阅读说明：本技术 一种基于双球杆仪的机床几何误差分离方法 (Machine tool geometric error separation method based on double-ball-bar instrument ) 是由 王文 许凯飞 孙涛 陈占锋 卢科青 王传勇 杨贺 桑志谦 于 2021-09-02 设计创作，主要内容包括：本发明公开了一种基于双球杆仪的机床几何误差分离方法。现有利用球杆仪获得机床的各单项误差的过程繁琐,需要对球杆仪进行三次安装,效率较低,且会引入误差。本发明将双球杆仪测量装置倾斜安装,并对应规划了倾斜的机床几何误差测量路径。该测量路径为与水平面有夹角的空间圆形,通过机床三个线性轴同时联动完成,这意味着使用双球杆仪装置可以通过该路径在一次测量中获取机床三个线性轴的所有几何误差信息。相比于现有机床误差信息获得方法,本发明可以提高机床几何误差的采集效率,并避免了多次安装所带来的其他误差。此外,本发明避免了多次测量时的误差相互耦合,相比于现有的误差分离方法,提高了机床各单项误差的分离准确性。(The invention discloses a machine tool geometric error separation method based on a double-ball bar instrument. The existing process of obtaining each single error of the machine tool by using the ball rod instrument is complicated, the ball rod instrument needs to be installed for three times, the efficiency is low, and errors can be introduced. The double-ball-bar instrument measuring device is obliquely installed, and an oblique machine tool geometric error measuring path is correspondingly planned. The measuring path is a space circle with an included angle with the horizontal plane and is completed through simultaneous linkage of three linear axes of the machine tool, which means that all geometric error information of the three linear axes of the machine tool can be acquired through the path in one measurement by using the double-ball-bar instrument device. Compared with the existing method for acquiring the machine tool error information, the method can improve the acquisition efficiency of the machine tool geometric error and avoid other errors caused by multiple times of installation. In addition, the invention avoids mutual coupling of errors in multiple measurements, and improves the separation accuracy of each single error of the machine tool compared with the existing error separation method.)

1. A machine tool geometric error separation method based on a double-ball-bar instrument is characterized in that: the adopted measuring device comprises a first ball arm instrument (4), a second ball arm instrument (8), a base (10), a tilting rod (12) and a mounting disc; the two precise balls on the first ball arm instrument (4) are respectively a first precise ball (3) and a second precise ball (6); the two precise balls on the second ball arm instrument (8) are respectively a third precise ball (7) and a fourth precise ball (9); the mounting disc is rotationally connected to the base (10); the second precision ball (6) is arranged on the central shaft at the top of the mounting disc; one end of the tilting rod (12) is connected with the second precise ball (6), and the other end is connected with the third precise ball (7); the distance between the centers of the second precision ball (6) and the third precision ball (7) and the distance between the centers of the second precision ball (6) and the fourth precision ball (9) are kept unchanged; the first precision ball (3) is used for connecting a main shaft of a machine tool to be tested;

the measuring method comprises the following specific steps:

the method comprises the following steps of firstly, obliquely installing a measuring device on a workbench of a machine tool to be measured; the included angle between the rotation axis of the mounting disc and the vertical axis in the measuring device is gamma; the value range of gamma is 5-20 degrees; connecting the first precision ball 3 with a machine tool spindle;

step two, establishing a machine tool body coordinate system o₁-x₁y₁z₁And a measurement coordinate system o-xyz; coordinate system o of machine tool₁-x₁y₁z₁And the measurement coordinate system o-xyz takes the sphere center of the second precision sphere as the origin of coordinates, and the x axis is coincident; the z axis of the measuring coordinate system o-xyz is parallel to the rotation axis of the mounting disc in the measuring device;

step three, establishing a machine tool geometric error model to obtain x, y and z axis errors delta x of the main shaft in the actual motion process₁、Δy₁、Δz₁The relation between the geometric errors and the geometric errors;

step four, obtaining error information of the machine tool; making the main shaft of the machine tool do circular interpolation motion around the mounting disc; the initial center distance between the first precision ball (3) and the second precision ball (6), the initial center distance between the third precision ball (7) and the second precision ball (6), the initial center distance between the fourth precision ball (9) and the second precision ball (6), and the initial center distance between the third precision ball (7) and the fourth precision ball (9) are respectively marked as L₁、L₂、L₃、L₄(ii) a The detection values of the first cue instrument (4) and the second cue instrument (8) are respectively recorded as delta r₁、Δr₂；

The expression of the included angle theta between the connecting line of the third precision ball and the second precision ball and the connecting line of the fourth precision ball and the second precision ball is as follows:

the deviation angle alpha of the connecting line of the third precision ball and the second precision ball is as follows:

calculating the three-dimensional error (delta x, delta y, delta z) of the spindle of the machine tool in the measurement coordinate system as follows:

wherein, Deltax, Delay, Deltaz represent the three-dimensional error component of the main shaft under the measurement coordinate system at the same time,the rotation central angle around the x axis on the xoy plane when the machine tool does circular motion on the measurement coordinate system is represented;

step five, calculating the three-dimensional error (delta x) of the machine tool under the bed coordinate system₁,Δy₂,Δz₃) The following were used:

step six, calculating the delta x of a plurality of different positions₁、Δy₁、Δz₁Substitution of Δ x₁、Δy₁、Δz₁Solving undetermined coefficients in the geometric errors by using a relational expression between the geometric errors and the geometric errors; and acquiring all geometric errors of the main shaft of the machine tool in three linear axis directions.

2. The method for separating geometrical errors of a machine tool based on a double-ball-bar instrument as claimed in claim 1, wherein: the measuring device is arranged on a workbench of a machine tool to be measured through an inclined platform (1); a base (10) of the measuring device is adsorbed on the inclined plane table through magnetic force and is fixed in an auxiliary mode through a clamp, and the clamp is fixed on the inclined plane table through bolts.

3. The method for separating geometrical errors of a machine tool based on a double-ball-bar instrument as claimed in claim 1, wherein: the included angle gamma between the rotating axis of the mounting disc and the vertical axis in the measuring device is 15 degrees.

4. The method for separating geometrical errors of a machine tool based on a double-ball-bar instrument as claimed in claim 1, wherein: the materials of the inclined plane platform and the special clamp for the base are invar steel.

5. The method for separating geometrical errors of a machine tool based on a double-ball-bar instrument as claimed in claim 1, wherein: the geometric error model of the machine tool established in the step three has 21 geometric errors; the x axis, the y axis and the z axis respectively correspond to three positioning errors and three angle errors; the x axis, the y axis and the z axis are respectively provided with a corresponding verticality error; each geometric error is expressed using a polynomial.

6. The method for separating geometrical errors of a machine tool based on a double-ball-bar instrument as claimed in claim 1, wherein: x, y, z axis error Deltax of main shaft in actual motion process₁、Δy₁、Δz₁The relation between the geometric errors is shown as a formula (17);

in the formula (17), δ_ij、ε_ij、S_xy、S_yz、S_zxFor each geometric error of the linear axis of the three-axis machine,wherein i is x, y, z, j is x, y, z; and x, y and z are three-dimensional coordinates of the machine tool in the motion process.

Technical Field

The invention belongs to the technical field of machine tool error detection, and particularly relates to a machine tool geometric error separation method based on a double-ball-bar instrument.

Background

With the continuous development of modern manufacturing industry, the precision requirement of high-end technical field on parts processed by numerical control machine tools is higher and higher, and the premise of effectively detecting and separating various geometric errors of the machine tools is to improve the processing precision of the machine tools. Therefore, the key to improve the machining precision of the machine tool is to quickly and accurately detect the machine tool error. The ball rod instrument has the advantages of high detection precision, low cost, high detection efficiency, simplicity in installation, convenience in operation and the like, so that the ball rod instrument becomes one of the most widely applied instruments for detecting the geometric precision of the numerical control machine.

The ball rod instrument can detect out the comprehensive error of the machine tool, and by analyzing the arc track, the error items of the machine tool, such as perpendicularity, servo mismatching, reverse jump, straightness, proportion mismatching and the like, can be obtained and separated. However, since the ball bar instrument can only detect the error change along the length direction of the bar during the movement of the spindle of the machine tool, when the traditional ball bar instrument is used for detecting the error of the machine tool, the arc track on a single plane can only be analyzed, and all geometric errors during the movement of the machine tool cannot be detected only through single measurement. The traditional solution is as follows: firstly, a ball bar instrument is used for detecting machine tool errors on three mutually orthogonal planes (respectively defined as xoy plane, yoz plane and xoz plane), then the detection results of the three planes are combined to analyze the space precision of the machine tool, and finally, all the geometric errors of the machine tool are separated. It can be seen that the process of obtaining each single error of the machine tool by using the method is complicated, the ball rod instrument needs to be installed for three times, and the efficiency is low. More importantly, other errors are inevitably introduced in the process of repeated installation, and the error separation result of the machine tool is influenced.

The invention patent (publication No. CN112192317A) proposes a machine tool geometric error measuring device based on a double-ball-bar instrument, but an error separation method based on the device is not established and perfected. The device can detect the change condition of the z axis while measuring the xy plane error, but the z linear axis does not work in the measuring process, so the error of the z axis cannot be obtained.

Disclosure of Invention

The invention provides a method for separating geometrical errors of a machine tool based on a double-ball bar instrument, which aims to perfect a method for separating geometrical errors of the machine tool based on the existing ball bar instrument, and is based on the invention patent (publication number CN 112192317A). The specific idea is as follows: firstly, planning a spatial circular path related to the movement of three linear axes of a machine tool, reasonably installing a double-ball-bar instrument device, enabling the machine tool to do circular interpolation movement along the spatial circular path, and simultaneously acquiring spatial three-dimensional error information of the machine tool by using the double-ball-bar instrument; then processing the acquired three-dimensional error information; and finally, combining the processed three-dimensional error information with a polynomial model of each single error of the machine tool and an error model of the machine tool to separate each single error of the machine tool.

In order to solve the technical problems, the invention adopts the technical scheme that:

a machine tool geometric error separation method based on a double-ball-bar instrument adopts a measuring device which comprises a first ball-bar instrument, a second ball-bar instrument, a base, a tilting rod and a mounting disc. The two precise balls on the first ball arm instrument are respectively a first precise ball and a second precise ball. The two precise balls on the second ball arm instrument are respectively a third precise ball and a fourth precise ball. The mounting disc is rotatably connected to the base. The second precision ball is arranged on the central shaft at the top of the mounting disc. One end of the tilting rod is connected with the second precision ball, and the other end of the tilting rod is connected with the third precision ball. The center distance between the second precision ball and the third precision ball and the center distance between the second precision ball and the fourth precision ball are kept unchanged. The first precision ball is used for connecting a main shaft of a machine tool to be tested.

The measuring method comprises the following specific steps:

step one, mounting the measuring device on a workbench of a machine tool to be measured in an inclined mode. The included angle between the rotation axis of the mounting disc and the vertical axis in the measuring device is gamma; the value range of gamma is 5-20 degrees. The first precision ball 3 is connected with the main shaft of the machine tool.

Step two, establishing a machine tool body coordinate system o₁-x₁y₁z₁And a measurement coordinate system o-xyz. Coordinate system o of machine tool₁-x₁y₁z₁And the measurement coordinate system o-xyz takes the sphere center of the second precision sphere as the origin of coordinates, and the x axis is coincident; the z-axis of the measurement coordinate system o-xyz is parallel to the axis of rotation of the mounting plate in the measuring device.

Step three, establishing a machine tool geometric error model to obtain x, y and z axis errors delta x of the main shaft in the actual motion process₁、Δy₁、Δz₁And geometric errors.

And step four, acquiring error information of the machine tool. The main shaft of the machine tool makes circular interpolation motion around the mounting disc. The initial center-to-center distances of the first and second precision balls, the third and second precision balls, the fourth and second precision balls, and the third and fourth precision balls 7 and 9 are respectively marked as L₁、L₂、L₃、L₄(ii) a The detection values of the first cue instrument and the second cue instrument are respectively recorded as delta r₁、Δr₂。

The expression of the included angle theta between the connecting line of the third precision ball and the second precision ball and the connecting line of the fourth precision ball and the second precision ball is as follows:

the deviation angle alpha of the connecting line of the third precision ball and the second precision ball is as follows:

calculating the three-dimensional error (delta x, delta y, delta z) of the spindle of the machine tool in the measurement coordinate system as follows:

wherein, Deltax, Delay, Deltaz represent the three-dimensional error component of the main shaft under the measurement coordinate system at the same time,the rotation central angle around the x axis on the xoy plane when the machine tool does circular motion on the measurement coordinate system is represented;

step five, calculating the three-dimensional error (delta x) of the machine tool under the bed coordinate system₁,Δy₂,Δz₃) The following were used:

step six, calculating the delta x of a plurality of different positions₁、Δy₁、Δz₁Substitution of Δ x₁、Δy₁、Δz₁Solving undetermined coefficients in the geometric errors by using a relational expression between the geometric errors and the geometric errors; and acquiring all geometric errors of the main shaft of the machine tool in three linear axis directions.

Preferably, the measuring device is arranged on a workbench of the machine tool to be measured through an inclined platform; the base of the measuring device is adsorbed on the inclined plane table through magnetic force and is fixed in an auxiliary mode through a clamp, and the clamp is fixed on the inclined plane table through a bolt.

Preferably, the angle γ between the rotation axis of the mounting plate and the vertical axis in the measuring device is 15 °.

Preferably, the material of the inclined plane platform and the base special fixture is invar steel.

Preferably, the geometric error model of the machine tool established in the step three has 21 geometric errors; the x axis, the y axis and the z axis respectively correspond to three positioning errors and three angle errors; and the x axis, the y axis and the z axis respectively correspond to a verticality error. Each geometric error is expressed using a polynomial.

Preferably, the x, y and z axis errors deltax of the main shaft in the actual motion process₁、Δy₁、Δz₁The relationship between the geometric errors is as follows:

wherein, delta_ij、ε_ij、S_xy、S_yz、S_zxThe geometric errors of the linear axes of the three-axis machine tool are shown, wherein i is x, y and z, and j is x, y and z. And x, y and z are three-dimensional coordinates of the machine tool in the motion process.

The invention has the beneficial effects that:

1. the invention obliquely installs a double-ball-bar instrument measuring device (publication number CN112192317A), and correspondingly plans an oblique machine tool geometric error measuring path. The measuring path is a space circle with an included angle with the horizontal plane and is completed through simultaneous linkage of three linear axes of the machine tool, which means that all geometric error information of the three linear axes of the machine tool can be acquired through the path in one measurement by using the double-ball-bar instrument device. Compared with the existing method for acquiring the machine tool error information, the method can improve the acquisition efficiency of the machine tool geometric error and avoid other errors caused by multiple times of installation.

2. The geometric error separation method of the machine tool provided by the invention avoids mutual coupling of errors in multiple measurements, and compared with the existing error separation method, the separation method has more accurate separation results of single errors of the machine tool.

Drawings

FIG. 1 is a block diagram of a measuring device used in the present invention mounted on a bevel table;

FIG. 2 is a schematic diagram of a bed coordinate system and a measurement coordinate system;

FIG. 3 is a schematic diagram of three-dimensional error measurement of a measuring device in a measurement coordinate system;

FIG. 4 is a flow chart of the present invention.

Detailed Description

The following further describes the embodiments of the present invention with reference to the attached drawings.

A method for separately measuring geometrical errors of a machine tool based on a double-ball bar instrument, wherein the method is described in claim 1, and the method is named as a method for measuring three-dimensional errors of a main shaft of the machine tool by using the double-ball bar instrument, wherein the method is in patent number 2020110695322.

The double-cue-instrument measuring device comprises a first cue instrument 4, a second cue instrument 8, a base 10, a tilting rod 12, a first connecting rod 13, a second connecting rod 14 and a mounting disc. The two precision balls on the first cue instrument 4 are a first precision ball 3 and a second precision ball 6 respectively. The two precision balls on the second cue instrument 8 are a third precision ball 7 and a fourth precision ball 9 respectively. The mounting plate is pivotally attached to the top of the base 10. The axis of rotation of the mounting plate is perpendicular to the mounting base of the base 10. The second precision ball 6 is mounted on the central shaft at the top of the mounting plate. One end of the first cue instrument 4 is fixedly connected with one end of the tilting rod 12 through threads. The end of the warped rod 12 connecting the first cue instrument 4 is connected with the second precision ball 6 through a first ball socket. One end of the horizontal first link 13 is fixed to the mounting plate. One end of the second link 14 is connected to the second precision ball 6 via a second ball socket. The middle portion of the second link 14 is hinged to the other end of the first link 13. The end part of the warped rod 12 far away from the first cue instrument 4 and the other end of the second connecting rod 14 are respectively connected with the third precision ball 7 and the fourth precision ball 9. The end of the first link 13 connected to the second link 14 is fixed with a stopper plate. The top of the limiting plate is provided with a limiting groove. The warped rod 12 extends into the limit groove.

The measuring method comprises the following specific steps:

step one, planning a space circular path. As shown in fig. 1, an inclined plane table 1 is arranged on a worktable of a machine tool, so that the machine tool can perform spatial circular interpolation motion parallel to the inclined plane (namely, a theoretical motion track of the machine tool is projected to the inclined plane to be a standard circle), a base 10 of the double-ball-rod instrument measuring device is fixed on the inclined plane table 1 in a magnetic adsorption mode, a special base clamp 2 is used for auxiliary fixation, the special base clamp 2 is fixed on the inclined plane table through a bolt 11, and a first precision ball 3 is connected with a tool cup 5 of a main shaft of the machine tool. The included angle between the inclined plane at the top of the inclined plane table 1 and the horizontal plane is gamma; the value range of γ is 5 ° to 20 °, and 15 ° is preferable in this embodiment. The first precision ball 3 is connected with the main shaft of the machine tool through a main shaft tool cup 5.

And step two, establishing a bed coordinate system of the machine tool and a measurement coordinate system of the double-sphere rod instrument device. As shown in fig. 2, a measurement coordinate system o-xyz is established with the center of the second precision ball 6 as the origin of coordinates o, the line connecting the centers of the first precision ball 3 and the second precision ball 6 at the beginning as the y-axis direction (parallel to the inclined plane), the line parallel to the plane of the inclined plane table 1 and perpendicular to the y-axis as the x-axis direction (parallel to the x-direction of the bed coordinate system), and the direction perpendicular to the inclined plane table 1 as the z-axis direction. Establishing a bed coordinate system o of the machine tool in the direction of the X, Y, Z axes of the bed of the machine tool₁-x₁y₁z₁And make the origin o of the coordinate system of the bed₁Coinciding with the origin o of the measurement coordinate system.

And step three, establishing a geometric polynomial model of each monomial error of the machine tool and an error model of the machine tool. The specific establishment process of the model is as follows:

1. and establishing a geometric polynomial model of each single error of the machine tool.

The kinematics principle shows that an object generates errors in six spatial directions in the motion process, namely displacement errors in three directions of an x axis, a y axis and a z axis and angle errors around the x axis, the y axis and the z axis. Taking the error in the x-axis direction as an example, there is a positioning error delta when the machine tool moves along the x-axis_xxStraightness error delta when the machine moves along the y-axis_yxStraightness error delta when the machine moves along the z-axis_zxAngular error e about x, y, z axes_xx、ε_yx、ε_zx. Therefore, a three-axis machine has 18 errors, and besides, the geometric error of the machine also includes the interaxial error of the machine, namely the verticality error S_xy、S_yz、S_zx. And (3) taking the error in the x-axis direction as an example to establish a geometric polynomial model of each monomial error of the machine tool (establishing the monomial error model in the y-axis direction and the z-axis direction in the same way).

1) Positioning error model:

in the formula, a_iIs the undetermined coefficient of the polynomial. r is the radius of the circular interpolation motion of the machine tool (the same applies below). 1, 2.

2) Straightness error model:

in the formula (d)_iAnd e_iAre the undetermined coefficients of the two polynomials. i 2, 3.

3) An angle error model:

in the formula (d)_i、e_iAnd k_iIs the undetermined coefficient of the polynomial. And d is_iAnd e_iThe undetermined coefficient is the same as that of the straightness error model.

The 18 geometric errors all have corresponding polynomial models, in order to facilitate calculation, each polynomial takes a first term, 4 pending coefficients exist in an x-axis, three linear axes of the machine tool coexist in 12 pending coefficients, 3 perpendicularity errors are added, a total of 15 pending coefficients exist in 21 geometric errors of the three-axis machine tool, and the pending coefficients are solved to obtain each single error of the machine tool.

2. And establishing an error model of the machine tool.

The existing machine tool error model establishing methods mainly comprise two methods, namely a multi-body system theoretical modeling method and a screw theoretical modeling method. The error model of the machine tool can be obtained by using the two modeling methods as follows (the specific derivation process is not described in detail), wherein Δ x₁、Δy₁、Δz₁Respectively representing the motion errors along the x direction, the y direction and the z direction generated by the influence of errors during the actual motion process of the machine tool.

Wherein E is_iRepresenting a polynomial containing 21 geometric errors, i.e. E_iIs a polynomial composed of the coefficients to be determined. i is 1,2, 3.

And step four, acquiring error information of the machine tool. And (3) enabling the machine tool to perform circular interpolation motion parallel to the inclined platform 1, and measuring the three-dimensional error of the machine tool under the measurement coordinate system by using the first ball rod instrument 4 and the second ball rod instrument 8. The specific method for acquiring the three-dimensional error is as follows:

as shown in fig. 2, the center of the first precision ball 3 is denoted by a, the center of the second precision ball 6 is denoted by O, the center of the third precision ball 7 is denoted by B, and the center of the fourth precision ball 9 is denoted by C, and the error of the machine tool is reflected by the deviation of the actual coordinates of the point a when the machine tool moves, which is the point a. When measuring the machine tool error, the machine tool is made to do circular interpolation motion, and the theoretical motion circular track of the machine tool is guaranteed to be projected to the plane of the inclined plane table 1 to be a standard circle all the time, due to the existence of the machine tool error, a measuring point A will deviate from a theoretical position, and the deviation amount is defined as a three-dimensional error (consisting of delta x, delta y and delta z in a measuring coordinate system) in the measuring coordinate system. Taking this offset (three-dimensional error) as a space vector, the offset can be decomposed into a parallel slope direction (denoted as Δ xy, which is the vector sum of Δ x and Δ y in the measurement coordinate system) and a perpendicular slope direction (denoted as Δ z) in the measurement coordinate system.

As shown in fig. 3, will be shiftedPoints A, B are denoted as points a 'and B', the angle of the BOC at the time of initial mounting of the device is denoted as θ, the change in the angle after the displacement is denoted as α, the initial distance OA between the first and second precision balls 3 and 6, the initial distance OB between the third and second precision balls 7 and 6, the initial length OC between the fourth and second precision balls 9 and 6, and the initial length BC between the third and fourth precision balls 7 and 9 are denoted as L₁、L₂、L₃、L₄(ii) a Wherein the lengths of OB and OC are not changed along with the movement of the machine tool after calibration, and the length changes of OA and OB are obtained by the readings of the first cue instrument 4 and the second cue instrument 8 and are respectively marked as delta r₁、Δr₂。

The overall measurement analysis procedure was as follows:

and 1, calculating an included angle theta between the OB and the OC.

In triangular OBC, θ and L are based on the cosine theorem₂、L₃、L₄Satisfies the relation shown in formula (8):

the value of θ is then:

and 2, calculating the deviation angle alpha of the theoretical position OB and the actual position OB.

In the triangle OB' C, according to the cosine theorem, α is associated with θ and L₂、L₃、L₄、Δr₂Satisfies the relation shown in formula (10):

in combination with equation (9), α has a value of:

3. calculation of Δ xy and Δ z.

In the triangular ODA ', OD ^ DA', then Δ xy, Δ z and α, L₁、Δr₁The following relations (12) and (13) are satisfied:

L₁+Δxy＝(L₁+Δr₁)cosα (12)

Δz＝(L₁+Δr₁)sinα (13)

in the case of the combination formula (11), Δ xy and Δ z have the values:

4. and acquiring the three-dimensional error of the machine tool under the measurement coordinate system.

Wherein, Deltax, Delay, Deltaz represent the three-dimensional error component of the measuring point under the measuring coordinate system at the same time,the rotation central angle around the x axis on the xoy plane when the machine tool makes a circular motion on the measurement coordinate system is shown.

And step five, processing the obtained machine tool space three-dimensional error information, and separating out each single error of the machine tool. The method specifically comprises the following steps: and converting the three-dimensional error measured in the measurement coordinate system into a bed coordinate system of the machine tool, and combining the three-dimensional error with a geometric polynomial model of the machine tool monomial error and an error model of the machine tool to separate out each monomial geometric error of the machine tool.

1. And (3) converting the measurement coordinate system of the double-ball-bar instrument and the bed coordinate system of the machine tool.

The machine tool error model is established based on the bed coordinate system of the machine tool, and therefore, in order to combine the measurement result with the machine tool error model, the measurement result needs to be converted from the measurement coordinate system into the bed coordinate system of the machine tool, as shown in equation (17).

Therefore, the three-dimensional error of the machine tool in the bed coordinate system is as follows:

2. separating the individual geometric errors of the machine tool.

The error model of the simultaneous machine tool and the obtained three-dimensional error are shown as formula (19).

The formula (19) is an error separation expression of the geometric error separation measuring method of the machine tool based on the double-ball bar instrument, and undetermined coefficients of all single errors are solved, so that all single error expressions of the machine tool can be obtained. Each single error expression can provide more accurate theoretical guidance for the compensation of the machine tool precision.

Δ x obtained from a plurality of different positions₁、Δy₁、Δz₁And (4) substituting an equation (17) for obtaining 15 undetermined coefficients in the 21 geometric errors, so that all the geometric errors of the three linear axes of the machine tool can be obtained through only one measurement.