers will also cause the azimuth axis to rotate about the X and Y axes by △ ×, respectively2、△y2：
(44) The four rollers act together to make the pitching axis rotate around X according to the right hand ruleaRotation of the shaftAround YaRotation of the shaft
4. The method of claim 3, wherein the azimuth frame torsion error φ is calculated in Step5tx、φtyAnd phitzThe following formulas are respectively adopted:
5. the method for calculating the pointing error of the large reflector antenna considering the influence of the track unevenness as claimed in claim 4, wherein in Step6, the method for calculating the pointing error of the antenna comprises:
(61) for a point P in space, the coordinate transformation matrix from the geodetic coordinate system to the azimuth coordinate system is
Wherein A is the azimuth angle of the antenna;
(62) the coordinate transformation matrix from the azimuth frame coordinate system to the pitch axis coordinate system is
Wherein: e is an antenna pitch angle;a translation conversion matrix from the origin of the azimuth coordinate system to the origin of the pitch axis coordinate system;
(63) the coordinate transformation matrix from the pitch axis coordinate system to the reflector coordinate system is
Wherein:a translation conversion matrix from the origin of the pitch axis coordinate system to the origin of the reflector coordinate system;
(64) orientation coordinate system disturbance matrix caused by track unevenness:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(65) the coordinate transformation after considering the track unevenness is shown as follows:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(66) the pointing error amount caused by the track unevenness in the reflector coordinate system is as follows:
wherein E is the antenna pitch angle, phitx，φty，φtzError amount of the coordinate system of the azimuth frame caused by uneven wheel track;
(67) the pointing error in the reflector coordinate system is converted into the azimuth and pitch deviation in the geodetic coordinate system, and the antenna pointing error caused by the track unevenness is as follows:
wherein, α ═ △ xr(e) antenna azimuth error, β ═ △ yrIs the antenna pitch angle error.
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