CN103411545B - Based on the multiple axes system error modeling of freeform optics surface and measurement mechanism and method - Google Patents

Abstract

The invention belongs to the field of multi-axis system detection and aims to provide a new measurement method capable of realizing high precision, low cost and comprehensively measuring the geometric errors of multi-axis systems. The optical free-form surface is used as the standard part for multi-axis system error measurement, the multi-axis system error measurement path is planned through the corresponding error modeling method, and the multi-dimensional displacement measurement system is used to detect the optical free-form surface to realize the comprehensive measurement of the multi-axis system geometric error. Then it is used to compensate the geometric error of the multi-axis system. In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is a multi-axis system error modeling and measurement device and method based on an optical free-form surface, including: a semiconductor laser, a collimated beam reduction system, a four-quadrant photodiode QPD, an imaging lens, 1/4 wave plate, optical free-form surface standard parts, polarization beam splitter PBS, image detector CCD, another imaging lens and data acquisition and processing platform. The invention is mainly applied to multi-axis system detection.

Description

Multi-axis system error modeling and measurement device and method based on optical free-form surface

technical field

The invention belongs to the field of multi-axis system detection, and specifically relates to a multi-axis system error modeling and measuring device and method based on an optical free-form surface.

technical background

With the rapid development of modern science and technology, multi-axis systems such as multi-axis CNC machine tools, three-coordinate measuring machines, multi-axis translation stages, and multi-axis manipulators have been widely used in many fields such as industrial production and industrial inspection. With the continuous development of modern industry towards high precision and diversification, it is of great significance to improve the precision of multi-axis systems. A multi-axis CNC machine tool is a typical representative of a multi-axis system. The background technology of the present invention will be described below by taking a multi-axis CNC machine tool as an example.

As the foundation and core of manufacturing technology, the precision of CNC machine tools is directly related to the precision of products processed by the machine tools. Among them, the geometric error of the machine tool is one of the main errors affecting the accuracy of the machine tool, accounting for more than 30% of the total error source of the machine tool, so reducing the geometric error of the machine tool is of great significance to improving the machining accuracy of the machine tool.

At present, the method of improving the accuracy of the machine tool is generally to measure the various errors of the machine tool first, and then use the corresponding error compensation method to compensate the various errors of the machine tool. The method of machine tool error compensation can not only greatly improve the accuracy of the machine tool, but also has low cost and simple operation. This method solves the problems of limited precision level and high cost simply by improving the accuracy of machine tool components and machine tool assembly. Many scholars at home and abroad have carried out in-depth research on this issue. In 1983, W.Knapp invented the reference disk—the two-way micro-displacement measuring head method, which can use the two-dimensional micro-displacement meter clamped at the end of the spindle to scan the outer or inner peripheral surface of the reference circular plate on the two-way workbench. To obtain the circular interpolation motion trajectory. In 1994, Japan's Okuyama Shigeki invented the full-circumference capacitor - the ball method. The steel ball clamped on the main shaft revolves around another steel ball fixed on the two-way workbench to perform circular interpolation motion. Two steel balls are used. As the two poles of the capacitor, the ball can detect the trajectory error of the circular interpolation motion according to the change of the gap between the two steel balls. In 2000, Park Hee-jae from South Korea proposed the ballbar method to evaluate the three-dimensional error technology of machine tools, and with the commercialization of the ballbar, the use of the ballbar method has become more and more mature. However, the mechanical measurement methods used above all use the circular interpolation movement of each machine tool to measure the machine tool error. The assembly and debugging of the measuring device before the measurement is complicated, and the measurement range is limited. Only part of the error of the machine tool can be measured and it cannot be realized. Comprehensive measurement of machine tool geometric errors. With the continuous development of laser technology, some scholars have proposed a method of machine tool error detection and compensation based on dual-frequency laser interferometer. At present, the more mature methods include 9-line method, 12-line method, 14-line method, 15-line method, 22-line method and space body diagonal method. The 9-line method, 12-line method, 14-line method, 15-line method, and 22-line method need to constantly change the position of the laser interferometer when measuring machine tool errors. The debugging time is long and time-consuming, and the algorithms of other methods except the 9-line method are complicated. leading to its limited application. The space body diagonal method has become one of the benchmarks for machine tool error measurement because of its simple measurement method and the ability to measure various geometric errors of machine tools. Although the space body diagonal method has greatly improved the accuracy of machine tool error measurement, the laser interferometer and its supporting devices are expensive, and it is difficult for machine tool manufacturers and machine tool manufacturers to pay such expensive measurement costs. The replacement of the measuring mirror by the object is complicated and time-consuming, which affects the normal production and processing of the machine tool.

To sum up, after years of development and exploration, the current machine tool error measurement and compensation technology has been developing in the direction of miniaturization, high precision and comprehensiveness. Although the traditional measurement method has low measurement cost, the installation and debugging of the measurement device are complicated, which increases the time for measuring the geometric error of the machine tool and affects the normal production and processing of the machine tool. Moreover, the measurement accuracy is low, and it is impossible to realize the comprehensive measurement of the geometric error of the machine tool. The new dual-frequency laser interferometer is used to measure the geometric error of the machine tool. Although the measurement accuracy is high, various geometric errors of the machine tool can also be obtained through the corresponding modeling method, but the cost of the laser interferometer and its supporting devices is high, which limits its large-scale promotional application.

With the development of the design and manufacturing technology of optical freeform surfaces in recent years, optical freeform surfaces have been widely used in various fields such as imaging, lighting, and measurement, and have become one of the current international research hotspots. Utilizing the feature that the shape of the optical free-form surface can be arbitrarily designed according to the needs of practical applications, the optical free-form surface can realize functions that cannot be realized by other surface types such as plane and spherical surfaces. For example, Professor Gao Wei, a Japanese scholar, realized the high-precision measurement of two-dimensional displacement by using double sine free-form surfaces. The invention fully utilizes the advantages of the optical free-form surface, and uses it as a standard part for error measurement by optimizing the shape of the optical free-form surface, so as to realize the rapid and high-precision measurement of the geometric error of the multi-axis system represented by the multi-axis numerical control machine tool .

Contents of the invention

The invention aims to overcome the deficiencies of the prior art and provide a new measuring method capable of realizing high precision, low cost and comprehensively measuring geometric errors of multi-axis systems. The optical free-form surface is used as the standard part for multi-axis system error measurement, the multi-axis system error measurement path is planned through the corresponding error modeling method, and the multi-dimensional displacement measurement system is used to detect the optical free-form surface to realize the comprehensive measurement of the multi-axis system geometric error. Then it is used to compensate the geometric error of the multi-axis system. In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is, based on the multi-axis system error modeling and measuring device of the optical free-form surface, including: semiconductor laser, collimation beam reduction system, four-quadrant photodiode QPD, imaging lens, 1/ 4 wave plates, optical free-form surface standard parts, polarization beam splitter PBS, image detector CCD, another imaging lens and data acquisition and processing platform; the thin straight beam emitted by the semiconductor laser is collimated and reduced to a diameter by the collimation and reduction system 200μm thin straight parallel light beam, the beam transmits P-polarized light through a polarization beam splitter (PBS), and then becomes circularly polarized light through a 1/4 wave plate and projects it on the optical free-form surface standard part, and the reflection reflected by the optical free-form surface standard part The light becomes S-polarized light through the 1/4 wave plate, reflected by the polarization beam splitter PBS, and then converged by the imaging lens to the four-quadrant photodiode QPD. When the optical free-form surface standard moves along the X or Y direction, the laser projection point The slope changes accordingly, so that the position of the imaging light spot on the four-quadrant photodiode QPD changes, and the position of the light spot on the four-quadrant photodiode QPD has a one-to-one correspondence with the position of the light spot projected on the optical free-form surface standard , so as to realize the measurement of displacement in the X and Y directions; the scattered light on the optical free-form surface standard part is imaged to the image detector CCD through another imaging lens, and when the optical free-form surface standard part produces a Z-direction displacement, the imaged light on the CCD The light spot changes accordingly, and there is a one-to-one correspondence between the two, so as to realize the measurement of the Z-direction displacement.

A multi-axis system error modeling and measurement method based on an optical free-form surface, comprising the following steps: completing the establishment of various geometric error transfer models of the multi-axis system through the multi-axis system geometric error modeling, and determining the geometric error of the multi-axis system Measurement scheme: when performing multi-axis system error measurement, fix the optical free-form surface standard at a specific position on the multi-axis system, install the multi-dimensional displacement measurement system at another specific position on the multi-axis system, and exchange the positions of the two Also, according to the determined geometric error measurement scheme of the multi-axis system, the joint movement of each motion unit of the multi-axis system is driven, so that the relative position of the optical free-form surface standard part and the multi-dimensional displacement measurement system changes, and the relative position changes are analyzed. Detection, to realize the measurement of multi-dimensional displacement errors of multi-axis systems, and then through error identification, various geometric errors of multi-axis systems are obtained, and then used to compensate geometric errors of multi-axis systems.

The method according to the invention is carried out by means of the device described.

The error modeling is specifically: the error is e={D _X , D _Y , D _Z } ^T , where D _X , D _Y , and D _Z are the magnitudes of the error components in the X, Y, and Z directions respectively. By establishing the The characteristic matrix and the characteristic matrix transmitted by various geometric errors can obtain the multinomial expressions of the error e about the movement position of each axis and various geometric errors, as shown in formulas (1)-(3):

Multi-axis system error modeling and measurement method based on optical free-form surface,

D _X =(R _yy +R _zx )*Z+T _ax -T _xx +T _yx +T _zx +R _xz *Y _w -S _yx *YR _xy *Z _w +T _bx *cos(B)+T _bz *sin(B)(1)

D _Y =(-R _yx -R _zy )*Z+T _yy -T _xy +T _zy -R _xz *X _w +R _xx *Z _w +(T _ay +T _by )*cos(A)-T _bz *cos(B)*sin(A)+T _bx *sin(A)*sin(B) (2)

D _Z =-T _xz +T _yz +T _zz +R _xy *X _w -R _xx *Y _w +T _az *cos(A)+(T _ay +T _by )*sin(A)-T _bx *cos (A)*sin(B) (3)

In formulas (1)-(3), D _X , D _Y , and D _Z represent the size of the error in the X, Y, and Z directions; T represents the movement error, R represents the rotation error, and the first subscript represents the name of the moving body , can be X guide rail, Y guide rail, Z guide rail, A turntable or B turntable, represented by letters x, y, z, a or b respectively, the second subscript represents the moving axis for T, and the rotating axis for R, respectively Indicated by x, y, z; X _w , Y _w , Z _w are the coordinate values of the theoretical machining point in the X, Y, and Z directions in the workpiece coordinate system; X, Y, Z, A, and B represent the corresponding moving axes The magnitude of the displacement and the rotation angle of the rotation axis; the movement error and rotation error in the geometric error model are functions of the movement amount X, Y, Z or the rotation angle A, B of the corresponding moving body, and the three times about the movement coordinates of each body are used. Polynomials are used to fit each individual error; each individual error is fitted with a polynomial, then formulas (1)-(3) constitute an equation that can be solved, and the equation contains a limited number of unknown fitting coefficients. Select a certain machine tool The linkage scheme of each motion axis measures a series of error values of the measurement points, and the measured errors are substituted into the equations to obtain the value of the unknown fitting coefficient, thereby obtaining the expression of the geometric error transfer model, and then It is used to compensate the geometric error of the machine tool.

Change the relative position of the optical free-form surface standard part and the multi-dimensional displacement measurement system, specifically, move the position of the optical free-form surface standard part or the position of the multi-dimensional displacement measurement system, and detect the change of the relative position, specifically to measure the optical freedom Displacement of curved surface standard parts or multi-dimensional displacement measurement systems along the X, Y, and Z axes of the natural coordinate system.

The displacement along the Z axis is measured by laser triangulation: the axis of the laser, the optical axis of the imaging objective lens and the CCD linear array are all located in the same plane, and the laser projects an ideal spot on the surface to be measured. The light spot will be displaced along the axis of the laser for the same distance as the position of its projected point changes. At the same time, the point light spot is imaged on the image sensor CCD through the objective lens, and the imaging position has a unique correspondence with the depth position of the light spot. Find out the center position of the real image formed on the CCD line array, then you can calculate the Z-direction coordinate of the light spot at this moment through the calculation method of geometric optics, so as to obtain the Z-direction displacement at this point on the measured surface.

The present invention has the following technical effects:

The invention provides a measuring method capable of realizing high precision and low cost, and capable of comprehensively measuring geometric errors of multi-axis systems. It uses optical free-form surface as the standard part for multi-axis system error measurement, and realizes high-precision measurement of multi-axis system geometric error through the detection of optical free-form surface by multi-dimensional displacement measurement system. There is no need to use expensive devices such as laser interferometers in the measurement system, which reduces the measurement cost of geometric errors in multi-axis systems. As shown in Figure 1, taking a CNC machine tool as an example, when measuring the geometric error of the machine tool, the optical free-form surface standard part is fixed at a specific position on the machine tool, and the multi-dimensional displacement measurement system is installed on the tool holder (replacing the two positions is also Yes), using the joint movement of each motion unit of the machine tool, the relative position of the optical free-form surface standard part and the multi-dimensional displacement measurement system changes, and the detection of the optical free-form surface by the multi-dimensional displacement measurement system, thereby realizing the measurement of the machine tool error, operation easy. By establishing the geometric error model of the machine tool, the error measurement scheme of the machine tool can be determined, so as to realize the comprehensive measurement of the geometric error of the machine tool. Although this method has the coupling of error terms in the error identification, and cannot identify all geometric errors of the machine tool, the invention can establish a geometric error model of the machine tool for generating actual NC instructions that can realize error compensation, and then be used for the machine tool Compensation for geometric errors. Based on the above measuring principles, the invention can not only be used for measuring the geometric error of machine tools, but also can be used for measuring the geometric errors of multi-axis systems such as multi-axis displacement tables, three-coordinate measuring machines, and multi-axis manipulators.

Description of drawings

Fig. 1 is the structure schematic diagram when the multi-axis system error measurement method based on the optical freeform surface is used for the geometric error measurement of the machine tool in the present invention;

Fig. 2 is the schematic diagram of the machine tool geometric error measurement system based on the optical freeform surface among the present invention;

Fig. 3 is the three-dimensional model diagram of the paraboloid of revolution adopted in the present invention;

The three-dimensional model diagram of Fig. 4 rotating paraboloid array;

Fig. 5 is a schematic diagram of the principle of the four-quadrant photodiode (QPD) used in the present invention to measure the deflection angle;

Fig. 6 is a schematic diagram of measuring the Z-direction displacement by the laser triangulation method adopted in the present invention.

Figure 7 is a graph of positioning errors in X, Y, and Z directions caused by A-axis rotation. (a) A-axis rotation angle causes X-direction positioning error D _X , (b) A-axis rotation angle causes Y-direction positioning error D _Y , (c) A-axis rotation angle causes Z-direction positioning error D _Z .

Fig. 8 is a curve diagram of positioning errors in X, Y and Z directions caused by the rotation of the B-axis. (a) B-axis displacement causes X-direction positioning error D _X , (b) B-axis displacement causes Y-direction positioning error D _Y , (c) B-axis displacement causes Z-direction positioning error D _Z .

Figure 9 is a curve diagram of positioning errors in X, Y, and Z directions caused by X-axis displacement. (a) X-axis displacement causes X-direction positioning error D _X , (b) X-axis displacement causes Y-direction positioning error D _Y , (c) X-axis displacement causes Z-direction positioning error D _Z .

Figure 10 is a curve diagram of positioning errors in X, Y, and Z directions caused by Y-axis displacement. (a) Y-axis displacement causes X-direction positioning error D _X , (b) Y-axis displacement causes Y-direction positioning error D _Y , (c) Y-axis displacement causes Z-direction positioning error D _Z .

Figure 11 is a graph of positioning errors in X, Y, and Z directions caused by Z-axis displacement.

(a) Z-axis displacement causes X-direction positioning error D _X , (b) Z-axis displacement causes Y-direction positioning error D _Y , (c) Z-axis displacement causes Z-direction positioning error D _Z .

detailed description

Taking the multi-axis numerical control machine tool as an example, the present invention adopts an optical free-form surface as the strategy of measuring the standard part, and realizes the high-precision and low-cost measurement of the geometric error of the numerical control machine tool. The present invention will be described in further detail below according to the accompanying drawings and examples.

(1) Machine tool error modeling

The invention adopts the method based on the multi-body system theory to realize the establishment of the mathematical model of the geometric error of the machine tool. A five-axis CNC machine tool contains 5 relative moving bodies, and each moving body m will produce 6 errors T _mx , T _my , T _mz , R _mx , R _my and R _mz during the motion process. Among them, T represents the movement error, and R represents the rotation error. The first subscript m represents the name of the moving body, and m can be X guide rail, Y guide rail, Z guide rail, A turntable or B turntable, represented by letters X, Y, Z, A or B respectively. The second subscript indicates the axis of movement for T and the axis of rotation for R. Therefore, the five-axis machine tool produces 30 (5*6) errors.

In addition, the perpendicularity errors S _yx , S _zx , S _zy between the three translational axes, and the perpendicularity (parallelism) errors _Say , S _az and S _bx , S _bz generated by the rotational axes A and B respectively. In this way, the 5-axis machine tool produced 7 items of verticality errors.

In summary, the five-axis machine tool contains a total of 37 (30+7) geometric errors.

The error refers to the deviation between the theoretical processing point and the actual processing point on the workpiece. Suppose the position vector of the tool tip in the tool coordinate system is t ₈ ={0,0,0,1} ^T , the position vector of the theoretical machining point in the workpiece coordinate system is w ₃ ={X _w ,Y _w ,Z _w ,1} ^T , where X _w , Y _w , and Z _w are the coordinates of the theoretical machining point in the workpiece coordinate system in the X, Y, and Z directions, respectively. Then, according to the coordinate transformation, the position vectors of the tool tip and the theoretical machining point in the reference coordinate system (bed coordinate system) can be obtained. Let the position vectors of the tool tip and the theoretical machining point in the reference coordinate system be t ₁ and w ₁ respectively. The processing error e is their difference. Let the error be e={D _X , D _Y , D _Z } ^T , where D _X , D _Y , and D _Z are the magnitudes of the error components in the X, Y, and Z directions respectively, then e=t ₁ -w ₁ . By establishing the characteristic matrix of each axis and the characteristic matrix of each geometric error transfer, the multinomial expressions of the error e with respect to the movement position of each axis and each geometric error can be obtained, as shown in formulas (1)-(3).

D _X =(R _yy +R _zx )*Z+T _ax -T _xx +T _yx +T _zx +R _xz *Y _w -S _yx *YR _xy *Z _w +T _bx *cos(B)+T _bz *sin(B)(1)

D _Y =(-R _yx -R _zy )*Z+T _yy -T _xy +T _zy -R _xz *X _w +R _xx *Z _w +(T _ay +T _by )*cos(A)-T _bz *cos(B)*sin(A)+T _bx *sin(A)*sin(B) (2)

D _Z =-T _xz +T _yz +T _zz +R _xy *X _w -R _xx *Y _w +T _az *cos(A)+(T _ay +T _by )*sin(A)-T _bx *cos (A)*sin(B) (3)

The movement error and rotation error in the geometric error model of the machine tool is a function of the movement amount X, Y, Z or the rotation angle A, B of the corresponding moving body, so the cubic polynomial about the movement coordinates of each body can be used to fit each individual error. Fit the 30 items of movement error and rotation error in the error model with the polynomials shown in formula (4) and formula (5). The specific implementation process is as follows:

Each error polynomial can be uniformly recorded as T _mx =f(m), T _my =f(m), T _mz =f(m), R _mx =f(m), R _my =f(m), R _mz = f(m). Among them, T represents the movement error, and R represents the rotation error. The first subscript m represents the name of the moving body, m can be X guide rail, Y guide rail, Z guide rail, A turntable or B turntable, represented by letters X, Y, Z, A or B respectively, and the second subscript is for T Represents the movement axis, and R represents the rotation axis, which can be represented by x, y, and z respectively; f(m) represents the fitting polynomial about the moving body m.

Of course, the higher the order of the fitted polynomial, the better, but it is often difficult to solve high-order equations. Referring to the fitting strategy in the relevant literature, a cubic polynomial is used to fit the movement and rotation errors of the machine tool:

T _mn (m)=T _mn3 m ³ +T _mn2 m ² +T _mn1 m ¹ +T _mn0 (4)

R _mn (m)=R _mn3 m ³ +R _mn2 m ² +R _mn1 m ¹ +R _mn0 (5)

In formulas (4)-(5), T _mn (m) and R _mn (m) represent the fitting polynomials of movement error and rotation error respectively; T _mn3 , T _mn2 , T _mn1 , and T _mn0 represent the fitting coefficients of movement error; R _mn3 , R _mn2 , R _mn1 , and R _mn0 represent rotational error fitting coefficients.

Therefore, formulas (1)-(3) constitute equations that can be solved, and the equations contain a finite number of unknown fitting coefficients. Therefore, as long as a certain linkage scheme of each movement axis of the machine tool is selected, a series of error values of the measurement points are measured, and the measured errors are substituted into the equation group to immediately obtain the value of the unknown fitting coefficient, thereby obtaining the individual error values and the expression of the machine tool error model, and then used to compensate the geometric error of the machine tool.

For multi-axis systems with 3-axis, 4-axis, 6-axis, 7-axis or more axes, although the number of error terms is increased, the method is still applicable.

(2) System structure composition

The overall architecture of the machine tool error measurement system based on the above principles is shown in Figure 2. The system includes a semiconductor laser, a collimator beam-splitting system, a four-quadrant photodiode (QPD), an imaging lens, a 1/4 wave plate, an optical free-form surface standard, a polarization beam splitter (PBS), an image detector (CCD), and an imaging lens and data collection and processing platform.

As shown in Figure 2, the thin straight beam emitted by the semiconductor laser is collimated and shrunk by the lens group into a thin straight parallel beam with a diameter of 200 μm. Become circularly polarized light projected on the optical free-form surface standard. The reflected light becomes S-polarized light through the 1/4 wave plate, reflected by the polarization beam splitter prism (PBS) and then converged by the imaging lens to the four-quadrant photodiode (QPD). When the optical free-form surface standard moves along the X or Y direction, The slope at the laser projection point changes accordingly, so that the position of the imaging spot on the four-quadrant photodiode (QPD) changes, and the position of the spot on the four-quadrant photodiode (QPD) and the spot projected on the optical free-form surface standard There is a one-to-one correspondence between the above positions, so as to realize the measurement of displacement in X and Y directions. The scattered light on the optical free-form surface standard is imaged onto the image detector (CCD) through the imaging lens. When the optical free-form surface standard is displaced in the Z direction, the spot imaged on the CCD changes accordingly, and the difference between the two There is a one-to-one correspondence, so as to realize the measurement of Z-direction displacement. Therefore, the measurement system can realize the measurement of three-dimensional displacement in X, Y, and Z directions.

(3) Optical free-form surface standard parts

The invention adopts the optical free-form surface as the standard part to be measured to realize the measurement of the three-dimensional displacement, and the curvature of each point of the standard part on the optical free-form surface has a one-to-one correspondence with its position coordinates, and the curvature changes continuously within the measurement range. The paraboloid of revolution is one of the optical free-form surface standard parts in the present invention, so that the measurement sensitivity of the measurement system is constant, ensuring the stability and practicability of the measurement system. As shown in Figure 3 is a three-dimensional model diagram of the paraboloid of revolution used in the invention.

The surface characteristics of the paraboloid of revolution can be described by the following formula:

$\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; z</span>}$

Among them (x, y, z) are the coordinates of each point of the rotating paraboloid, and a is a constant.

Deriving x and y respectively, the slope of each point on the rotating paraboloid is:

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

It can be seen that the slope of each point of the paraboloid of revolution corresponds to its coordinate position one by one. Then find the second-order derivative of the characteristic formula of the paraboloid of revolution:

${\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

${\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{{{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

The rate of change of the slope of the rotating paraboloid is obtained as a constant. Since the measurement sensitivity of the measurement system in the X and Y directions is proportional to the rate of change of the surface characteristic slope of the optical free-form surface standard part, the paraboloid is selected as the three-dimensional displacement measurement standard part, so that the measurement system The X and Y measurement sensitivities are:

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; N</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

δ _x , δ _y are the measurement sensitivities in X and Y directions respectively, and N is a constant. Therefore, choosing a rotating paraboloid as a free-form surface standard can make the measurement sensitivity of the X and Y-direction measurement systems constant. In the design, the curvature of the rotating paraboloid is 0.005, and the diameter is 5mm. As shown in Figure 5, it is the actual processed rotating paraboloid. A ring plane with a width of 2.5mm is processed at the edge of the paraboloid, which can be used for the vertical alignment of the laser beam and the free-form surface standard during measurement.

In order to increase the displacement measurement range in X and Y directions, the scheme in Figure 4 is used to design the free-form surface standard parts in the form of an array. The surface shape of each paraboloid in the array is the same as that of the paraboloids designed above. The single-point diamond turning method is used to process the array shown in Figure 7. In order to improve the machining accuracy, there should be a distance between the two paraboloids that is greater than the radius of the machining tool edge. For the comprehensive consideration of processing efficiency and processing accuracy, a tool with a cutting edge radius of 1.0 mm is selected to process the array shown, so the interval between two adjacent paraboloids is set to 1 mm. Since the shape of each paraboloid and the distance between the paraboloids have been determined, the coordinates of each point in the array are also uniquely determined. When there are multiple cycles between the measurement points, it is necessary to include the caliber of multiple paraboloids and the distance between the paraboloids, so that Calculate the distance between two measuring points. During the actual measurement, properly select the displacement of each moving axis of the multi-axis device under test to ensure that each measurement point is always on the paraboloid in the array, and record the number of cycles experienced by the X and Y output of the measurement system as well as the measurement start point and end point The measurement value can realize the measurement of displacement in X and Y direction. The size of the array can be changed according to the needs of the measurement range, and the free selection of the displacement measurement range in the X and Y directions can be realized.

(4) X, Y direction displacement measurement

The X- and Y-direction displacement measurement scheme adopted by the present invention is developed according to the scheme in Fig. 5 . The position of the light spot on the quadrant photodiode (QPD) can be obtained by converging the incident light on the quadrant photodiode (QPD) through the lens.

In the figure, Δθ is the slope angle of the measured point of the rotating paraboloid, f is the focal length of the convex lens, and dy is the distance between the center of the imaging spot and the center of the four-quadrant photodiode. From the geometric relation:

$\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; dy</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}$

Since the slope of the rotating paraboloid is very small, tanΔθ=Δθ can be obtained:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; dy</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}$

Similarly, for the X direction, there are:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; dx</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}$

Therefore, by verifying the change of the spot position on the QPD, the change value of the beam inclination can be calculated, and the change of the slope of the measured point on the rotating paraboloid can be obtained, so as to obtain the displacement in the X and Y directions.

Through theoretical calculation, the four-quadrant photodiode X, Y direction measured value output is as follows:

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; out</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; RDx</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; Dx</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;R</span>}}<span\; class="notranslate">\; \&ap;</span>\frac{\mathrm{<span\; class="notranslate">\; R\&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}$

Where R, D, X _out and λ are the radius of the light spot on the four-quadrant photodiode (QPD), the diameter of the incident light, the X-direction measurement output value of the four-quadrant photodiode (QPD) and the laser wavelength.

In the same way:

${\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; out</span>}}<span\; class="notranslate">\; \&ap;</span>\frac{\mathrm{<span\; class="notranslate">\; R\&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}$

Y _out is the Y-direction measurement output value of the four-quadrant photodiode (QPD)

Thus it can be concluded that:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; out</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}$

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; out</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}$

From the previous analysis:

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Therefore, the coordinates of the measured point are obtained as:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; out</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1.22</span>}\mathrm{<span\; class="notranslate">\; f</span>}}$

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; out</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1.22</span>}\mathrm{<span\; class="notranslate">\; f</span>}}$

In the above formula, D is the radius of the incident laser beam (D=100μm), a is the characteristic parameter of the paraboloid of rotation (a=20), and f is the focal length of the lens (f=30mm).

(5) Z direction displacement measurement

As a kind of photoelectric detection technology, Laser Triangulation ^[10-12] is widely used in the detection of length, distance and three-dimensional shape due to its advantages of simple structure, fast test speed and strong real-time processing ability. In view of the above characteristics of the laser triangulation method, the Z-direction displacement measurement of the three-dimensional displacement measurement system is realized by the laser triangulation distance measurement method.

The basic structure of measuring object displacement by laser triangulation is shown in Figure 6. In order to satisfy Gauss's theorem, in the figure, the axis of the laser, the optical axis of the imaging objective lens and the CCD linear array are located in the same plane. The laser light source is used as the indicator light source for measurement, projecting an ideal point spot on the measured surface. The light spot will be displaced along the axis of the laser for the same distance as the position of its projection point changes. At the same time, the point spot is imaged on the image sensor (CCD) through the objective lens, and the imaging position has a unique correspondence with the depth position of the spot. By measuring the center position of the real image formed on the CCD linear array, the Z-direction coordinate of the light spot at this moment can be obtained by the calculation method of geometric optics, so as to obtain the Z-direction displacement at the point on the measured surface.

In the figure above, a ₀ and b ₀ are the distance from the intersection point of the laser axis and the optical axis of the objective lens to the optical center of the objective lens, and the distance from the intersection point of the CCD line array and the optical axis of the objective lens to the optical center of the objective lens. α is the angle between the laser axis and the optical axis of the objective lens; β is the angle between the CCD line array and the optical axis. Define the intersection point of the optical axis of the objective lens and the laser beam as the center point of the measured displacement, and the intersection point of the optical axis of the objective lens and the CCD as the center point of the displacement of the imaging spot. D is the displacement of the measured surface from the center point in the Z direction, and d is the displacement of the corresponding spot on the CCD from the center point.

It can be seen from geometric optics that when the side surface is moved x along the Z axis, the imaging spot of the objective lens moves y on the CCD, and the following geometric relationship exists:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The sensitivity δ of the triangulation is:

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;y</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

It can be obtained from the above formula that the measurement sensitivity of laser triangulation is not a fixed value, and the measurement sensitivity is related to x, a0, b0, α, β, etc., so appropriate values of a0 and α should be selected. Select a0=75mm, α=1/3π. Through the determination of the above conditions, the obtained sensitivity range is: 1.6110<δ<1.8263, the measuring range is: -1.7981mm～~1.9698mm, and the measuring range is: 3.7679mm.

Apply the above-mentioned implementation method to carry out system integration, take the five-axis tool swing type (TTTRR) machine tool as an example, through the measurement of the three-dimensional displacement error of the machine tool by the above-mentioned three-dimensional displacement sensor, solve the geometric error model equation of the machine tool, and obtain the X , Y, Z direction positioning error (D _X , D _Y , D _Z ), the effect is shown in the figure below. Among them, Fig. 7 shows the positioning error curves in the X, Y, and Z directions caused by the rotation of the A axis. Figure 8 shows the X, Y, and Z direction positioning error curves caused by the rotation of the B axis. Figure 9 shows the X, Y, and Z positioning error curves caused by the X-axis displacement. Figure 10 shows the X, Y, and Z positioning error curves caused by the Y-axis displacement. Figure 11 shows the X, Y, and Z positioning error curves caused by the Z-axis displacement.

Fig. 7, Fig. 8, Fig. 9, Fig. 10, and Fig. 11 are the X, Y, and Z direction positioning errors (D _X , D _Y , D _Z ). Through the measurement of the three-dimensional displacement error of the machine tool by the above-mentioned three-dimensional displacement sensor, the error model equation of the machine tool can be solved, which can be used to generate actual numerical control commands that can realize error compensation, and then used to compensate the geometric error of the machine tool. The invention realizes the comprehensive measurement of the geometric error of the machine tool, and the measurement result can be used for the purpose of compensating the geometric error of the machine tool.

To sum up, the multi-axis system error modeling and measurement method based on the optical free-form surface can solve the relationship between measurement accuracy and measurement cost well, and can measure various geometric errors of the machine tool with high precision, and greatly Reducing measurement cost and shortening measurement time is conducive to the application and promotion of machine tool error measurement and compensation technology. Moreover, the invention can not only be used to measure the geometric errors of machine tools, but also can be used to measure the geometric errors of multi-axis devices such as multi-axis translation tables, three-coordinate measuring machines, multi-axis manipulators, etc., and has very important application value.

Claims (5)

1. the multiple axes system error modeling based on freeform optics surface and measurement mechanism, it is characterized in that, comprising: semiconductor laser, collimation contracting beam system, four-quadrant photodiode QPD, imaging len, quarter wave plate, freeform optics surface standard component, polarization splitting prism PBS, image detector CCD, another imaging len and data acquisition and processing (DAP) platform, the thin straight parallel beam that the thin collimated optical beam that semiconductor laser sends is diameter 200 μm through collimation contracting beam system collimation contracting bundle, light beam transmits P polarized light through polarization splitting prism PBS, becoming circularly polarized light through quarter wave plate again projects on freeform optics surface standard component, the reflected light that freeform optics surface standard component reflects becomes S polarized light through quarter wave plate, converged to by imaging len again on four-quadrant photodiode QPD through polarization splitting prism PBS reflection, when freeform optics surface standard component moves along X or Y-direction, the slope at laser projection point place changes thereupon, thus the position of imaging facula on four-quadrant photodiode QPD is changed, there is relation one to one the position of hot spot on four-quadrant photodiode QPD and the position of dot projection on freeform optics surface standard component, thus realize X, the measurement of Y-direction displacement, scattered light on freeform optics surface standard component is imaged onto on image detector CCD through another imaging len, when freeform optics surface standard component produces Z-direction displacement, the hot spot be imaged onto on CCD changes thereupon, and have relation one to one between the two, thus realize the measurement of Z-direction displacement.

2. the multiple axes system error modeling based on freeform optics surface and measuring method, it is characterized in that, realize by means of device according to claim 1, comprise the steps: to complete foundation to the every geometric error TRANSFER MODEL of multiple axes system by multiple axes system geometrical error modeling, determine the measurement scheme of multiple axes system geometric error, when carrying out multiple axes system error measure, freeform optics surface standard component is fixed on a certain ad-hoc location on multiple axes system, multi-dimensional displacement measuring system is arranged on another ad-hoc location on multiple axes system, also can in both exchanges position, according to fixed multiple axes system geometric error measurement scheme, drive each moving cell Union Movement of multiple axes system, the relative position of freeform optics surface standard component and multi-dimensional displacement measuring system is changed, the situation that relative position changes is detected, realize the measurement of multiple axes system multi-dimensional displacement error, pass through error identification again, obtain every geometric error of multiple axes system, and then for the compensation to multiple axes system geometric error.

3., as claimed in claim 2 based on multiple axes system error modeling and the measuring method of freeform optics surface, it is characterized in that, error modeling is specially: error is e={D _x, D _y, D _z} ^t, by setting up the eigenmatrix that the eigenmatrix of each axle and every geometric error are transmitted, obtain the multi-term expression of error e about each axle movement position and every geometric error, as shown in formula (1)-(3):

Based on multiple axes system error modeling and the measuring method of freeform optics surface,

D _X＝(R _yy+R _zx)*Z+T _ax-T _xx+T _yx+T _zx+R _xz*Y _w-S _yx*Y-R _xy*Z _w+

T _bx*cos(B)+T _bz*sin(B)(1)

D _Y＝(-R _yx-R _zy)*Z+T _yy-T _xy+T _zy-R _xz*X _w+R _xx*Z _w+(T _ay+T _by)*cos(A)-

T _bz*cos(B)*sin(A)+T _bx*sin(A)*sin(B)(2)

D _Z＝-T _xz+T _yz+T _zz+R _xy*X _w-R _xx*Y _w+T _az*cos(A)+(T _ay+T _by)*sin(A)-

T _bx*cos(A)*sin(B)(3)

D in formula (1)-(3) _x, D _y, D _zrepresent that error is at X, Y respectively, the size of Z-direction component; T represents displacement error, R represents rotation error, first subscript represents movable body title, can be X guide rail, Y guide rail, Z guide rail, A turntable or B turntable, represent with alphabetical x, y, z, a or b respectively, second subscript represents shifting axle for T, represents rotation axis, represent respectively with x, y, z for R; X _w, Y _w, Z _wbe respectively theoretical processing stand x, y, z direction coordinate figure in workpiece coordinate system; X, Y, Z, A, B represent corresponding shifting axle displacement and the size of rotation axis rotational angle respectively; Displacement error in geometric error model and rotation error are the functions of amount of movement X, Y, Z about corresponding movable body or rotational angle A, B, adopt the cubic polynomial about each body coordinates of motion to carry out each individual error of matching; Each individual error polynomial expression is carried out matching, then formula (1)-(3) just constitute the equation that can solve, fitting coefficient containing limited the unknown in equation, select the interlock scheme of certain each kinematic axis of lathe, record a series of error amounts of measurement point, substitute into recording error the value that system of equations simultaneous can obtain unknown fitting coefficient, thus also just obtain the expression formula of geometric error TRANSFER MODEL, and then for the compensation to lathe geometric error.

4. as claimed in claim 2 based on multiple axes system error modeling and the measuring method of freeform optics surface, it is characterized in that, the relative position of freeform optics surface standard component and multi-dimensional displacement measuring system is changed, the specifically position of mobile optical free form surface standard component, the situation that relative position changes is detected, specifically measures the displacement along natural system of coordinates X, Y, Z axis direction of freeform optics surface standard component or multi-dimensional displacement measuring system.

5. as claimed in claim 2 based on multiple axes system error modeling and the measuring method of freeform optics surface, it is characterized in that, displacement along Z-direction adopts laser triangulation: the axis making laser instrument, the optical axis of imaging len and image detector CCD, three is positioned at same plane, laser instrument by a desirable some dot projection on measured surface, the displacement of same distance is done in change with its position, incident point by this hot spot along the axis of laser instrument, the while of some hot spot, scioptics are imaged on image detector CCD again, and the depth location of image space and hot spot has unique corresponding relation, to measure on image detector CCD become the center of real image, namely the computing method by geometrical optics obtain hot spot Z-direction coordinate this moment, thus obtain the Z-direction displacement at this some place of measured surface.