阅读说明：本技术 四轴坐标测量机回转台误差辨识方法 (Error identification method for rotary table of four-axis coordinate measuring machine ) 是由 张旭 沈毅君 杨康宇 朱利民 于 2020-06-09 设计创作，主要内容包括：本发明提供一种四轴坐标测量机回转台误差辨识与补偿方法,包括：在回转台中心建立转台坐标系,根据回转台几何误差模型获得不同旋转角度下实际坐标与理论坐标的位置关系,将标准球安装在回转台三个不同位置旋转一周获得三组对应位置关系构建误差矩阵方程,通过最小二乘法得到不同角度下回转台的回转轴几何误差,最后通过线性插值获得360°内任意角度的几何误差。与机床上广泛应用球杆仪辨识方法相比,本方法安装次数少,操作要求低,降低了实验难度,对具有三平动轴的坐标测量机和机床均适用。(The invention provides a method for identifying and compensating errors of a rotary table of a four-axis coordinate measuring machine, which comprises the following steps: a rotary table coordinate system is established in the center of a rotary table, the position relation between actual coordinates and theoretical coordinates under different rotation angles is obtained according to a geometrical error model of the rotary table, a standard ball is arranged at three different positions of the rotary table and rotates for a circle to obtain three groups of corresponding position relations to construct an error matrix equation, the geometrical errors of the rotary table under different angles are obtained through a least square method, and finally the geometrical errors of any angle within 360 degrees are obtained through linear interpolation. Compared with the method for identifying the ball arm instrument widely applied to the machine tool, the method has the advantages of less installation times, low operation requirement, reduced experiment difficulty and suitability for the coordinate measuring machine with three moving axes and the machine tool.)

1. A method for identifying and compensating errors of a rotary table of a four-axis coordinate measuring machine is characterized by comprising the following steps:

a rotary table coordinate system is established in the center of a rotary table, the position relation between actual coordinates and theoretical coordinates under different rotation angles is obtained according to a geometrical error model of the rotary table, a standard ball is arranged at three different positions of the rotary table and rotates for a circle to obtain three groups of corresponding position relations to construct an error matrix equation, the geometrical errors of the rotary table under different angles are obtained through a least square method, and finally the geometrical errors of any angle within 360 degrees are obtained through linear interpolation.

2. The method for error identification and compensation of a four-axis coordinate measuring machine turret of claim 1, further comprising the steps of:

step S1, establishing a turntable coordinate system OXYZ at the center of the turntable;

step S2, installing a standard ball at a position on the rotary table, and measuring the initial coordinate P of the center of the standard ball₁ ⁰(x₁,y₁,z₁)；

Step S3, rotating the rotary table for one circle at certain angle intervals, and calculating the theoretical coordinate of the sphere center according to the formula (1) at each rotation angle theta;

the theoretical coordinates of the centre of sphere are:

measuring the actual coordinates of the center of the standard ball;

the actual coordinates of the center of the sphere are:

the error of the actual coordinates of the center of sphere from the theoretical coordinates is expressed as:

wherein_xc、_ycAnd_zcis the translational error of the rotating shaft of the rotary table in three directions,_xc、_ycand_zcthe rotation errors of the rotating shaft of the rotary table in three directions are obtained;

step S4, respectively installing the standard balls at the other two positions on the rotary table, repeating the steps S2 and S3 at the same angle interval, and obtaining the position relation between the actual coordinates and the theoretical coordinates of the three groups of ball centers under each rotation angle theta; for each rotation angle theta, the corresponding error matrix equation is as follows:

wherein, in the other two positions,

the initial coordinates of the center of the standard ball are respectively P₂ ⁰(x₂,y₂,z₂)、P₂ ⁰(x₃,y₃,z₃)；

At each rotation angle theta, the theoretical coordinates of the sphere center of the standard sphere are respectively as follows:

at each rotation angle θ, the actual coordinates of the center of the standard sphere are:

the above formula (6) is noted as: AX ═ b, then according to the least squares method:

according to the method, the geometric errors of the rotary table under the discrete angles can be obtained, for any rotation angle alpha, firstly, the range from 0 to 360 degrees is periodically adjusted to be recorded as beta, then two discrete angles theta nearest to the beta are searched, and the six geometric errors corresponding to the alpha angle, namely the translation errors in three directions of the rotary shaft of the rotary table and the rotation errors in three directions of the rotary shaft of the rotary table, are obtained by utilizing linear interpolation.

3. The method for error identification and compensation of a four-axis coordinate measuring machine turret of claim 2,

in step S2, specifically, five different points on the standard sphere are detected by using the measuring head, and the initial coordinates of the sphere center are obtained by the least square method;

or, scanning a plurality of tracks on the spherical surface of the standard sphere by using the measuring head to perform fitting so as to obtain the initial coordinate of the sphere center.

4. The method for error identification and compensation of a four-axis coordinate measuring machine turret of claim 2,

in step S3, specifically, a measuring head is used to detect five different points on the standard sphere at each rotation angle θ, and the actual coordinates of the sphere center are obtained by a least square method;

or, scanning a plurality of tracks on the spherical surface of the standard sphere by using the measuring head to perform fitting to obtain the actual coordinate of the sphere center.

5. The four-axis CMM turret error identification and compensation method of claim 3 or 4,

five different points on the standard sphere are four points uniformly distributed on the north pole and the equator.

Technical Field

The invention belongs to the field of measurement of coordinate measuring machines and precision machinery, and particularly relates to an error identification method for a rotary table of a four-axis coordinate measuring machine.

Background

The three-coordinate measuring machine can detect the size, the shape and the position of parts and has wide application in the machining and measuring fields of mechanical manufacture, automobile production line, aerospace and the like. However, increased production requirements place higher demands on the measurement efficiency. For the measurement of revolving body type parts, such as engine sleeves, aero-engine blades and the like, the measurement efficiency is low only by means of a traditional three-coordinate measuring machine, and therefore, a revolving platform is arranged on the traditional three-coordinate measuring machine to form a four-axis coordinate measuring machine.

Different from the well-established geometric error modeling and identification of a translational axis, the error modeling method and the identification method of the rotational axis have a plurality of explorations. Due to the development of machining and manufacturing technologies, the numerical control machining center has been developed in the direction of multi-axis linkage, particularly a five-axis numerical control machine tool, which is provided with two rotary tables, so that a large number of methods for modeling and identifying the geometric errors of the double rotary tables of the five-axis machine tool have been proposed, and among these methods, a ball bar instrument is widely used due to its good measurement performance. The coordinate measuring machine with the rotary table is obviously simpler in structure than a five-axis numerical control machine tool, so that a rotary table error identification method on the five-axis numerical control machine tool can be used for reference with respect to a modeling and identification method of the rotary table.

However, only one geometric error can be obtained at one time of installation position of the ball rod instrument, the ball rod instrument needs to be installed for many times in order to identify six geometric errors of the rotary table, and the ball rod instrument needs to be kept parallel to the coordinate axis in real time, so that the requirement on experimental operation is high.

Disclosure of Invention

In order to overcome the defects of repeated installation, high operation requirement and the like in the process of identifying the geometric error of the rotary table by the ball rod instrument, the invention provides the error identification method of the rotary table of the four-axis coordinate measuring machine, which can utilize a high-precision standard ball to replace the ball rod instrument to carry out geometric identification on the rotary table and finally obtain the geometric error of the rotary table.

The embodiment of the invention adopts the technical scheme that:

a method for identifying and compensating errors of a rotary table of a four-axis coordinate measuring machine comprises the following steps:

a rotary table coordinate system is established in the center of a rotary table, the position relation between actual coordinates and theoretical coordinates under different rotation angles is obtained according to a geometrical error model of the rotary table, a standard ball is arranged at three different positions of the rotary table and rotates for a circle to obtain three groups of corresponding position relations to construct an error matrix equation, the geometrical errors of the rotary table under different angles are obtained through a least square method, and finally the geometrical errors of any angle within 360 degrees are obtained through linear interpolation.

Further, the method specifically comprises the following steps:

step S1, establishing a turntable coordinate system OXYZ at the center of the turntable;

step S2, installing a standard ball at a position on the rotary table, and measuring the initial coordinate P of the center of the standard ball₁ ⁰(x₁,y₁,z₁)；

Step S3, rotating the rotary table for one circle at certain angle intervals, and calculating the theoretical coordinate of the sphere center according to the formula (1) at each rotation angle theta;

the theoretical coordinates of the centre of sphere are:

measuring the actual coordinates of the center of the standard ball;

the actual coordinates of the center of the sphere are:

the error of the actual coordinates of the center of sphere from the theoretical coordinates is expressed as:

wherein_xc、_ycAnd_zcis the translational error of the rotating shaft of the rotary table in three directions,_xc、_ycand_zcthe rotation errors of the rotating shaft of the rotary table in three directions are obtained;

step S4, respectively installing the standard balls at the other two positions on the rotary table, repeating the steps S2 and S3 at the same angle interval, and obtaining the position relation between the actual coordinates and the theoretical coordinates of the three groups of ball centers under each rotation angle theta; for each rotation angle theta, the corresponding error matrix equation is as follows:

wherein, in the other two positions,

the initial coordinates of the center of the standard ball are respectively P₂ ⁰(x₂,y₂,z₂)、P₂ ⁰(x₃,y₃,z₃)；

At each rotation angle theta, the theoretical coordinates of the sphere center of the standard sphere are respectively as follows:

at each rotation angle θ, the actual coordinates of the center of the standard sphere are:

the above formula (6) is noted as: AX ═ b, then according to the least squares method:

according to the method, the geometric errors of the rotary table under the discrete angles can be obtained, for any rotation angle alpha, firstly, the range from 0 to 360 degrees is periodically adjusted to be recorded as beta, then two discrete angles theta nearest to the beta are searched, and the six geometric errors corresponding to the alpha angle, namely the translation errors in three directions of the rotary shaft of the rotary table and the rotation errors in three directions of the rotary shaft of the rotary table, are obtained by utilizing linear interpolation.

Further, in step S2, specifically, the probe is used to detect five different points on the standard sphere, and the initial coordinates of the sphere center are obtained by the least square method;

or, scanning a plurality of tracks on the spherical surface of the standard sphere by using the measuring head to perform fitting so as to obtain the initial coordinate of the sphere center.

Further, in step S3, specifically, the measuring head is used to detect five different points on the standard sphere at each rotation angle θ, and the actual coordinates of the sphere center are obtained by the least square method;

or, scanning a plurality of tracks on the spherical surface of the standard sphere by using the measuring head to perform fitting to obtain the actual coordinate of the sphere center.

Furthermore, the five different points on the standard sphere are four points evenly distributed on the north pole and the equator.

The invention has the advantages that:

1) the coordinate measuring machine with 21 geometric errors and the carried high-precision measuring head are used to ensure that the coordinate measuring machine has higher precision; a high-precision standard ball is used as a detection feature, five points of the spherical surface are detected at each rotation angle, the spherical center coordinate of the five points can be obtained by using a least square algorithm, and the high precision of the spherical center coordinate is ensured by the high precision of the measuring head and the standard ball.

2) The standard ball is only required to be arranged at three different positions of the rotary table, and the installation has low requirement on operation.

3) The method can be directly used for identifying the accuracy of the rotary table after compensating the geometric error of the rotary table.

4) The method has low requirement on the rotary table, only needs high repeated positioning precision of the rotary table, and has no high requirement on the absolute positioning precision of the rotary table, so that a direct-drive precise rotary table can be selected when the rotary table is configured, and an air-float rotary table is not required.

Drawings

FIG. 1 is a schematic structural diagram of a four-axis coordinate measuring machine with a turntable according to an embodiment of the present invention.

Fig. 2 is a schematic diagram of a coordinate system of a turntable in an embodiment of the invention.

Fig. 3 is a diagram of five-point detection of the trigger probe according to the embodiment of the present invention.

Fig. 4 is a scanning probe scanning route diagram in the embodiment of the present invention.

Detailed Description

The invention is further illustrated by the following specific figures and examples.

The embodiment of the invention provides an error identification and compensation method for a rotary table of a four-axis coordinate measuring machine, which comprises the following steps: a rotary table coordinate system is established in the center of a rotary table, the position relation between actual coordinates and theoretical coordinates under different rotation angles is obtained according to a geometrical error model of the rotary table, a standard ball is arranged at three different positions of the rotary table and rotates for a circle to obtain three groups of corresponding position relations to construct an error matrix equation, the geometrical errors of the rotary table under different angles are obtained through a least square method, and finally the geometrical errors of any angle within 360 degrees are obtained through linear interpolation.

In fig. 1, a three-coordinate measuring machine 1 is provided with a rotary table 2, and a measuring head 3 is arranged above the rotary table 2;

firstly, according to a modeling mode of a translation axis of a traditional three-coordinate measuring machine, a 21-item geometric error model including three verticality is established, the 21 errors are measured through matching of laser and an optical lens group, the geometric error identification and compensation of the traditional three-coordinate measuring machine are completed, then a high-precision measuring head is installed, and the measuring head parameters are calibrated; this section is not of interest for the present invention, but is presented for simplicity;

the embodiment of the invention provides an error identification and compensation method for a rotary table of a four-axis coordinate measuring machine, which comprises the following steps:

establishing a turntable coordinate system OXYZ at the center of the rotary table, as shown in FIG. 2; let a certain point under the coordinate system of the turntable be marked as P (x)₁,y₁,z₁) When the turntable rotates by an angle θ, theoretical coordinates of a corresponding point of the point are (superscript i represents ideal:

because of the existence of geometric errors, the actual coordinates and the theoretical coordinates of the corresponding points of the points have deviation, a revolving shaft geometric error model of a revolving platform similar to a horizontal axis is established based on a small error deformation hypothesis and a rigid body homogeneous coordinate transformation principle, and the corresponding transformation matrix is as follows:

wherein_xc、_ycAnd_zcis the translational error of the rotating shaft of the rotary table in three directions,_xc、_ycand_zcthe rotation errors of the rotating shaft of the rotary table in three directions are obtained; the actual coordinates of the corresponding point of that point are:

the error between the actual coordinate and the theoretical coordinate of the corresponding point of the point is:

the arrangement into a matrix form is:

the unknowns at each angle θ are six quantities, as defined by the geometric error: three translational errors and three rotational errors; the unknowns at each angle θ are six quantities, as defined by the geometric error: three translational errors and three rotational errors; obviously, only three equations of one point can not solve the six quantities, and at least one point is needed to be in a position relation; if only the corresponding position relationship of two points is available, the coefficient matrix is easy to be singular, and the obtained six quantities cannot be uniquely determined, so that the position corresponding relationship of three points can be selected for solving; when three points are used, the error matrix equation is:

the above formula is noted as: AX ═ b, then according to the least squares method:

according to the theoretical derivation, the geometric error at each angle needs the position relation of three points, the three-coordinate measuring machine is provided with the high-precision measuring head 3, and the measuring head is calibrated by adopting a high-precision standard ball, so that the measuring head and the standard ball can be repeatedly utilized to identify 6 geometric errors at each angle;

the specific process is as follows:

step S1, establishing a turntable coordinate system OXYZ at the center of the turntable;

step S2, installing a standard ball 4 at a position on the rotary table 3, and measuring the initial coordinate P of the center of the standard ball₁ ⁰(x₁,y₁,z₁)；

Specifically, the measuring head can be used for detecting five different points on a standard sphere, preferably four points uniformly distributed on the north pole and the equator, and the initial coordinate of the sphere center is obtained by a least square method; the measuring head can adopt a trigger measuring head; as shown in fig. 3;

or, scanning a plurality of tracks on the spherical surface of the standard sphere by using the measuring head to perform fitting to obtain an initial coordinate of the sphere center; the measuring head can adopt a scanning type measuring head; as shown in fig. 4;

step S3, rotating the turntable 3 by one rotation at a certain angle interval (for example, 30 degrees), and calculating the theoretical coordinates of the center of sphere according to the formula (1) at each rotation angle θ;

the theoretical coordinates of the centre of sphere are:

measuring the actual coordinates of the center of the standard ball;

specifically, a measuring head is used for detecting five different points on a standard sphere under each rotation angle theta, preferably four points uniformly distributed on a north pole and an equator, and the actual coordinates of the sphere center are obtained through a least square method; the measuring head can adopt a trigger measuring head; as shown in fig. 3;

or, scanning a plurality of tracks on the spherical surface of the standard sphere by using the measuring head to perform fitting to obtain the actual coordinate of the sphere center; the measuring head can adopt a scanning type measuring head; as shown in fig. 4;

recommending five tracks, wherein the equations of the five tracks are as follows:

x is 0, z is more than 0(or z is less than 0, and the circle is selected to be half circle)

y is 0, z is more than 0(or z is less than 0, and the circle is selected to be half circle)

z＝0

x is y, z is more than 0(or z is less than 0, and the circle is selected to be half circle)

x is-y, z is more than 0(or z is less than 0, selected from semicircle)

In order to fit the center of the sphere, two tracks are selected from the five tracks for scanning and measurement;

the actual coordinates of the center of the sphere are:

the error of the actual coordinates of the center of sphere from the theoretical coordinates is expressed as:

wherein_xc、_ycAnd_zcis the translational error of the rotating shaft of the rotary table in three directions,_xc、_ycand_zcthe rotation errors of the rotating shaft of the rotary table in three directions are obtained;

step S4, respectively installing the standard balls at the other two positions on the rotary table 3, repeating the steps S2 and S3 at the same angle interval, and obtaining the position relation between the actual coordinates and the theoretical coordinates of the three groups of ball centers under each rotation angle theta; for each rotation angle theta, the corresponding error matrix equation is as follows:

wherein, in the other two positions,

the initial coordinates of the center of the standard ball are respectively P₂ ⁰(x₂,y₂,z₂)、P₂ ⁰(x₃,y₃,z₃)；

At each rotation angle theta, the theoretical coordinates of the sphere center of the standard sphere are respectively as follows:

at each rotation angle θ, the actual coordinates of the center of the standard sphere are:

the above formula (6) is noted as: AX ═ b, then according to the least squares method:

according to the method, the geometric errors of the rotary table under the discrete angles can be obtained, for any rotation angle alpha, firstly, the range from 0 to 360 degrees is periodically adjusted to be recorded as beta, then two discrete angles theta nearest to the beta are searched, and the six geometric errors corresponding to the alpha angle, namely the translation errors in three directions of the rotary shaft of the rotary table and the rotation errors in three directions of the rotary shaft of the rotary table, are obtained by utilizing linear interpolation.

Compared with the method for identifying the ball arm instrument widely applied to the machine tool, the method has the advantages of less installation times, low operation requirement, reduced experiment difficulty and suitability for the coordinate measuring machine with three moving axes and the machine tool.

Finally, it should be noted that the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to examples, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.