CN109032070B - A non-contact R-test measuring instrument calibration method using eddy current displacement sensor - Google Patents

Abstract

The invention discloses a method for calibrating a non-contact R-test measuring instrument using an eddy current displacement sensor, which includes the calibration of the measurement coordinate system and the calibration of the plane surface of the displacement sensor. Install the measuring ball on the spindle of the machine tool, place the bottom of the measuring instrument on the machine tool table, move the spindle so that the center of the measuring ball is roughly at the intersection of the three displacement sensor axes, calibrate the origin of the measuring coordinate system of the R‑test measuring instrument, and use the machine tool coordinate The system direction is used as the measurement coordinate system direction; moving the spindle moves the ball head to different coordinate points, and completes the calibration of the sensor sensing plane of the non-contact R‑test measuring instrument according to the distance from each coordinate point to the sensor sensing plane. The invention can greatly reduce the influence of the non-contact R-test measuring instrument in the processing and assembly and the installation error on the machine tool on the measurement accuracy, thereby reducing the manufacturing and use costs of the instrument, and improving the measurement accuracy and efficiency.

Description

Calibration of a non-contact R-test measuring instrument using eddy current displacement sensor method

technical field

The invention relates to the technical field of error measurement of numerically controlled machine tools, in particular to a non-contact R-test measuring instrument calibration method using an eddy current displacement sensor.

Background technique

With the improvement of machining accuracy, the geometric error measurement of five-axis CNC machine tools is becoming more and more important. For the geometric error measurement of the rotating axis of five-axis CNC machine tools, the commonly used measuring instruments are ballbar and laser interferometer. However, these measuring instruments are not dedicated to the error measurement of the rotating shaft, and have disadvantages such as low efficiency and difficulty in eliminating installation errors. Compared with the shortcomings of the above instruments, the R-test measuring instrument has the advantages of simple structure and high measurement efficiency, and can better meet the geometric error measurement requirements of the rotating axis of the five-axis CNC machine tool. FIDIA, IBS and other companies have corresponding commercial products, and they have been well used in the industry.

The R-test measuring instrument mainly adopts two measurement methods, that is, measuring the coordinates of the center of the center sphere through a contact displacement sensor or a non-contact displacement sensor. Most of the existing research on the R-test measuring instrument focuses on the contact measurement method. Liu Dawei, Li Liangliang and others proposed the measurement principle of the R-test instrument using the contact displacement sensor, and optimized its structure. Bringmann B, Ibaraki S, etc. applied the R-test instrument using the contact displacement sensor to analyze the error identification theory of the rotary axis of the five-axis CNC machine tool, and verified the effectiveness of the equipment with corresponding experiments and simulations. Li J proposed an R-test instrument using a non-contact displacement sensor, and analyzed the identification algorithm of the device. The measurement algorithm of the contact R-test measuring instrument is relatively simple, and the deviation of the sensor installation position will not affect the measurement results, but the reading sensitivity of the sensor is not high due to mechanical structure problems, and the contact wear also affects the measurement accuracy to a certain extent. . The non-contact R-test measuring instrument can avoid measurement errors caused by measurement wear, and can measure under the condition of high-speed rotation of the spindle, with better measurement sensitivity and stability. However, the structural processing and assembly of the non-contact measuring instrument have a great influence on the measurement accuracy, and it is very difficult to improve the accuracy of the instrument itself. In addition, limited by the conditions of the measurement site, it is difficult to install the instrument on the machine tool to achieve the installation accuracy when pre-calibrated. Therefore, an on-site calibration method (including calibration of the measurement coordinate system, calibration of the sensor sensing plane under the measurement coordinate system, and calibration of the center of the induction plane under the measurement coordinate system) is urgently needed. Contact measuring instrument structure processing and assembly and field installation requirements.

SUMMARY OF THE INVENTION

In view of the above problems, the purpose of the present invention is to provide a non-contact R-test measuring instrument that can greatly reduce the influence of the non-contact R-test measuring instrument in the processing and assembly and the installation error on the machine tool on the measurement accuracy, thereby reducing the manufacturing and use costs of the instrument , the calibration method of the non-contact R-test measuring instrument to improve the measurement efficiency. The technical solution is as follows:

A method for calibrating a non-contact R-test measuring instrument using an eddy current displacement sensor, comprising the following steps;

Step 1: Calibrate the non-contact R-test measuring instrument to measure the coordinate system:

Install the measuring ball on the spindle of the machine tool, place the bottom surface of the measuring instrument on the machine tool table, move the spindle so that the center of the measuring ball is roughly at the intersection of the axes of the three eddy current displacement sensors, and establish the measuring coordinate system with the center of the ball at this time as the origin , the direction of the coordinate axis is consistent with the direction of the machine tool coordinate system;

Step 2: Calibrate the eddy current displacement sensor sensing plane of the non-contact R-test measuring instrument:

The radius of the sensor end is recorded as R _probe , and the radius of the measuring ball is R _ball ;

a) When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is negligible, the sensor induced voltage characteristic curve equation is:

Among them, U _i is the induced voltage, _Li is the distance from the center of the measuring sphere to the sensing plane of the _i -th sensor, and _ki , _mi , and qi are the characteristic parameters of the sensor induced voltage (all constants, provided by the sensor manufacturer);

In the measurement coordinate system, the induction plane equation of the sensor 1 is set as a ₁ x+b ₁ y+c ₁ z+d ₁ =0;

Operate the machine tool, move the spindle to move the ball head to 4 different coordinate points P _j (x _j , y _j , z _j ), j=1, 2, 3, 4; the distance L ₁ from P _j to the sensing plane of sensor 1 _,j is converted according to the induced voltage U _1,j of sensor 1 at this time and the above formula, namely:

The values of sensor 1 sensing plane parameters a ₁ , b ₁ , c ₁ , d ₁ are obtained through the above equations; similarly, the plane equation coefficients of the other two sensor sensing planes in the measurement coordinate system are obtained;

Further, when the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is negligible, in the process of solving the parameters of the induction plane equation, the differential evolution algorithm is used to transform the solution of the above equations into an optimization problem. , construct the following nonlinear equation:

According to the above formula, the objective function is set as:

The closer the value of the objective function is to zero, the more precise the solution of the above nonlinear equation.

b) When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is not negligible, the sensor induced voltage curve equation is:

Among them, U _i is the induced voltage of the _ith sensor, Li is the distance from the center of the measuring sphere to the sensing plane of the _ith sensor, t _i , _ki , m _i , _ni , qi are the characteristic parameters of the sensor induced voltage ( are constants, provided by the sensor manufacturer);

In the measurement coordinate system, the plane equation of the sensor 1 is set as a ₁ x+b ₁ y+c ₁ z+d ₁ =0, and the main axis is moved to move the ball head to 12 different coordinate points P _j (x _j , y _j , z _j ), j=1,...,12;

According to the point-to-plane distance equation and the Pythagorean theorem, combined with the sensor 1 induced voltage characteristic curve equation, the following equations are obtained:

Through the above equations, the sensing plane parameters a ₁ , b ₁ , c ₁ , d ₁ of the sensor 1 and the coordinates of the center of the sensing plane (x _1-0 , y _1-0 , z _1-0 ) can be obtained; The sensing plane parameters of the other two sensors and the coordinates of the center of the sensing plane.

Further, when the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is not negligible, in the process of solving the parameters of the induction plane equation, the differential evolution algorithm is used to transform the solution of the above equations into an optimization problem. , according to the distance formula from the point to the plane and the sensor induced voltage characteristic curve equation at this time, the following nonlinear equation is constructed:

f _j (a ₁ ,b ₁ ,c ₁ ,d ₁ )=(x _j -x _1-0 ) ² +(y _j -y _1-0 ) ² +(z _j -z _1-0 ) ² -r _1-j ² -L _1-j ² j=1,...,12

According to the above formula, the objective function is set as:

The closer the value of the objective function is to zero, the more precise the solution of the above nonlinear equation.

The beneficial effects of the invention are: the invention aims at the non-contact R-test five-axis CNC machine tool rotation axis error measuring instrument, and the designed instrument calibration method can greatly reduce the non-contact R-test measuring instrument in processing and assembly and in the machine tool. The impact of installation errors on the measurement accuracy, thereby reducing the manufacturing and use costs of the instrument, improving the measurement efficiency, and regularly calibrating the instrument itself can better ensure the measurement accuracy of the instrument.

Description of drawings

Figure 1 is a structural model diagram of a non-contact R-test measuring instrument using an eddy current displacement sensor.

FIG. 2 is a schematic diagram of the spatial relationship between the eddy current displacement sensor and the measuring ball.

FIG. 3 is a schematic diagram of the sensing plane calibration of the eddy current displacement sensor.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

(1) Structure description of non-contact R-test measuring instrument:

The structural model of the non-contact R-test measuring instrument is shown in Figure 1, which mainly includes 3 non-contact eddy current displacement sensors and a standard measuring ball distributed evenly. According to the spatial positional relationship between the sensor sensing plane and the shortest distance of the measuring sphere, the coordinates of the center point P of the measuring sphere are calculated.

In Figure 1, AA ₁ , BB ₁ , and CC ₁ are three sensor axes (A ₁ , B ₁ , and C ₁ are the center points of the sensing planes of the three sensors, and A, B, and C are the center points of the bottom ends of the three sensors) , the end of the sensor is a sensing plane circle with a radius of R _probe , and the radius of the measuring sphere is an R _sphere . Define the plane where ΔABC is located as the reference plane, and the sensor elevation angle (the angle between the sensor axis and the reference plane) is α. Establish a measurement coordinate system, the origin of which is basically the same as the distance between the three sensing planes, and the XY coordinate plane is parallel to the reference plane.

The spatial relationship between the sensor and the measuring sphere is shown in Figure 2. Let the distance from the center of the measuring sphere to the sensing plane of the _i -th sensor be Li, the distance from the center of the sphere to the center axis of the sensor is _{ri, and the corresponding induced voltage is U i .} According to the induction principle of the sensor and the calibration test, the characteristic curve equation of the induced voltage of the sensor can be obtained as:

where U _i is the induced voltage value measured by the sensor; _{ri is the distance from the center of the sphere away from the sensor axis; t i , ki , mi , ni , q i are the characteristic parameters of} the sensor induced voltage, which can pass the sensor calibration test Or obtain the factory certificate.

According to whether the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range can be ignored, the calibration of the sensor sensing plane can be divided into the following two cases:

1) When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is negligible, that is, the influence of the sensor induced voltage characteristic parameters t and n on the induced voltage U is negligible, the characteristic parameters t and n can be ignored, The equation of the sensor induced voltage characteristic curve can be simplified as

2) When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range cannot be ignored, that is, the influence of the sensor induced voltage characteristic parameters t and n on the induced voltage U cannot be ignored, otherwise the accuracy of the measurement results will be greatly affected. , the sensor induced voltage characteristic curve is equation (1).

(2) Calibration of the measurement coordinate system of the non-contact R-test measuring instrument:

Before the sensor sensing plane coefficient is calibrated, the measurement coordinate system needs to be calibrated first. As shown in Figure 1, during calibration, the measuring ball is installed on the spindle of the machine tool, and the bottom surface of the measuring instrument is placed on the machine tool table. After the equipment is powered on, move the spindle so that the measuring ball is roughly in the center of the three sensors (the coordinates can be adjusted by observing the induced voltage of the sensors), and the measurement coordinate system is established with the center of the ball as the origin at this time. The direction of the coordinate axis is the same as the machine tool coordinate system. the same direction.

(3) Calibration of the sensing plane of the displacement sensor of the non-contact R-test measuring instrument:

According to whether the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range can be ignored, the calibration method of the sensor sensing plane is also divided into the following two cases.

1) When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is negligible, it means that the center offset r of the sphere perpendicular to the sensor axis direction will not affect the sensor induced voltage value, and the sensor induced voltage characteristic parameter t The influence of n and n on the measurement results can be ignored, and it is only necessary to calibrate the three sensor sensing plane equation coefficients of the measuring instrument.

Take the sensing plane of sensor 1 as an example. As shown in FIG. 3 , the sensing plane equation of the sensor 1 is set as a ₁ x+b ₁ y+c ₁ z+d ₁ =0 under the measurement coordinate system. Operate the machine tool, move the spindle to move the ball head to 4 different coordinate points P _j (x _j , y _j , z _j ) (j=1, 2, 3, 4), the distance from P _j to the sensing plane of sensor 1 can be According to the sensor induced voltage and formula (2) conversion, namely:

The values of the sensing plane parameters a ₁ , b ₁ , c ₁ , and d ₁ of the sensor 1 can be obtained through the equation group (3). Similarly, the plane equation coefficients of the other two sensor planes in the measurement coordinate system can be obtained.

In the process of solving the above induction plane equation parameters, since the induced voltage value is an approximate value, the solved plane equation coefficient is also an approximate value. In order to solve the accuracy of the result, the present invention adopts the differential evolution algorithm to transform the solution of the equation group (3) into an optimization problem, so as to improve the calibration accuracy as much as possible.

According to equation system (3), the following nonlinear equations can be constructed:

According to formula (4), the objective function is set as

Obviously, if equation (4) has a solution, the minimum value of objective function (5) is zero. In the algorithm, the closer the value of the objective function (5) is to zero, the more accurate the solution of the corresponding equation system (4).

The parameter settings of the differential evolution algorithm adopted in the present invention are shown in Table 1 (D=4).

2) When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range cannot be ignored, it means that the sensor induced voltage value is greatly affected by the sphere center offset r perpendicular to the sensor axis direction, and the sensor induced voltage characteristics The influence of parameters t and n on the measurement results cannot be ignored. Not only the induction plane equation coefficients of the three sensors of the measuring instrument need to be calibrated, but also the centers P _1-0 , P _2-0 and P _3-0 of the three induction plane circles need to be calibrated.

Take the sensing plane of the sensor 1 as an example for illustration, as shown in FIG. 3 . In the measurement coordinate system, the plane equation of the sensor 1 is set as a ₁ x+b ₁ y+c ₁ z+d ₁ =0. Move the spindle to move the ball head to 12 different coordinate points P _j (x _j , y _j , z _j ) (j=1,...12) in the measurement coordinate system. According to the point-to-plane distance equation and the Pythagorean theorem, combined with the sensor 1 induced voltage characteristic curve equation, the following equations can be obtained:

The sensing plane parameters a ₁ , b ₁ , c ₁ , d ₁ of the sensor 1 and the coordinates of the center of the sensing plane (x _1-0 , y _1-0 , z _1-0 ) can be obtained through the equation group (6). Similarly, the sensing plane parameters of the other two sensors and the coordinates of the center of the sensing plane can be obtained.

In the process of solving the above induction plane equation parameters, since the induced voltage value is an approximate value, the solved plane equation coefficient is also an approximate value. In order to solve the accuracy of the result, the present invention also adopts the differential evolution algorithm to transform the solution of the equation group (6) into an optimization problem, so as to improve the calibration accuracy as much as possible. According to the distance formula from point to plane and formula (1), the following nonlinear equation can be constructed:

f _j (a ₁ ,b ₁ ,c ₁ ,d ₁ )=(x _j -x _1-0 ) ² +(y _j -y _1-0 ) ² +(z _j -z _1-0 ) ² -r _1-j ² -L _1-j ² (j=1,...,12)(7)

The objective function form is consistent with formula (5) (where j=1, 2, . . . , 12). If there is a solution to equation (7), the minimum value of the objective function is zero. In the algorithm, the closer the value of the objective function is to zero, the more accurate the solution of the corresponding equation system (7).

The parameter settings of the differential evolution algorithm adopted in the present invention are shown in Table 1 (D=7).

Table 1 Differential evolution algorithm parameter settings

(1) Verification of calibration method

Now select 16U eddy current displacement sensor (range of 4mm) and standard measuring ball from kaman company, manufacture and assemble the measuring instrument, the length, width and height of the instrument (excluding measuring ball) are 170mm, 170mm and 120mm respectively.

When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measuring range is negligible, move the main shaft to obtain 4 different ball center positions as calibration points P ₁ , P ₂ , P ₃ , P ₄ (the calibration points cannot be For measuring the origin of the coordinate system), the coordinates of the calibration point and the voltage readings of each sensor are shown in Table 2. According to the data in Table 2, the coefficients of the sensing plane equations of each sensor can be solved by the differential evolution algorithm, as shown in Table 3.

Table 2 The coordinates of the calibration point and the sensor's induced voltage reading when the induced voltage change is negligible

Note: U ₁ =0.512L ₁ -6.251; U ₂ =0.501L ₂ -6.062; U ₃ =0.524L ₃ -6.456.

Table 3. Coefficients of sensor induction plane equation when the induced voltage change is negligible

When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measuring range is not negligible, move the main shaft to obtain 12 different ball center positions as calibration points P ₁ , P ₂ , ..., P ₁₁ and P ₁₂ (calibration points can not be the origin of the measurement coordinate system), the calibration point coordinates and the voltage readings of each sensor are shown in Table 4. According to the data in Table 4, through the differential evolution algorithm, the coefficients of the sensing plane equation of each sensor and the coordinates of the center of the sensing plane can be obtained as shown in Tables 5 and 6.

Table 4 The coordinates of the calibration point and the induced voltage readings of each sensor when the induced voltage change cannot be ignored

Note: U ₁ =0.532L ₁ ^0.5 +0.065r ₁ ^0.5 +0.168; U ₂ =0.526L ₂ ^0.5 +0.072r ₂ ^0.5 +0.183; U ₃ =0.531L ₃ ^0.5 +0.068r ₃ ^0.5 +0.168.

Table 5 Coefficients of the sensor induction plane equation when the induced voltage change is not negligible

Table 6 The coordinates of the center of the sensor sensing plane when the induced voltage change is not negligible (unit: mm)

(2) Calculation and verification of spherical center coordinates

When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is negligible, three different ball center positions are taken as verification points, and the voltage readings of each sensor at the three verification points are shown in Table 7. Table 8 shows the comparison between the calculation results of the spherical center coordinates of the R-test measuring instrument using this calibration method and the theoretical coordinate values. From the data comparison in Table 8, it can be found that the difference between the coordinates of the spherical center measured by this method and the theoretical coordinates is not greater than 0.0001 mm.

Table 7 Induced voltage reading of each sensor at the verification point when the induced voltage change is negligible (unit: V)

Table 8 Comparison of the calculated coordinates of the verification point and the theoretical coordinates when the induced voltage change is negligible (unit: mm)

When the induced voltage change caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is not negligible, three different ball center positions are taken as verification points, and the voltage readings of each sensor at the three verification points are shown in Table 9. Table 10 shows the comparison between the calculation results of the spherical center coordinates of the R-test measuring instrument using this calibration method and the theoretical coordinate values. From the data comparison in Table 10, it can be found that the difference between the spherical center coordinates measured by this method and the theoretical coordinates is not greater than 0.00039mm.

Table 9 Induced voltage reading of each sensor at the verification point when the induced voltage change cannot be ignored (unit: V)

Table 10 Comparison of the calculated coordinates of the verification point and the theoretical coordinates when the induced voltage change is not negligible (unit: mm)

Claims (3)

1. A non-contact R-test measuring instrument calibration method adopting an eddy current displacement sensor is characterized by comprising the following steps:

step 1: calibrating a measurement coordinate system of the non-contact R-test measuring instrument:

installing a measuring ball on a machine tool main shaft, placing the bottom surface of a measuring instrument on a machine tool workbench, moving the main shaft to enable the center of the measuring ball to be approximately positioned at the intersection point position of the axes of the 3 eddy current displacement sensors, establishing a measuring coordinate system by taking the center of the measuring ball at the moment as an original point, and enabling the directions of coordinate axes to be consistent with the directions of a machine tool coordinate system;

step 2: calibrating the induction plane of the eddy current displacement sensor of the non-contact R-test measuring instrument:

a) when the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is negligible, the equation of the induced voltage characteristic curve of the sensor is as follows:

wherein, U_iTo induce a voltage, L_iFor measuring the distance, k, from the centre of the sphere to the sensing plane of the ith sensor_i、m_i、q_iThe characteristic parameters of the induced voltage of the sensor are constants;

the induction plane equation of the sensor 1 is set as a under the measurement coordinate system₁x+b₁y+c₁z+d₁＝0；

Operating the machine tool, moving the spindle to move the ball head to 4 different coordinate points P_j(x_j,y_j,z_j)，j＝1,2,3,4；P_jDistance L to the sensing plane of the sensor 1_1,jAccording to the induced voltage U of the sensor 1 at the moment_1,jAnd the above formula is converted, namely:

the induction plane parameter a of the sensor 1 is obtained through the equation set₁、b₁、c₁、d₁A value of (d); obtaining plane equation coefficients of the induction planes of the other two sensors under the measurement coordinate system in the same way;

b) when the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, the equation of the induced voltage characteristic curve of the sensor is as follows:

wherein, U_iIs the induced voltage of the ith sensor, L_iFor measuring the distance from the centre of the sphere to the sensing plane of the ith sensor, t_i、k_i、m_i、n_i、q_iThe characteristic parameters of the induced voltage of the sensor are constants;

the plane equation of the sensor 1 is set as a under the measurement coordinate system₁x+b₁y+c₁z+d₁Moving the spindle to move the ball head to the measurement position12 different coordinate points P under the coordinate system_j(x_j,y_j,z_j)，j＝1,…12；

According to the distance equation and the Pythagorean theorem from the point to the plane, the following equation set is obtained by combining the induction voltage characteristic curve equation of the sensor 1:

the parameter a of the sensing plane of the sensor 1 can be determined by the equation system₁、b₁、c₁、d₁And sensing the coordinates (x) of the center of the circle of the plane_1-0、y_1-0、z_1-0) In the same way, the sensing plane parameters and the circle center coordinates of the sensing planes of the other two sensors can be obtained.

2. The method for calibrating the non-contact R-test measuring instrument by using the eddy current displacement sensor as claimed in claim 1, wherein when the variation of induced voltage generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is negligible, in the process of solving the equation parameters of the induced plane, the solution of the above equation set is converted into an optimization problem by using a differential evolution algorithm, and the following nonlinear equation is constructed:

according to the above formula, the objective function is set as:

the closer the value of the objective function is to zero, the more accurate the solution of the above non-linear equation.

3. The method for calibrating the non-contact R-test measuring instrument by using the eddy current displacement sensor as claimed in claim 1, wherein when the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, in the process of solving the equation parameters of the induction plane, the solution of the equation set is converted into an optimization problem by using a differential evolution algorithm, and the following nonlinear equation is constructed according to a point-to-plane distance formula and a characteristic curve equation of the induced voltage of the sensor at the moment:

f_j(a₁,b₁,c₁,d₁)＝(x_j-x_1-0)²+(y_j-y_1-0)²+(z_j-z_1-0)²-r_1-j ²-L_1-j ²j＝1,...,12

according to the above formula, the objective function is set as:

the closer the value of the objective function is to zero, the more accurate the solution of the above non-linear equation.

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