阅读说明：本技术 圆柱坐标测量机下非正交非线性三维扫描测头标定方法 (Non-orthogonal non-linear three-dimensional scanning measuring head calibration method under cylindrical coordinate measuring machine ) 是由 张旭 杨康宇 朱利民 于 2020-06-09 设计创作，主要内容包括：本发明提供一种圆柱坐标测量机下非正交非线性三维扫描测头标定方法,包括：采用标准球作为标定参考物,构建多条扫描轨迹,建立以球面约束为目标函数的优化问题,并针对三阶项系数过小,进行系数估计调整,得到适合优化的球面约束目标函数,利用Levenberg-Marquardt算法实现优化。以多元泰勒函数展开理论建立非正交三维扫描测头三阶非线性优化模型,是正交三维扫描测头的推广,模型适用性广。优化时分两次进行,第一次优化低阶系数,据此预估三阶系数,第二次优化时调整系数数量级大概至同一数量级,同步微调目标函数,直接优化出三阶所有系数,避免了直接进行三阶优化时因数量级差别过大而无法优化出第三阶系数的问题。(The invention provides a calibration method of a non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine, which comprises the following steps: the method comprises the steps of constructing a plurality of scanning tracks by using a standard ball as a calibration reference, establishing an optimization problem by using spherical constraint as a target function, carrying out coefficient estimation and adjustment aiming at the condition that the coefficient of the third order term is too small to obtain a spherical constraint target function suitable for optimization, and realizing optimization by using a Levenberg-Marquardt algorithm. A three-order nonlinear optimization model of the non-orthogonal three-dimensional scanning measuring head is established by using a multivariate Taylor function expansion theory, so that the method is popularization of the orthogonal three-dimensional scanning measuring head and has wide model applicability. The optimization is carried out in two times, the low-order coefficient is optimized for the first time, the third-order coefficient is estimated, the order of magnitude of the coefficient is adjusted to be approximately the same order of magnitude during the second optimization, the objective function is finely adjusted synchronously, all the third-order coefficients are directly optimized, and the problem that the third-order coefficient cannot be optimized due to overlarge difference of the order of magnitude of the factor during the direct third-order optimization is solved.)

1. A non-orthogonal non-linear three-dimensional scanning measuring head calibration method under a cylindrical coordinate measuring machine is characterized by comprising the following steps: the method comprises the steps of constructing a plurality of scanning tracks by using a standard ball as a calibration reference, establishing an optimization problem by using spherical constraint as a target function, carrying out coefficient estimation and adjustment aiming at the condition that the coefficient of the third order term is too small to obtain a spherical constraint target function suitable for optimization, and realizing optimization by using a Levenberg-Marquardt algorithm.

2. The method for calibrating the non-orthogonal non-linear three-dimensional scanning measuring head under the cylindrical coordinate measuring machine according to claim 1, wherein the method specifically comprises the following steps:

defining three axes including two translation axes X and Z and a rotation axis C in a cylindrical coordinate measuring machine; and correspondingly establishing a coordinate system;

establishing a machine coordinate system W of a cylindrical coordinate measuring machine_MAnd a measuring head coordinate system W of a measuring head on the cylindrical coordinate measuring machine_T(ii) a The machine coordinate system takes a zero position of a cylindrical coordinate measuring machine as an original point of coordinates, and the measuring head coordinate system takes a measuring ball center on the measuring head as an original point; the three-axis directions of the measuring head coordinate system and the machine coordinate system are the same;

establishing a turntable coordinate system W_C: the axis of the rotary table is taken as the Z axis of the coordinate system of the rotary table, and the origin of the coordinates is taken as the axis and the machine coordinate system W_MThe cross multiplication result of the Z axis of the turntable coordinate system and the X axis of the machine coordinate system is used as the Y axis of the turntable coordinate system, and then the X axis of the turntable coordinate system is determined according to a right-hand rule;

establishing a coordinate system W of a movable turntable_R: initial position and W_CA coordinate system which is completely overlapped and rotates along with the rotary table;

determining points under a coordinate system of a stylus^TP and points under the coordinate system of the movable turntable^RP is a mutual transformation relation;

step two, mounting a standard ball on the rotary table, and measuring the center of the standard ball;

step three, taking the deformation of the measuring head as the standard sphere center coordinate S₀Planning six scanning tracks: selecting two appropriate deformation quantities according to the properties of the measuring head₁And₂planning a scanning track and obtaining motion control quantities of three shafts of the cylindrical coordinate measuring machine;

step four, recording the output quantity p of the initial voltage of the measuring head before scanning₀、q₀、r₀(ii) a Then controlling a cylindrical coordinate measuring machine to scan six tracks on a standard ball in a three-axis linkage manner, recording the three-axis motion amount corresponding to each position during real-time scanning, and outputting the voltage output p of a measuring head₁、q₁、r₁；

The voltage output quantity corresponding to the deformation of the measuring head is respectively as follows:

and step five, obtaining a third-order equation relation between the measuring head deformation amount and the voltage output amount corresponding to the measuring head deformation according to the Taylor function expansion theory:

all measurement points are on a spherical surface with S as the center and the radius R, and R is R₁+R₂，R₁Is a standard spherical radius, R₂The radius of a measuring ball on a measuring head; constructing an optimization problem taking spherical constraint as an objective function:

step six, substituting the data into the objective function to carry out optimization twice: setting the third-order coefficient C as 0 for the first time, and optimizing coefficients A and B by utilizing a Levenberg-Marquardt algorithm; estimating the magnitude of C for the second time according to the magnitude of A and B, and then adjusting the magnitude of B and C to be approximately the same as the magnitude of A, so that the problem that the C cannot be optimized because the coefficient is too small is avoided; the objective function is adjusted accordingly and the coefficients A, B, C are then optimized again using the Levenberg-Marquardt algorithm, as well as the center position S and the gage radius of the gage head.

3. The method for calibrating a non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine according to claim 2,

in the first step, points under the coordinate system of the measuring head^TP and points under the coordinate system of the movable turntable^RThe P mutual transformation relation is as follows:

note the book

^RP＝Trans(Z,X,θ)^TP

^TP＝Trans^-1(Z,X,θ)^RP

Wherein the content of the first and second substances,for the transformation of the turntable coordinate system to the machine coordinate system,

4. The method for calibrating a non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine according to claim 2,

and in the second step, three axes of the cylindrical coordinate measuring machine are manually controlled to move to detect five points on the standard sphere, and the sphere center is obtained by fitting with a least square method.

5. The method for calibrating a non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine according to claim 2,

in step three, six scanning tracks are:

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)

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)

z＝0

Wherein R is₁Is the standard sphere radius.

6. The method for calibrating a non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine according to claim 2,

and step six, before data substitution, removing a part of points of each track entering and leaving the spherical surface.

7. The method for calibrating a non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine according to claim 2,

after the sixth step, the method also comprises the following steps:

and seventhly, after the result is optimized, the error and the root mean square RMS of each point are solved, and the calibration accuracy of the measuring head parameters is evaluated.

Technical Field

The invention belongs to the field of precision measurement, and particularly relates to a calibration method of a non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine.

Background

The coordinate measuring machine can detect the size, the shape and the position of the part, and is widely applied to industrial production. The measurement precision is closely related to the precision of the adopted measuring head except the coordinate axis motion control precision. With the development of sensor technology and measurement technology, three-dimensional scanning probes play an increasingly important role in scanning measurement due to their high-precision characteristics. The three-dimensional scanning measuring head can be divided into an orthogonal measuring head and a non-orthogonal measuring head, and for the orthogonal measuring head, three-dimensional output quantities are not related to each other, so that the measuring head parameter calibration is relatively simple; for a non-orthogonal measuring head, three-dimensional output quantities are mutually coupled, and in order to achieve measurement accuracy, a high-order polynomial must be adopted to describe the relation between the measuring head deformation quantity and the three-dimensional output quantities, so that the characteristics of nonlinearity, multiple parameters and difficult calibration are presented.

The non-orthogonal three-dimensional measuring head calibration under the three-coordinate measuring machine has been realized by some foreign companies (such as Renishaw) to realize high-precision calibration, but the parameter calibration under the cylindrical coordinate measuring machine is not realized. The parameter calibration of the non-orthogonal three-dimensional scanning measuring head is essentially a three-dimensional non-linear optimization problem, the non-linear optimization is a difficult problem originally, and for the non-orthogonal three-dimensional scanning measuring head, in order to obtain higher precision, a third-order polynomial is generally adopted to describe the distance between the measuring head deformation and the three-dimensional voltage output, so that the measuring head has a large number of parameters, large optimization difficulty and easy falling into a local optimal solution. For the nonlinear least square problem, there are Gauss-Newton method, Levenberg-Marquardt method, belief domain method, and the like. The Levenberg-Marquardt method can be regarded as the combination of the steepest descent method and the Gauss-Newton method, when the current optimal solution of dissociation is far away, the algorithm is closer to the steepest descent method, and the calculation is slow but the descent is guaranteed; the current solution is close to the optimal solution, the algorithm is close to the Gauss-Newton method, and rapid convergence can be achieved.

Disclosure of Invention

In order to overcome the defects of multiple calibration parameters, difficulty in optimization and the like of a non-orthogonal three-dimensional scanning measuring head, the invention provides a calibration method of the non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine. The technical scheme adopted by the invention is as follows:

a non-orthogonal non-linear three-dimensional scanning measuring head calibration method under a cylindrical coordinate measuring machine comprises the following steps: the method comprises the steps of constructing a plurality of scanning tracks by using a standard ball as a calibration reference, establishing an optimization problem by using spherical constraint as a target function, carrying out coefficient estimation and adjustment aiming at the condition that the coefficient of the third order term is too small to obtain a spherical constraint target function suitable for optimization, and realizing optimization by using a Levenberg-Marquardt algorithm.

Further, the method specifically comprises the following steps:

defining three axes including two translation axes X and Z and a rotation axis C in a cylindrical coordinate measuring machine; and correspondingly establishing a coordinate system;

establishing a machine coordinate system W of a cylindrical coordinate measuring machine_MAnd a measuring head coordinate system W of a measuring head on the cylindrical coordinate measuring machine_T(ii) a The machine coordinate system takes a zero position of a cylindrical coordinate measuring machine as an original point of coordinates, and the measuring head coordinate system takes a measuring ball center on the measuring head as an original point; the three-axis directions of the measuring head coordinate system and the machine coordinate system are the same;

establishing a turntable coordinate system W_C: the axis of the rotary table is taken as the Z axis of the coordinate system of the rotary table, and the origin of the coordinates is taken as the axis and the machine coordinate system W_MThe cross multiplication result of the Z axis of the turntable coordinate system and the X axis of the machine coordinate system is used as the Y axis of the turntable coordinate system, and then the X axis of the turntable coordinate system is determined according to a right-hand rule;

establishing a coordinate system W of a movable turntable_R: initial position and W_CA coordinate system which is completely overlapped and rotates along with the rotary table;

determining points under a coordinate system of a stylus^TP and points under the coordinate system of the movable turntable^RP is a mutual transformation relation;

step two, mounting a standard ball on the rotary table, and measuring the center of the standard ball;

step three, taking the deformation of the measuring head as the standard sphere center coordinate S₀Planning six scanning tracks: selecting two appropriate deformation quantities according to the properties of the measuring head₁And₂planning a scanning track and obtaining motion control quantities of three shafts of the cylindrical coordinate measuring machine;

step four, recording the output quantity p of the initial voltage of the measuring head before scanning₀、q₀、r₀(ii) a Then controlling a cylindrical coordinate measuring machine to scan six tracks on a standard ball in a three-axis linkage manner, recording the three-axis motion amount corresponding to each position during real-time scanning, and outputting the voltage output p of a measuring head₁、q₁、r₁；

The voltage output quantity corresponding to the deformation of the measuring head is respectively as follows:

p＝p₁-p₀

q＝q₁-q₀；

r＝r₁-r₀

and step five, obtaining a third-order equation relation between the measuring head deformation amount and the voltage output amount corresponding to the measuring head deformation according to the Taylor function expansion theory:

all measurement points are on a spherical surface with S as the center and the radius R, and R is R₁+R₂，R₁Is a standard spherical radius, R₂The radius of a measuring ball on a measuring head; constructing an optimization problem taking spherical constraint as an objective function:

step six, substituting the data into the objective function to carry out optimization twice: setting the third-order coefficient C as 0 for the first time, and optimizing coefficients A and B by utilizing a Levenberg-Marquardt algorithm; estimating the magnitude of C for the second time according to the magnitude of A and B, and then adjusting the magnitude of B and C to be approximately the same as the magnitude of A, so that the problem that the C cannot be optimized because the coefficient is too small is avoided; the objective function is adjusted accordingly and the coefficients A, B, C are then optimized again using the Levenberg-Marquardt algorithm, as well as the center position S and the gage radius of the gage head.

Furthermore, in the first step, the points in the coordinate system of the measuring head^TP and points under the coordinate system of the movable turntable^RThe P mutual transformation relation is as follows:

note the book

^RP＝Trans(Z,X,θ)^TP

^TP＝Trans-¹(Z,X,θ)^RP

Wherein the content of the first and second substances,for the transformation of the turntable coordinate system to the machine coordinate system,for the transformation relationship from the movable turntable coordinate system to the turntable coordinate system,

is the transformation relation from the translation axis Z-axis coordinate system of the cylindrical coordinate measuring machine to the machine coordinate system,is the transformation relation from a translation axis X-axis coordinate system of the cylindrical coordinate measuring machine to a translation axis Z-axis coordinate system of the cylindrical coordinate measuring machine,the conversion relation from a measuring head coordinate system to a cylindrical coordinate measuring machine translation axis X-axis coordinate system is obtained; trans (Z, X, θ) is a conversion formula between coordinate systems under three-axis motion amounts (Z, X, θ) of the cylindrical coordinate measuring machine.

Furthermore, in the second step, the three axes of the cylindrical coordinate measuring machine are manually controlled to move to detect five points on the standard sphere, and the sphere center is obtained by using least square fitting.

Furthermore, in step three, the six scanning tracks are:

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)

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)

z＝0

Or

Wherein R is₁Is the standard sphere radius.

Furthermore, in step six, before the data substitution, a part of points of each track entering and leaving the sphere are removed.

Further, after the sixth step, the method further comprises:

and seventhly, after the result is optimized, the error and the root mean square RMS of each point are solved, and the calibration accuracy of the measuring head parameters is evaluated.

The invention has the advantages that: .

(1) A three-order optimization model of the non-orthogonal non-linear three-dimensional scanning measuring head is constructed by using a multivariate Taylor function expansion theory, so that the method is popularization of the orthogonal three-dimensional scanning measuring head and is wide in model applicability.

(2) The standard ball is used as a calibration reference, the spherical scanning track is similar to the measuring head posture in the actual measurement of the rotary part, and the actual production condition is met.

(3) The optimization is carried out in two times, the low-order coefficient is optimized for the first time, the third-order coefficient is estimated, the order of magnitude of the coefficient is adjusted to be approximately the same order of magnitude during the second optimization, the objective function is finely adjusted synchronously, all the third-order coefficients are directly optimized, and the problem that the third-order coefficient cannot be optimized due to overlarge difference of the order of magnitude of the factor during the direct third-order optimization is solved.

Drawings

FIG. 1 is a schematic diagram of a cylindrical coordinate measuring machine and coordinate system setup in an embodiment of the present invention.

Fig. 2 is a schematic diagram of probe scanning according to an 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 a calibration method of a non-orthogonal non-linear three-dimensional scanning measuring head under a cylindrical coordinate measuring machine, which comprises the following steps:

step one, as shown in fig. 1, defining three axes including two translational axes, an X axis and a Z axis, and a rotation axis, a C axis (i.e. a rotation axis of a turntable) in a cylindrical coordinate measuring machine; and correspondingly establishing a coordinate system;

establishing a machine coordinate system W of a cylindrical coordinate measuring machine_MAnd a measuring head coordinate system W of a measuring head on the cylindrical coordinate measuring machine_T(ii) a The machine coordinate system takes a zero position of a cylindrical coordinate measuring machine as an original point of coordinates, and the measuring head coordinate system takes a measuring ball center on the measuring head as an original point; the three-axis directions of the measuring head coordinate system and the machine coordinate system are the same;

the measuring head 1 comprises a measuring rod 101 and a measuring ball 102, wherein the measuring rod 101 can deform under the action of an acting force, and the measuring ball 102 is a ruby ball; as shown in fig. 2;

establishing a turntable coordinate system W_C: the axis of the rotary table is taken as the Z axis of the coordinate system of the rotary table, and the origin of the coordinates is taken as the axis and the machine coordinate system W_MThe cross multiplication result of the Z axis of the turntable coordinate system and the X axis of the machine coordinate system is used as the Y axis of the turntable coordinate system, and then the X axis of the turntable coordinate system is determined according to a right-hand rule;

establishing a coordinate system W of a movable turntable_R: initial position and W_CA coordinate system which is completely overlapped and rotates along with the rotary table;

determining points under a coordinate system of a stylus^TP and points under the coordinate system of the movable turntable^RThe P mutual transformation relation is as follows:

note the book

^RP＝Trans(Z,X,θ)^TP

^TP＝Trans^-1(Z,X,θ)^RP

Wherein the content of the first and second substances,

for the transformation of the turntable coordinate system to the machine coordinate system,

for the transformation relationship from the movable turntable coordinate system to the turntable coordinate system,

is the transformation relation from the translation axis Z-axis coordinate system of the cylindrical coordinate measuring machine to the machine coordinate system,

is the transformation relation from a translation axis X-axis coordinate system of the cylindrical coordinate measuring machine to a translation axis Z-axis coordinate system of the cylindrical coordinate measuring machine,

the conversion relation from a measuring head coordinate system to a cylindrical coordinate measuring machine translation axis X-axis coordinate system is obtained; trans (Z, X, theta) is a conversion formula among coordinate systems under three-axis motion quantities (Z, X, theta) of the cylindrical coordinate measuring machine;

step two, installing a standard ball on the rotary table, manually controlling the three axes of the cylindrical coordinate measuring machine to move to detect five points on the standard ball (distributed in a larger range as much as possible and improve the fitting precision of the center of the ball), fitting by using a least square method to obtain the center of the ball, and recording as S₀＝(S_0x,S_0y,S_0z)^T；

Step three, taking the deformation of the measuring head as the standard sphere center coordinate S₀Planning six scanning tracks:

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)

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)

z＝0

Or

Wherein R is₁Is the standard sphere radius;

for continuous scanning, connecting points can be properly inserted between different scanning paths, and during actual scanning, the friction force borne by the ruby measuring ball is opposite to the moving direction, and each scanning track scans once clockwise and once anticlockwise by considering the influence of the friction force;

selecting two appropriate deformation quantities according to the properties of the measuring head₁And₂planning a scanning track and obtaining motion control quantities of three shafts of the cylindrical coordinate measuring machine;

step four, recording the output quantity p of the initial voltage of the measuring head before scanning₀、q₀、r₀(ii) a Then controlling a cylindrical coordinate measuring machine to scan six tracks on a standard ball in a three-axis linkage manner, recording the three-axis motion amount corresponding to each position during real-time scanning, and outputting the voltage output p of a measuring head₁、q₁、r₁；

The voltage output quantity corresponding to the deformation of the measuring head is respectively as follows:

p＝p₁-p₀

q＝q₁-q₀；

r＝r₁-r₀

and step five, obtaining a third-order equation relation between the measuring head deformation amount and the voltage output amount corresponding to the measuring head deformation according to the Taylor function expansion theory:

all measurement points are on a spherical surface with S as the center and the radius R, and R is R₁+R₂，R₁Is a standard spherical radius, R₂The radius of a measuring ball on a measuring head; constructing an optimization problem taking spherical constraint as an objective function:

and step six, after removing a part of points of each track entering and leaving the spherical surface, substituting data into the objective function to carry out optimization twice: setting the third-order coefficient C as 0 for the first time, and optimizing coefficients A and B by utilizing a Levenberg-Marquardt algorithm; estimating the magnitude of C for the second time according to the magnitude of A and B, and then adjusting the magnitude of B and C to be approximately the same as the magnitude of A, so that the problem that the C cannot be optimized because the coefficient is too small is avoided; adjust the objective function accordingly and then optimize the coefficients A, B, C, as well as the center of sphere position S and the gauge sphere radius of the gauge head (optimized radius R minus the standard sphere radius) again using the Levenberg-Marquardt algorithm;

step seven, A, B, C unknown numbers in the optimization model respectively comprise 9 unknown numbers, 18 unknown numbers and 30 unknown numbers, the sphere center coordinate S comprises 3 unknown numbers, and the sphere radius R is measured₂So for the second order model one there are 31 unknowns and the third order model one there are 61 unknowns;

after the result is optimized, the error and the root mean square RMS of each point can be solved, and the calibration accuracy of the measuring head parameters is evaluated:

f_i＝||^RP_i-S||-R

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.