CN116659549B - Method for detecting verticality and intersection of three-axis turntable based on laser tracking interferometer - Google Patents
Method for detecting verticality and intersection of three-axis turntable based on laser tracking interferometer Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
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Abstract
The invention discloses a method for detecting verticality and intersection of a three-axis turntable based on a laser tracking interferometer, which comprises the following steps: firstly, three measuring stations formed by three laser tracking interferometers are self-calibrated, then a three-axis turntable is leveled, a target ball seat is sequentially arranged on a rotary working surface of a turntable shaft system, the laser tracking interferometer target ball is led to the target ball seat, finally, the perpendicularity phi is calculated through the number product relation between the direction vectors of the two shaft systems, and the intersection degree d is calculated through establishing a public plumb line equation of the two shaft systems. The invention has the advantages of high detection precision, wide application range, simple installation and debugging, easy realization of dynamic detection and capability of being used for monitoring the verticality and intersection degree change condition of the shaft system in the whole running process of the turntable.
Description
Technical Field
The invention relates to the field of detection of the verticality and the intersection of an axis of a triaxial rotary table, in particular to a method for detecting the verticality and the intersection of the triaxial rotary table of a laser tracking interferometer.
Background
The three-axis turntable is used as a space angle generating device to play an important role in key links in the fields of navigation positioning, robot gesture control, measurement and calibration of an inertial sensor and the like; the verticality and the intersection degree are important parameters for the precision design of the three-axis turntable, and the measurement of the verticality and the intersection degree is carried out separately by the current detection method; the verticality detection method comprises a photoelectric auto-collimator method, an electronic level meter method, a vision measurement method, a three-coordinate measuring machine method and a laser gyro strapdown inertial navigation method; the intersection degree detection method comprises five methods of shaft end binocular calibration, laser tracker calibration, surface beating, filament method and vision measurement.
The method for simultaneously obtaining the verticality and the intersection degree through one-time measurement only comprises a three-coordinate measuring machine method and a visual measuring method, wherein the measurement accuracy of the visual measuring method is limited by the calibration error and the resolution of a CCD camera, and the detection accuracy is moderate; the three-coordinate measuring machine method has high measuring precision, but is limited by the size of the three-coordinate measuring machine method, and only a small turntable can be measured.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for detecting the verticality and the intersection of a three-axis turntable of a laser tracking interferometer, which can simultaneously solve the problems of small measuring range and low measuring precision; the method is characterized in that a target ball is directly arranged on a rotary working surface of a rotary table, a plane parameter equation is obtained through space track coordinate fitting of the target ball, the plane is parallel to the rotary working surface of the rotary table, the normal vector direction of the plane coincides with an average rotary axis, the circle center is a point on the average rotary axis, a linear equation of each axis of the three-axis rotary table can be obtained by combining the two points, the perpendicularity phi is calculated through the number product relation between the direction vectors of the two axes, and the intersection degree d is solved through establishing a common vertical line equation of the two axes.
The invention is realized by the following technical scheme:
step 1: setting up a three-axis turntable verticality and intersection degree measurement system based on a laser tracking interferometer, carrying out self-calibration of three laser tracking interferometers, integrating coordinate systems of all measuring stations under a measurement coordinate system, and determining that coordinates of three measuring stations under the measurement coordinate system are P respectively A (x A ,y A ,z A )，P B (x B ,y B ,z B ) And P C (x C ,y C ,z C ) The method comprises the steps of carrying out a first treatment on the surface of the The measuring system comprises three laser tracking interferometers, a target ball seat and a measured three-axis turntable;
step 2: leveling the three-axis turntable to enable the outer frame shaft and the inner frame shaft to be plumb, enabling the middle frame shaft to be horizontal, sequentially installing target balls on the detected shaft, and measuring the distance s between the same target ball and each measuring station in real time by three measuring stations in the sequential rotation process of the detected shaft of the three-axis turntable AP_i 、s BP_i Sum s CP_i The method comprises the steps of carrying out a first treatment on the surface of the According to the principle of space distance intersection positioning, the space track coordinate P of the target ball i (x i ,y i ,z i ) The solution formula of (i=1, 2,3, … …, n) is as follows:
wherein the space track coordinate P of the target ball in the process of moving the inner frame shaft in_i (x i ,y i ,z i ) (i=1, 2,3, … …, n), spatial trajectory coordinate P of target ball during middle frame axis motion mid_i (x i ,y i ,z i ) (i=1, 2,3, … …, n), spatial trajectory coordinate P of target ball during the movement of outer frame axis out_i (x i ,y i ,z i )(i＝1,2,3,……,n)；
Step 3: establishing a space plane parameter equation ax+by+cz-1=0 of the track of the target ball, and setting the space track coordinate P of the target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n) is substituted into the plane equation to obtain an overdetermined equation set as follows:
MX＝S (14)
wherein the parameters are expanded as follows:
the direction coefficient X of the plane normal vector is obtained by solving the least square method as follows:
X＝(M T M) -1 M T S (16)
further, determining a plane parameter equation ax+by+cz-1=0 of the target ball track, wherein the target ball is directly arranged on the shafting rotary working surface through the target ball seat, so that the fitting plane of the target ball track is parallel to the shafting rotary working surface, and the normal vector of the fitting plane points to coincide with the average rotary axis;
step 4: establishing a space track coordinate P of a target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n), the constraint between the planar parameter equation of the target ball trajectory ax+by+cz-1=0 and the center of the target ball trajectory P0 (x 0, y0, z 0):
(1) Space track coordinates P of any two target balls on target ball track i (x i ,y i ,z i ) (i=1, 2,3, … …, n) and P j (x j ,y j ,z j ) The perpendicular bisectors of (j=1, 2,3, … …, n) necessarily pass through the center P 0 (x 0 ,y 0 ,z 0 ) And is connected withIntersecting at the midpoint->i and j are only used as serial numbers to distinguish the sequence of coordinate points, the represented physical meanings are the same, and the perpendicular bisectors are mutually perpendicular to line segments connecting two coordinate points, namely:
thereby establishing k linear independent sagging plane equations and bringing the sagging plane equations into the space track coordinates P of the target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n), the resulting error equation is as follows:
wherein the parameters are expanded as follows:
the error equation is abbreviated as follows:
v＝B×C-s (20)
(2) Will center of circle P 0 (x 0 ,y 0 ,z 0 ) The constraint is within the fitting plane ax+by+cz-1=0, namely:
X T ×C＝1 (21)
based on the constraint conditions, an optimization problem is constructed, and the relation is as follows:
f(C)＝||BC-s|| 2 +K s (X T C-1) (22)
wherein K is S Represents the Lagrangian multiplier for f (C) with respect to C and K S The derivative is calculated, and the derivative value is set to be 0, and the following relation is obtained:
obtain the center of circle P 0 The least squares solution of (2) is as follows:
and then calculate the linear equation of the corresponding axisWherein the inner frame axis l in Center axis l mid And an inner frame axis l out The linear equation of (2) is as follows:
in the inner frame axis l in Direction vector of (a)And a point P on the axis in Are respectively->P in ＝(x in ,y in ,z in ) The method comprises the steps of carrying out a first treatment on the surface of the Center axis l mid Is>And a point P on the axis mid Respectively areP mid ＝(x mid ,y mid ,z mid ) The method comprises the steps of carrying out a first treatment on the surface of the Outer frame axis l out Is>And a point P on the axis out ，/>P out ＝(x out ,y out ,z out ) One point on the axis is the center of the circle P 0 (x 0 ,y 0 ,z 0 )；
Step 5: combining the linear equations of the axes of the three-axis turntable in pairs, wherein the two axes are respectively l v And l h The representation is made of a combination of a first and a second color,is the axis l v Direction vector of>Is the axis l h The perpendicularity of the two can be calculated by the following formula:
based on which a mid-frame axis l can be obtained mid And the outer frame axis l out Is phi of the perpendicularity of (2) mid_out Middle frame shaft l mid And an inner frame shaft l in Is phi of the perpendicularity of (2) mid_in ；
Step 6: the straight line equations of the axes of the three-axis rotary table are set up into a common vertical line equation, the intersection degree d between the two axes can be directly calculated, and the two axes are respectively l v And l h Represented by O v0 (x vo ,y vo ,z vo ) Is the axis l v At a point on the upper surface of the plate,is the axis l v Direction vector of (2), O h0 (x ho ,y ho ,z ho ) Is the axis l h One point above->Is the axis l h Through axis l v And l h Plane A and plane B are respectively made, the common line segment and direction vector of plane A and plane B +.>Parallel and respectively perpendicular to axis l v And l h With axis l v Intersecting at O 1 Point and axis l h Intersecting at O 2 Point, intersection degree d of two axes is line segment O 1 O 2 Length of (2) intersection direction vector +.>Can pass through the axis l v And l h Is obtained by the product of the vectors:
degree of intersection d isIn vector->Upper projection, namely:
based on which a mid-frame axis l can be obtained mid And the outer frame axis l out Degree of intersection d of (2) mid_out Middle frame shaft l mid And an inner frame shaft l in Is d of the perpendicularity of (2) mid_in The axis l of the outer frame out And an inner frame axis l in Degree of intersection d of (2) out_in 。
Has the positive beneficial effects that:
1. the measuring system is simple, the installation and the debugging are simple and convenient, the target ball is installed without coaxiality requirement and is directly installed on the rotating working surface of the shafting, the application range is wide, no special requirement is required for the turntable to be measured, and the in-situ calibration is convenient to realize; 2. the measurement principle is simple, the measurement precision is high, the uncertainty U=0.2 μm+0.3 μm/m of the distance measurement, and two parameters of verticality and intersection degree can be obtained at the same time through one-time detection; 3. the dynamic measurement is easy to realize, and the perpendicularity and intersection degree change condition in the shafting operation process are observed in real time.
Drawings
FIG. 1 is a schematic diagram of a detection apparatus according to the present invention.
FIG. 2 is a schematic view of a specific installation position of a target ball when measuring an axis in the present invention.
Fig. 3 is a schematic diagram of the principle of the axis intersection resolution in the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The method for detecting the verticality and the intersection degree of the three-axis turntable based on the laser tracking interferometer comprises the following steps:
step 1: the schematic diagram of the system for measuring verticality and intersection based on the laser tracking interferometers is shown in fig. 1, and the system comprises a measuring station A, B, C and a target ball P, which are formed by three laser tracking interferometers, the three measuring stations are self-calibrated, the coordinate system of each measuring station is integrated under the measuring coordinate system, and the coordinates of the three measuring stations under the measuring coordinate system are respectively defined as P A (x A ,y A ,z A )，P B (x B ,y B ,z B ) And P C (x C ,y C ,z C )；
Step 2: leveling the three-axis turntable to enable the outer frame shaft and the inner frame shaft to be plumb, enabling the middle frame shaft to be horizontal, sequentially installing the target ball P on the detected shaft, and measuring the distance s between the same target ball and each measuring station in real time by three measuring stations in the sequential rotation process of the detected shaft of the three-axis turntable AP_i 、s BP_i Sum s CP_i The method comprises the steps of carrying out a first treatment on the surface of the According to the principle of space distance intersection positioning, the space track coordinate P of the target ball i (x i ,y i ,z i ) The solution formula of (i=1, 2,3, … …, n) is as follows:
the installation position of the target ball P is shown in figure 2, the target ball P is installed in the target ball seat 2 on the outer frame shaft 1, and the space track coordinate P of the target ball in the movement process of the outer frame shaft out_i (x i ,y i ,z i ) (i=1, 2,3, … …, n); the target ball P is arranged in the target ball seat 4 on the middle frame shaft 3, and the space track coordinate P of the target ball during the movement process of the middle frame shaft mid_i (x i ,y i ,z i ) (i=1, 2,3, … …, n); the target ball P is arranged in the target ball seat 6 on the inner frame shaft 5, and the space track coordinate P of the target ball during the movement of the inner frame shaft in_i (x i ,y i ,z i )(i＝1,2,3,……,n)；
Step 3: establishing a space plane parameter equation ax+by+cz-1=0 of the track of the target ball, and setting the space track coordinate P of the target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n) is substituted into the plane equation to obtain an overdetermined equation set as follows:
MX＝S (30)
wherein the parameters are expanded as follows:
the direction coefficient X of the plane normal vector is obtained by solving the least square method as follows:
X＝(M T M) -1 M T S (32)
further, determining a plane parameter equation ax+by+cz-1=0 of the target ball track, wherein the target ball is directly arranged on the shafting rotary working surface through the target ball seat, so that the fitting plane of the target ball track is parallel to the shafting rotary working surface, and the normal vector of the fitting plane points to coincide with the average rotary axis;
step 4: establishing a space track coordinate P of a target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n), the plane parameter equation of the target ball trajectory ax+by+cz-1=0 and the center P of the target ball trajectory 0 (x 0 ,y 0 ,z 0 ) Constraint conditions between:
(1) Space track coordinates P of any two target balls on target ball track i (x i ,y i ,z i ) (i=1, 2,3, … …, n) and P j (x j ,y j ,z j ) The perpendicular bisectors of (j=1, 2,3, … …, n) necessarily pass through the center P 0 (x 0 ,y 0 ,z 0 ) And is connected withIntersecting at the midpoint->i and j are only used as serial numbers to distinguish the sequence of coordinate points, the represented physical meanings are the same, and the perpendicular bisectors are mutually perpendicular to line segments connecting two coordinate points, namely:
thereby establishing k linear independent sagging plane equations and bringing the sagging plane equations into the space track coordinates P of the target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n), the resulting error equation is as follows:
wherein the parameters are expanded as follows:
the error equation is abbreviated as follows:
v＝B×C-s (36)
(2) Will center of circle P 0 (x 0 ,y 0 ,z 0 ) The constraint is within the fitting plane ax+by+cz-1=0, namely:
X T ×C＝1 (37)
based on the constraint conditions, an optimization problem is constructed, and the relation is as follows:
f(C)＝||BC-s|| 2 +K s (X T C-1) (38)
wherein K is S Represents the Lagrangian multiplier for f (C) with respect to C and K S The derivative is calculated, and the derivative value is set to be 0, and the following relation is obtained:
obtain the center of circle P 0 The least squares solution of (2) is as follows:
and then calculate the linear equation of the corresponding axisWherein the inner frame axis l in Center axis l mid And an inner frame axis l out The linear equation of (2) is as follows:
in the inner frame axis l in Direction vector of (a)And a point P on the axis in Are respectively->Pin= (xin, yin, zin); center axis l mid Is>And a point P on the axis mid Respectively arePmid= (xmid, ymid, zmid); outer frame axis l out Is>And a point P on the axis out ，/>Pout= (xout, yout, zout), one point on the axis is the center P 0 (x 0 ,y 0 ,z 0 )；
Step 5: combining the linear equations of the axes of the three-axis turntable in pairs, wherein the two axes are respectively l v And l h The representation is made of a combination of a first and a second color,is the axis l v Direction vector of>Is the axis l h The perpendicularity of the two can be calculated by the following formula:
based on which a mid-frame axis l can be obtained mid And the outer frame axis l out Is phi of the perpendicularity of (2) mid_out Middle frame shaft l mid And an inner frame shaft l in Is phi of the perpendicularity of (2) mid_in ；
Step 6: the intersection degree d between two shaft systems can be directly calculated by establishing a common perpendicular line equation of the straight line equation of the two shaft systems, as shown in figure 3, the two shaft systems respectively use l v And l h Represented by O v0 (x vo ,y vo ,z vo ) Is the axis l v At a point on the upper surface of the plate,is the axis l v Direction vector of (2), O h0 (x ho ,y ho ,z ho ) Is the axis l h At a point on the upper surface of the plate,is the axis l h Through axis l v And l h Plane A and plane B are respectively made, the common line segment and direction vector of plane A and plane B +.>Parallel and respectively perpendicular to axis l v And l h With axis l v Intersecting at O 1 Point and axis l h Intersecting at O 2 Point, intersection degree d of two axes is line segment O 1 O 2 Length of (2) intersection direction vector +.>Can pass through the axis l v And l h Is obtained by the product of the vectors:
degree of intersection d isIn vector->Upper projection, namely:
based on which a mid-frame axis l can be obtained mid And the outer frame axis l out Degree of intersection d of (2) mid_out Middle frame shaft l mid And an inner frame shaft l in Is d of the perpendicularity of (2) mid_in The axis l of the outer frame out And an inner frame axis l in Degree of intersection d of (2) out_in 。
While specific embodiments of the present invention have been described above, it will be understood by those skilled in the art that these specific embodiments are by way of example only, and that various omissions, substitutions, and changes in the form and details of the methods and systems described above may be made by those skilled in the art without departing from the spirit and scope of the invention. For example, it is within the scope of the present invention to combine the above-described method steps to perform substantially the same function in substantially the same way to achieve substantially the same result. Accordingly, the scope of the invention is limited only by the following claims.
Claims (8)
1. The method for detecting the verticality and the intersection degree of the three-axis turntable based on the laser tracking interferometer is characterized by comprising the following steps of:
step 1: setting up a three-axis turntable verticality and intersection degree measurement system based on a laser tracking interferometer, carrying out self-calibration of three laser tracking interferometers, integrating coordinate systems of all measuring stations under a measurement coordinate system, and determining that coordinates of three measuring stations under the measurement coordinate system are P respectively A (x A ,y A ,z A )，P B (x B ,y B ,z B ) And P C (x C ,y C ,z C ) The method comprises the steps of carrying out a first treatment on the surface of the The measuring system comprises three laser tracking interferometers, a target ball seat and a measured three-axis turntable;
step 2: leveling the three-axis turntable to enable the outer frame shaft and the inner frame shaft to be plumb, enabling the middle frame shaft to be horizontal, sequentially installing target balls on the detected shaft, and measuring the distance s between the same target ball and each measuring station in real time by three measuring stations in the sequential rotation process of the detected shaft of the three-axis turntable AP_i 、s BP_i Sum s CP_i The method comprises the steps of carrying out a first treatment on the surface of the According to the principle of space distance intersection positioning, the space track coordinate P of the target ball is obtained by calculation i (x i ,y i ,z i )(i＝1,2,3,……,n)；
Step 3: establishing a space plane parameter equation ax+by+cz-1=0 of the track of the target ball, and setting the space track coordinate P of the target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n) is substituted into the plane equation to obtain an overdetermined equation set, and the solution is carried out by a least square methodObtaining direction coefficients (a, b, c) of a plane normal vector, and determining a plane parameter equation ax+by+cz-1=0 of a target ball track, wherein the target ball is directly arranged on a shafting rotary working surface through a target ball seat, so that a fitting plane of the target ball track is parallel to the shafting rotary working surface, and the normal vector of the fitting plane points to and coincides with an average rotary axis;
step 4: establishing a space track coordinate P of a target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n), the plane parameter equation of the target ball trajectory ax+by+cz-1=0 and the center P of the target ball trajectory 0 (x 0 ,y 0 ,z 0 ) Constraint conditions between the two to obtain a circle center P 0 The least square solution of (2) is adopted, so that the linear equation of each axis of the three-axis turntable is solved;
step 5: the straight line equations of the axes of the three-axis turntable are combined pairwise, and the perpendicularity phi of the middle frame shaft and the outer frame shaft mid_out Perpendicularity phi of the middle frame shaft and the inner frame shaft mid_in The number product relation between the direction vectors of the two shafting can be calculated;
step 6: combining the linear equations of the axes of the three-axis turntable in pairs, and the intersection degree d of the middle frame shaft and the outer frame shaft mid_out Intersection degree d of middle frame shaft and inner frame shaft mid_in Intersection degree d of outer frame shaft and inner frame shaft out_in Can be obtained by establishing a common perpendicular equation of two axes and solving the equation.
2. The method for detecting verticality and intersection of three-axis turntable based on laser tracking interferometer according to claim 1, wherein in step 2, the spatial trajectory coordinates P of the target ball i (x i ,y i ,z i ) The solution formula of (i=1, 2,3, … …, n) is as follows:
wherein the space track coordinate P of the target ball in the process of moving the inner frame shaft in_i (x i ,y i ,z i )(i＝1,2,3,……, n), the spatial trajectory coordinate P of the target ball during the motion of the middle frame shaft mid_i (x i ,y i ,z i ) (i=1, 2,3, … …, n), spatial trajectory coordinate P of target ball during the movement of outer frame axis out_i (x i ,y i ,z i )(i＝1,2,3,……,n)。
3. The method for detecting the verticality and the intersection of a three-axis turntable based on a laser tracking interferometer according to claim 1, wherein in the step 3, a direction coefficient X of a plane normal vector is obtained by solving by a least square method as follows:
X＝(M T M) -1 M T S (2)
the parameters in the formula are expanded as follows:
4. a method for detecting verticality and intersection of a three-axis table based on a laser tracking interferometer according to claim 3, wherein in step 4, the spatial trajectory coordinates P of the target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n), the plane parameter equation of the target ball trajectory ax+by+cz-1=0 and the center P of the target ball trajectory 0 (x 0 ,y 0 ,z 0 ) The constraints between include the following:
(1) Space track coordinates P of any two target balls on target ball track i (x i ,y i ,z i ) (i=1, 2,3, … …, n) and P j (x j ,y j ,z j ) The perpendicular bisectors of (j=1, 2,3, … …, n) necessarily pass through the center P 0 (x 0 ,y 0 ,z 0 ) And is connected withIntersecting at a midpointi and j are only used as serial numbers to distinguish the sequence of coordinate points, the represented physical meanings are the same, and the perpendicular bisectors are mutually perpendicular to line segments connecting two coordinate points, namely:
thereby establishing k linear independent sagging plane equations and bringing the sagging plane equations into the space track coordinates P of the target ball i (x i ,y i ,z i ) (i=1, 2,3, … …, n), the resulting error equation is as follows:
wherein the parameters are expanded as follows:
the error equation is abbreviated as follows:
v＝B×C-s (7)
(2) Will center of circle P 0 (x 0 ,y 0 ,z 0 ) The constraint is within the fitting plane ax+by+cz-1=0, namely:
X T ×C＝1 (8)
wherein X is the direction coefficient of the normal vector of the plane, C is the center of circle P 0 (x 0 ,y 0 ,z 0 ) In matrix form, i.e. c= [ x 0 y 0 z 0 ] T 。
5. The method for detecting verticality and intersection of three-axis turntable based on laser tracking interferometer as claimed in claim 4, wherein in step 4, the relation for constructing the optimization problem based on constraint condition is f (C) = ||BC-s|| 2 +K s (X T C-1), wherein K S Represents the Lagrangian multiplier for f (C) with respect to C and K S Deriving and setting the derivative value to be 0 to obtain the circle center P 0 The least squares solution of (2) is as follows:
6. the method for detecting verticality and intersection of three-axis table based on laser tracking interferometer according to claim 1, wherein in step 4, a linear equation of axis is solvedInner frame axis l in Center axis l mid And an inner frame axis l out The linear equation of (2) is as follows:
in the inner frame axis l in Direction vector of (a)And a point P on the axis in Are respectively->P in ＝(x in ,y in ,z in ) The method comprises the steps of carrying out a first treatment on the surface of the Center axis l mid Is>And a point P on the axis mid Respectively areP mid ＝(x mid ,y mid ,z mid ) The method comprises the steps of carrying out a first treatment on the surface of the Outer frame axis l out Is>And a point P on the axis out ，/>P out ＝(x out ,y out ,z out )。
7. The method for detecting verticality and intersection of a three-axis table based on a laser tracking interferometer according to claim 1, wherein in step 5, straight line equations of axes of the three-axis table are combined two by two, and two axes are respectively represented by l v And l h The representation is made of a combination of a first and a second color,is the axis l v Direction vector of>Is the axis l h The perpendicularity phi of the middle frame shaft and the outer frame shaft mid_out Perpendicularity phi of the middle frame shaft and the inner frame shaft mid_in Calculated by the following formula:
8. the method for detecting verticality and intersection of a three-axis table based on a laser tracking interferometer according to claim 1, wherein in step 6, a common vertical line equation is built by two of straight line equations of axes of the three-axis table, and two axes are respectively represented by l v And l h Represented by O v0 (x vo ,y vo ,z vo ) Is the axis l v At a point on the upper surface of the plate,is the axis l v Direction vector of (2), O h0 (x ho ,y ho ,z ho ) Is the axis l h One point above->Is the axis l h Through axis l v And l h Plane A and plane B are respectively made, the common line segment and direction vector of plane A and plane B +.>Parallel and respectively perpendicular to axis l v And l h With axis l v Intersecting at O 1 Point and axis l h Intersecting at O 2 Point, intersection degree d of two axes is line segment O 1 O 2 The length of (a), i.e. the degree of intersection d is +.>In vector->Upper projection, intersection degree d of middle frame axis and outer frame axis mid_out Intersection degree d of middle frame shaft and inner frame shaft mid_in Intersection degree d of outer frame shaft and inner frame shaft out_in Calculated by the following formula:
in the method, in the process of the invention,
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