CN104019750B - Device and method for measuring effective arm length of swing arm type contourgraph - Google Patents

Abstract

The present invention is a measuring device and method for the effective arm length of a swing-arm type profiler. The device consists of a first target ball, a second target ball, a fine-tuning mechanism, a cross arm, a cross-arm support, a counterweight, a computer, a first Angle block, cross-arm turntable, second angle block, laser tracker, workpiece turntable, mirror to be tested, contact sensor and worktable; the cross-arm rotates around the axis of the cross-arm turntable, and the ball center of the contact sensor probe 1. The center of the first target ball and the center of the second target ball form an arc trajectory that rotates around the axis of the cross-arm turntable in space, and the laser tracker tracks and measures the center of the first target ball and the second target ball respectively. The arc trajectory formed by the center of the sphere in space, through the data processing of the computer, the distance from the sphere center of the touch sensor probe to the axis line of the cross-arm turntable is obtained, that is, the effective arm length of the swing-arm profiler.

Description

Device and method for measuring effective arm length of swing arm profiler

technical field

The invention belongs to the field of precise measurement of geometric quantities, relates to a measuring device and method for the effective arm length of a swing-arm profiler, and is suitable for measuring the effective arm length of a swing-arm profiler.

Background technique

The effective arm length of the swing arm profiler refers to the vertical distance from the sphere center of the probe head of the contact sensor to the axis line of the cross arm turntable.

The swing arm profiler is an effective in-situ inspection instrument for optical mirror processing. Its biggest feature is that it is directly installed next to the optical mirror to be tested, and the turntable of the optical mirror processing machine tool to be tested is used as the swing arm profiler. The working turntable is used to realize in-situ inspection of the mirror surface to be tested. During the measurement process of the swing-arm profiler, the effective arm length will affect the surface shape measured by the swing-arm profiler; the effective arm length will affect the point coordinates on the surface shape, and it cannot be guaranteed under the premise that there is an error in the point coordinates Continue to accurately process the mirror surface; when using the swing-arm profiler dual-probe scanning data stitching technology to realize the error separation of the workpiece turntable, the measurement error of the effective arm length will affect the accuracy of the data stitching.

Since the effective arm length of the swing-arm profiler is a virtual geometric dimension of space, it cannot be measured by traditional geometric measurement methods. There are no relevant reports on the measurement of the effective arm length of the swing-arm profiler at home and abroad.

Contents of the invention

(1) Technical problems to be solved

In order to solve the technical problem that the effective arm length affects the point coordinates on the surface and the measurement error of the effective arm length affects the accuracy of data splicing in the prior art, the purpose of the present invention is to provide the measurement of the effective arm that can accurately measure the swing arm type profiler Apparatus and methods.

(2) Technical solution

The first aspect of the present invention provides a measuring device for the effective arm length of a swing-arm type profiler, the device consists of a first target ball, a second target ball, a fine-tuning mechanism, a cross arm, a cross arm support, a counterweight, Composed of computer, first angle block, cross-arm turntable, second angle block, laser tracker, workpiece turntable, mirror to be tested, contact sensor and worktable, among which: the first target ball and the second target ball are connected by magnetic adsorption On the fine-tuning mechanism; one end of the cross-arm is placed in the installation hole of the fine-tuning mechanism; one end of the cross-arm support has a through hole, and the other end of the cross-arm is placed and passes through the through-hole; the counterweight and the other end of the cross-arm Connection, used to balance the touch sensor and the cross arm, to ensure the stable rotation of the cross arm turntable; the upper end surface of the first angle block is fixedly connected with the bottom end surface of the cross arm support; the upper end surface of the cross arm turntable and the first angle The inclined end face of the block is fixedly connected; the inclined end face of the second angle block is fixedly connected with the lower end face of the cross-arm turntable; the lower end face of the second angle block is fixedly installed on the worktable; the laser tracker is placed close to the axis of the cross-arm turntable line, and ensure that the laser tracker does not interfere with the rotation of the cross-arm turntable. The bottom end of the laser tracker is placed on the worktable; the mirror surface to be measured is placed on the workpiece turntable; The outer contour of the probe is in contact with the mirror surface to be tested; the cross arm rotates around the axis of the cross arm turntable, driving the contact sensor, the first target ball and the second target ball to rotate around the axis of the cross arm turntable, and the first target The center of the ball and the center of the second target ball form an arc trajectory around the axis of the cross-arm turntable in space, and the laser tracker tracks and measures the center of the first target ball and the center of the second target ball respectively. The arc trajectory formed in space; the computer is connected to the data terminal of the laser tracker through the data acquisition line, and the arc trajectory data processing of the center of the first target ball and the center of the second target ball is obtained to obtain the swing arm profile The effective arm length of the instrument.

The second aspect of the present invention provides a method for measuring the effective arm length of a swing-arm profiler, comprising the following steps:

Step S1: Carry out coordinate translation transformation based on the known spatial position relationship of the center of the touch sensor probe, the center of the first target ball, and the center of the second target ball to obtain the first coordinate system, thereby obtaining the contact type The coordinates of the center of the measuring head of the sensor, the center of the first target ball and the center of the second target ball in the first coordinate system;

Step S2: the laser tracker measures the initial positions of the center of the first target ball and the center of the second target ball, and the data on the arc trajectory formed by the rotation of the first target ball and the second target ball around the cross-arm turntable;

Step S3: transforming the rotation and translation of the first coordinate system to the laser tracker coordinate system to obtain the coordinates of the probe sphere center of the touch sensor in the laser tracker coordinate system;

Step S4: Process the above data by computer to obtain the distance from the sphere center of the probe of the contact sensor to the axis of the cross-arm turntable, that is, the effective arm length of the swing-arm profiler.

(3) Beneficial effects

Compared with the prior art, the present invention has the following advantages: the present invention uses a laser tracker to measure the effective arm length of a swing-arm type profiler, utilizes the high-precision measurement characteristics of the laser tracker, accurately measures the effective arm length, and improves the effective arm length. The measurement accuracy of the arm length eliminates the influence of the point coordinates on the surface under the premise of the error of the effective arm length, which can ensure the continuous precise processing of the mirror surface; ensure the use of the swing arm profiler dual probe scanning data splicing technology to realize the workpiece Accuracy of turntable error separation. At the same time, this method can measure the effective arm length more conveniently and quickly, and provides a practical solution for the in-situ measurement of the swing arm profiler in the optical processing site.

Description of drawings

Fig. 1 is a schematic structural view of the device for measuring the effective arm length of a swing-arm profiler according to the present invention.

Fig. 2 is a flow chart of the method for measuring the effective arm length of a swing-arm profiler according to the present invention.

Fig. 3 is the spatial positional relationship of the center of the first target ball, the center of the second target ball and the center of the measuring head of the touch sensor.

Fig. 4 is the new first coordinate system oxyz after coordinate translation.

Fig. 5 is the scanning measurement of the center of the first target ball and the center of the second target ball by the laser tracker.

Figure 6 is a reference diagram for solving the circular surface and the center of the circle.

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be described in further detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

As shown in Figure 1, the structure of the device for measuring the effective arm length of a swing arm profiler by a laser tracker includes: a first target ball 1, a second target ball 2, a fine-tuning mechanism 3, a cross arm 4, a cross arm support 5, Counterweight 6, computer 7, first angle block 8, cross-arm turntable 9, second angle block 10, laser tracker 11, workpiece turntable 12, mirror surface to be measured 13, contact sensor 14 and worktable 15, wherein: The first target ball 1 and the second target ball 2 are connected to the fine-tuning mechanism 3 by magnetic adsorption; one end of the cross arm 4 is placed in the installation hole of the fine-tuning mechanism 3; The other end of the counterweight 6 is connected to the other end of the cross arm 4 to balance the touch sensor 14 and the cross arm 4, so as to ensure the smooth rotation of the cross arm turntable 9; the first The upper end face of the angle block 8 is fixedly connected with the bottom end face of the cross arm support 5; the upper end face of the cross arm turntable 9 is fixedly connected with the oblique end face of the first angle block 8; The end face is fixedly connected; the lower end face of the second angle block 10 is fixedly installed on the worktable 15; the laser tracker 11 is placed close to the axis line of the cross-arm turntable 9, and the laser tracker 11 cannot interfere with the cross-arm turntable 9 Rotate, the bottom surface of the laser tracker 11 is placed on the worktable 15; the mirror surface 13 to be measured is located on the workpiece turntable 12; the workpiece turntable 12 is installed on the worktable 15; one end of the contact sensor 14 is connected with the fine-tuning mechanism 3, and the contact The outer contour of the measuring head of the sensor 14 is in contact with the mirror surface 13 to be tested, and the cross arm 4 rotates around the axis of the cross arm turntable 9, driving the contact sensor 14, the first target ball 1 and the second target ball 2 around the cross arm turntable 9 At the same time, the center of the first target ball 1 and the center of the second target ball 2 form an arc trajectory in space that rotates around the axis of the cross-arm turntable 9, and the laser tracker 11 tracks and measures the first target ball respectively. The arc trajectory formed by the center of a target ball 1 and the center of a second target ball 2 in space; the computer 7 is connected with the data end of the laser tracker 11 through a data collection line to obtain and check the ball of the first target ball 1 center and the arc track data processing of the center of the second target ball 2 to obtain the effective arm length of the swing arm type profiler.

The first target ball 1 and the second target ball 2 are made of iron material, and are reflective, with a diameter of 0.5 inches, mainly reflecting the laser light from the laser tracker 10, so as to ensure that the laser tracker 10 can track and measure the first target ball 1 and the center of the second target ball 2 on the arc trajectory data formed in space.

The ranging range of the laser tracker 11 is greater than 60m, the static measurement accuracy is 5 μm/m, the dynamic measurement accuracy is 10 μm/m, and the coordinate repeatability is better than 2.5 μm/m.

The workpiece turntable 12 is a machine tool turntable on the processing site, and is used to support the mirror surface 13 to be measured.

The resolution of the touch sensor 14 is 25nm, and the measurement accuracy is 50nm.

The fine-tuning mechanism 3 can realize fine-tuning in the X-axis direction, the Y-axis direction, the Z-axis direction, the pitch direction and the yaw direction.

The cross arm 4 and the cross arm support 5 are used to connect the cross arm turntable 9 and the touch sensor 14 , and complete the rotation movement of the touch sensor 14 .

The first angle block 8 and the second angle block 10 are used to support the cross arm turntable 9 and the cross arm support 5, and keep the cross arm turntable 9 at a set inclination angle; the angle range of the first angle block 8 is 20° ~40°, the angle range of the second angle block 10 is 20°~40°.

The cross-arm turntable 9 is a high-precision air-floating turntable. The end surface runout of the cross-arm turntable 9 is 25nm, and the angular shake of the cross-arm turntable 9 is 0.02″, which is used to realize the rotary motion of the contact sensor 14.

When the measuring device for the effective arm length of the swing arm type profiler of the present invention works, the cross arm 4 rotates around the axis of the cross arm turntable 9, driving the contact sensor 14, the first target ball 1 and the second target ball 2 around the cross arm The axis line of the turntable 9 rotates, and at the same time, the center of the first target ball 1 and the center of the second target ball 2 form an arc trajectory in space that rotates around the axis line of the cross-arm turntable 9, and the laser tracker 11 tracks them respectively. Measure the arc trajectory formed by the center of the first target ball 1 and the center of the second target ball 2 in space, through the data processing of the computer, the center of the first target ball 1 and the center of the second target ball 2 The arc trajectory data processing is to obtain the center coordinates of the circular surface where the two arc trajectories are located, and use the center coordinates of the circular surface where the two arc trajectories are located to obtain the space linear equation of the two center coordinates, which is the axis line of the cross-arm turntable Equation; then use the distance equation of the space point and the space straight line to obtain the distance from the center of the stylus of the touch sensor 14 to the center line of the cross-arm turntable 9 axes, that is, the effective arm length of the swing-arm type profiler.

As shown in Figure 2, it is the measurement method of the effective arm length of the swing-arm type profiler, and the measuring method utilizes the measurement steps of the measuring device of the swing-arm type profiler effective arm length to include:

Step S1: Carry out coordinate translation transformation based on the known spatial position relationship of the center of the stylus of the touch sensor 14, the center of the first target ball 1, and the center of the second target ball 2 to obtain the first coordinate system, thereby Obtain the coordinates of the center of the stylus of the touch sensor 14, the center of the first target 1 and the center of the second target 2 in the first coordinate system;

As shown in Figure 3, the spatial position relationship of the center of the first target ball 1, the center of the second target ball 2, and the probe center of the touch sensor 14 in a certain coordinate system: the ball of the first target ball 1 The coordinates of the center are (X ₁ Y ₁ Z ₁ ), the coordinates of the center of the second target ball 2 are (X ₂ Y ₂ Z ₂ ), and the coordinates of the center of the sphere of the touch sensor 14 are (X ₃ Y ₃ Z ₃ ) . According to the coordinate translation formula, the coordinate origin of a certain coordinate system is translated to the center of the second target ball 2, and the new rectangular coordinate system obtained at this time is designated as the first coordinate system oxyz, as shown in Fig. 4 . The translation matrix from a certain coordinate system to the first coordinate system is [Δx ₁ Δy ₁ Δz ₁ ] ^T , then:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&Lambda;y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&Delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, Δx ₁ , Δy ₁ , Δz ₁ are translation matrix parameters, then: [Δx ₁ Δy ₁ Δz ₁ ] ^T ＝[-X ₂ -Y ₂ -Z ₂ ] ^T , thus the first target ball 1 can be obtained The coordinates of the center of the sphere and the center of the stylus of the touch sensor 14 in the first coordinate system are (X ₁ -X ₂ Y ₁ -Y ₂ Z ₁ -Z ₂ ), (X ₃ -X ₂ Y ₃ - Y ₂ Z ₃ -Z ₂ ).

In summary, the coordinates of the center of the first target ball 1, the center of the second target ball 2, and the center of the probe of the touch sensor 14 in the first coordinate system are (X ₁ -X ₂ Y ₁ -Y ₂ Z ₁ -Z ₂ ), (000), (X ₃ -X ₂ Y ₃ -Y ₂ Z ₃ -Z ₂ ).

Step S2: The laser tracker 11 measures the initial positions of the center of the first target ball 1 and the center of the second target ball 2, and the circle formed by the rotation of the first target ball 1 and the second target ball 2 around the cross-arm turntable 9 Data on the arc trajectory.

The first target ball 1, the second target ball 2 and the contact sensor 14 are placed in the initial position shown in Fig. The space coordinates of the initial position in the coordinate system of the tracker 11, the coordinates of the center of the first target ball 1 and the center of the second target ball 2 are (X ₁₀ Y ₁₀ Z ₁₀ ), (X ₂₀ Y ₂₀ Z ₂₀ ), respectively. Then the laser tracker 11 tracks and scans the center of the first target ball 1, the center of the second target ball 2 rotates around the center line of the horizontal arm turntable 9 axes, and the laser tracker 11 measures the center of the first target ball 1 The coordinate data on the rotation track are (X ₁₁ Y ₁₁ Z ₁₁ ), (X ₁₂ Y ₁₂ Z ₁₂ ), ..., (X _1i Y _1i Z _1i ), ..., (X _1n Y _1n Z _1n ), laser The data of the coordinates of the center of the second target ball 2 on the rotation track measured by the tracker 11 are (X ₂₁ Y ₂₁ Z ₂₁ ), (X ₂₂ Y ₂₂ Z ₂₂ ), ..., (X _2i Y _2i Z _2i ) , ..., (X _2n Y _2n Z _2n ), as shown in FIG. 5 .

Step S3: Transform the rotation and translation of the first coordinate system into the laser tracker coordinate system to obtain the coordinates of the probe sphere center of the touch sensor 14 in the laser tracker coordinate system.

The coordinates (X ₁ -X ₂ Y ₁ -Y ₂ Z ₁ - Z ₂ ), (000), (X ₃ -X ₂ Y ₃ -Y ₂ Z ₃ -Z ₂ ) are transformed into the coordinate system of the laser tracker 11, which requires a rotation and translation transformation of the coordinate system. May wish to record the rotation matrix as R and the translation matrix as PL.

Since the center of the first target ball 1 and the center of the second target ball 2 are located in the first coordinate system and the laser tracker 11 coordinate system respectively, then:

$\left\{\begin{array}{c}\begin{array}{c}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; PL</span>}\end{array}\\ \left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; PL</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

where R is the rotation matrix and PL is the translation matrix, we can get:

PL＝[X ₂₀ Y ₂₀ Z ₂₀ ] ^T (3)

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}\end{array}\right]<span\; class="notranslate">\; /</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula, "/" is the right division of the matrix.

Note that the position of the stylus center of the contact sensor 14 under the coordinate system of the laser tracker 11 is point P, and the coordinate of P is (X ₀ Y ₀ Z ₀ ), then:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; PL</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Step S4: Process the above data by computer to obtain the distance from the sphere center of the probe of the contact sensor to the axis of the cross-arm turntable, that is, the effective arm length of the swing-arm profiler.

To fit the equation of the 9-axis center line of the cross-arm turntable in the 11 coordinate system of the laser tracker, it is necessary to fit the center of the first target ball 1 and the center of the second target ball 2 in the 11 coordinate system of the laser tracker The center coordinates of the circular surface where it is located, the following is the solution process of the center coordinates of the plane where the center arc trajectory of the first target ball 1 is located, and is explained in conjunction with FIG. 6 .

O is the center of the circular surface where the arc track of the center of the first target ball 1 is located, and P ₀ , P ₁ , and P ₀₁ are points on the track. First find the equation of the plane P ₀ P ₁ O, and set AX _1i +BY _1i +CZ _1i -D=0. The plane does not pass through the origin when measuring, so D=1 can be set here. The arc trajectory of the center of the first target ball 1 is all on this plane, then:

$\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}& {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; no</span>}}& {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; no</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\end{array}\right]<span\; class="notranslate">\; *</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; A</span>}\\ \mathrm{<span\; class="notranslate">\; B</span>}\\ \mathrm{<span\; class="notranslate">\; C</span>}\end{array}\right]<span\; class="notranslate">\; -</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In the formula, A, B, and C are the parameters of the plane equation, and N is the coefficient matrix, then $N=\left[\begin{array}{ccc}{x}_{10}& Y_{10}& Z_{10}\\ x_{11}& Y_{11}& Z_{11}\\ .& .& .\\ .& .& .\\ .& .& .\\ x_{1\mathrm{no}}& Y_{1\mathrm{no}}& Z_{1\mathrm{no}}\end{array}\right],l=\left[\begin{array}{c}1\\ 1\\ .\\ .\\ .\\ 1\end{array}\right],$ can get: $\left[\begin{array}{c}A\\ B\\ C\end{array}\right]={\left(N^{T}N\right)}^{-1}{N}^{T}l.$

In Figure 6, let the coordinates of O be (x ₀ y ₀ z ₀ ), the vector $\stackrel{\&Right\; Arrow;}{P_0{P}_1}=(x_{11}-x_{10},Y_{11}-Y_{10},Z_{11}-Z_{10}),$ P ₀₁ is the midpoint of points P ₀ and P ₁ , it is easy to get $\stackrel{\&Right\; Arrow;}{{\mathrm{OP}}_{01}},$ Then there are:

Δx ₀₁ x ₀ +Δy ₀₁ y ₀ +Δz ₀₁ z ₀ -l ₀ =0(7)

In the formula, Δx ₀₁ =X ₁₁ -X ₁₀ , Δy ₀₁ =Y ₁₁ -Y ₁₀ , Δz ₀₁ =Z ₁₁ -Z ₁₀ , $l_0=\frac{(x_{11}^2+Y_{11}^2+Z_{11}^2)-(x_{10}^2+Y_{10}^2+Z_{10}^2)}{2}.$

From the center arc trajectory data of the first target ball 1 (X ₁₀ Y ₁₀ Z ₁₀ ), (X ₁₁ Y ₁₁ Z ₁₁ ), (X ₁₂ Y ₁₂ Z ₁₂ ),..., (X _1i Y _1i Z _1i ) , ..., (X _1n Y _1n Z _1n ) These (n+1) points can list n linearly independent vertical surface equations, which can be combined with (6) to get:

$\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; A</span>}& \mathrm{<span\; class="notranslate">\; B</span>}& \mathrm{<span\; class="notranslate">\; C</span>}\\ {\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; 01</span>}}& {\mathrm{<span\; class="notranslate">\; \&Delta;y</span>}}_{\mathrm{<span\; class="notranslate">\; 01</span>}}& {\mathrm{<span\; class="notranslate">\; \&Delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; 01</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; \&Delta;y</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; \&Delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; no</span>}}& {\mathrm{<span\; class="notranslate">\; \&Delta;y</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; no</span>}}& \mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; no</span>}}\end{array}\right]<span\; class="notranslate">\; *</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; l</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

In the formula, x ₀ , y ₀ , z ₀ are the coordinate parameters of point O, record W as the coefficient matrix, $W=\left[\begin{array}{ccc}A& B& C\\ {\mathrm{\&Delta;x}}_{01}& {\mathrm{\&Delta;y}}_{01}& {\mathrm{\&Delta;z}}_{01}\\ {\mathrm{\&Delta;x}}_{12}& {\mathrm{\&Delta;y}}_{12}& {\mathrm{\&Delta;z}}_{12}\\ .& .& .\\ .& .& .\\ .& .& .\\ {\mathrm{\&Delta;x}}_{(\mathrm{no}-1)\mathrm{no}}& {\mathrm{\&Delta;y}}_{(\mathrm{no}-1)\mathrm{no}}& \mathrm{\&Delta;}{z}_{(\mathrm{no}-1)\mathrm{no}}\end{array}\right],L_1=\left[\begin{array}{c}1\\ l_0\\ l_1\\ .\\ .\\ .\\ l_{(\mathrm{no}-1)}\end{array}\right],$ can get $\left[\begin{array}{c}{x}_0\\ {\mathrm{the\; y}}_0\\ z_0\end{array}\right]={\left(W^{T}W\right)}^{-1}{W}^T{L}_1.$

The processing process of the center coordinates of the circular surface where the arc track of the center of the second target ball 2 is the same as the process of processing the coordinates of the center of circle of the arc track of the first target ball 2, no more detailed introduction here, assuming Obtain the coordinates of the circle center O ₁ of the circular surface where the arc track of the center of the second target ball 2 is (x ₁ y ₁ z ₁ ), and at this time the straight line in the space where the axis center line of the cross-arm turntable 9 is OO ₁ , as shown in Figure 5 shown.

At this time, the effective arm length L refers to the vertical distance from the center of the probe sphere P of the touch sensor ₁₄ to the space line OO1 where the axis center line of the cross-arm turntable 9 is located, The equation of line OO ₁ is:

$\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

From the distance equation from a spatial point to a spatial straight line, the vertical distance from P(X ₀ Y ₀ Z ₀ ) to the straight line OO ₁ can be obtained:

$\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>\frac{<span\; class="notranslate">\; |</span>\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; i</span>}& \mathrm{<span\; class="notranslate">\; j</span>}& \mathrm{<span\; class="notranslate">\; k</span>}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}<span\; class="notranslate">\; |</span>}{\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

In the formula, i, j, k are the unit vectors of the Cartesian coordinate system.

The above is only a specific implementation mode in the present invention, but the scope of protection of the present invention is not limited thereto. Anyone familiar with the technology can understand the conceivable transformation or replacement within the technical scope disclosed in the present invention. All should be covered within the scope of the present invention.

Claims (8)

1. the measurement apparatus of a swing-arm profilometry effective rake, it is characterized in that: be made up of the first target ball, the second target ball, micro-adjusting mechanism, transverse arm, transverse arm bearing, balancing weight, computer, the first angle block gauge, transverse arm turntable, the second angle block gauge, laser tracker, workpiece rotary table, minute surface to be measured, touch sensor and work top, wherein: the first target ball, the second target ball are connected on micro-adjusting mechanism by magnetic-adsorption；One end of transverse arm is placed in the installing hole of micro-adjusting mechanism；One end of transverse arm bearing has a through hole, and the other end of transverse arm is placed in and passes through hole；Balancing weight is connected with the other end of transverse arm, for equilibrium contact formula sensor and transverse arm, in order to ensure the rotation of transverse arm turntable held stationary；The upper surface of the first angle block gauge is fixing with the bottom face of transverse arm bearing to be connected；Transverse arm turntable upper surface is fixing with the angled end-face of the first angle block gauge to be connected；The angled end-face of the second angle block gauge is fixing with transverse arm turntable lower surface to be connected；The lower surface of the second angle block gauge is fixedly mounted on work top；Laser tracker is disposed adjacent to the position of the axial line of transverse arm turntable, and ensures that laser tracker can not interfere transverse arm turntable to rotate, and the bottom face of laser tracker is placed on work top；Minute surface to be measured is positioned on workpiece rotary table；One end of touch sensor is connected with micro-adjusting mechanism, and the gauge head outline of touch sensor contacts with minute surface to be measured；Transverse arm rotates around the axial line of transverse arm turntable, touch sensor, the first target ball and the second target ball is driven to rotate around the axial line of transverse arm turntable, simultaneously the centre of sphere of the first target ball and the centre of sphere of the second target ball form the arc track that the axial line around transverse arm turntable rotates, the arc track that the centre of sphere of the centre of sphere and the second target ball that laser tracker distinguishes tracking measurement the first target ball is formed in space in space；Computer is connected with the data terminal of laser tracker by data acquisition line concentration, the arc track data process to the centre of sphere of the first target ball and the centre of sphere of the second target ball, it is thus achieved that swing-arm profilometry effective rake。

2. the measurement apparatus of swing-arm profilometry effective rake according to claim 1, it is characterised in that: the finding range of described laser tracker is more than 60m, 5 μm/m of static measurement precision, and 10 μm/m of dynamic measurement precision, coordinate repeatability is better than 2.5 μm/m。

3. the measurement apparatus of swing-arm profilometry effective rake according to claim 1, it is characterized in that: the arc track data of the centre of sphere of the described centre of sphere to the first target ball and the second target ball process, it it is the central coordinate of circle obtaining two sections of arc track place discs, utilize the central coordinate of circle of two sections of arc track place discs, it is thus achieved that namely the space line equation of two central coordinate of circle is the axial line equation of transverse arm turntable；The range equation of recycling spatial point and space line, obtains the gauge head centre of sphere distance to transverse arm turntable axial line of touch sensor, is the effective rake of swing-arm profilometry。

4. the measurement apparatus of swing-arm profilometry effective rake according to claim 1, it is characterized in that: described first target ball, the second target ball are made up of iron material, and be reflective, for reflecting the laser from laser tracker, thus ensureing the centre of sphere of the centre of sphere of laser tracker tracking measurement the first target ball and the second target ball data on the arc track that space is formed。

5. the measurement apparatus of swing-arm profilometry effective rake according to claim 1, it is characterised in that: the resolving power of described touch sensor is 25nm, and certainty of measurement is 50nm。

6. the measurement apparatus of swing-arm profilometry effective rake according to claim 1, it is characterised in that: described micro-adjusting mechanism is the fine setting that can realize X-direction, Y direction, Z-direction, pitch orientation and beat direction。

7. the measurement apparatus of swing-arm profilometry effective rake according to claim 1, it is characterized in that: described transverse arm turntable is air-float turntable, the end face run-out of transverse arm turntable is 25nm, and it is 0.02 that the angle of transverse arm turntable is rocked ", for realizing the rotary motion of touch sensor。

8. the method that swing-arm profilometry effective rake is measured by the measurement apparatus according to any one of claim 1～7, comprises the following steps that

Step S1: carried out coordinate translation conversion by the spatial relation of the gauge head centre of sphere of known touch sensor, the centre of sphere of the first target ball and the centre of sphere of the second target ball, obtain the first coordinate system, thus obtaining the centre of sphere of the gauge head centre of sphere of touch sensor, the centre of sphere of the first target ball and the second target ball coordinate under the first coordinate system；

Step S2: laser tracker measures the centre of sphere of the first target ball and the initial position of the centre of sphere of the second target ball, and the first target ball and the second target ball rotate the data on the arc track formed around transverse arm turntable；

Step S3: the first coordinate system is rotated translation and transforms to laser tracker coordinate system, obtains the gauge head centre of sphere of the touch sensor coordinate under laser tracker coordinate system；

Step S4: realize the process to data above by computer, obtain the gauge head centre of sphere distance to transverse arm turntable axial line of touch sensor, i.e. swing-arm profilometry effective rake。