CN109032069B - A method for calculating spherical center coordinates of non-contact R-test measuring instrument using eddy current displacement sensor - Google Patents

Abstract

The invention discloses a method for calculating the center coordinates of a non-contact R-test measuring instrument by adopting an eddy current displacement sensor, which is used for calibrating a measuring coordinate system of the non-contact R-test measuring instrument according to the design and measuring characteristics of the non-contact R-test measuring instrument; and solving a coordinate result of the accurate sphere center point in the measurement coordinate system by using a differential evolution algorithm according to an induced voltage characteristic curve equation of the eddy current displacement sensor and an induced plane equation of the sensor. The invention can realize the accurate measurement of the three-dimensional displacement error of the cutter point of the five-axis numerical control machine tool, and has better measurement precision, range and stability.

Description

A non-contact R-test measuring instrument using eddy current displacement sensor Standard calculation method

technical field

The invention relates to the technical field of error measurement of numerically controlled machine tools, in particular to a method for calculating spherical center coordinates of a non-contact R-test measuring instrument 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 rotating axis of five-axis CNC machine tools, accurate measurement of the error of the tool nose point of the machine tool is the key to error compensation to improve its machining accuracy. There is no special precision measuring instrument and specification for the geometric error measurement of the rotating axis of the machine tool. At present, 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 instrument is relatively simple, and the deviation of the sensor installation position will not affect the measurement results. However, due to the mechanical structure problem, the sensor reading sensitivity is not high, and the contact wear also affects the measurement accuracy to a certain extent. The non-contact R-test instrument can avoid the measurement error caused by measurement wear, and can measure under the condition of high-speed rotation of the spindle, with better measurement sensitivity and stability, but the spherical center coordinate measurement algorithm is complex and not yet perfect.

SUMMARY OF THE INVENTION

In view of the above problems, the purpose of the present invention is to provide a kind of accurate measurement of the three-way runout error of the tool position of the machine tool spindle, and avoid the measurement error caused by contact wear, and at the same time, the measurement can be carried out under the condition of high-speed rotation of the spindle, and the measurement range And the calculation method of the spherical center coordinates of the non-contact R-test measuring instrument with better stability. The technical solution is as follows:

A method for calculating spherical center coordinates of a non-contact R-test measuring instrument using an eddy current displacement sensor, comprising the following steps:

Step 1: Establish the measurement 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 measuring ball is roughly at the center of the three eddy current displacement sensors; establish a measuring coordinate system, whose origin is the sensing plane of the three sensors The distance is basically the same, the XY coordinate plane is parallel to the reference plane;

Step 2: Calculate the coordinates of the measuring sphere center of the non-contact R-test measuring instrument:

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 induced voltage characteristic curve equation of the sensor 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 , m i ,} and qi are the coefficients of the sensor induced voltage characteristic curve equation, which are all constants;

The equations of the three sensor sensing planes in the measurement coordinate system are:

a _i x+b _i y+c _i z+d _i =0 i=1,2,3 (2)

According to the formula of the distance from the point to the plane, combined with the formula (1), the following equations are constructed:

The coordinates of the sphere center point P in the measurement coordinate system are obtained through this equation system;

b) When the change of the induced voltage caused by the radial deviation of the measuring ball from the sensor axis in the measurement range is not negligible, the sensor induced voltage characteristic 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 curve equation of the sensor induced voltage coefficients, all constants; _ri is the distance from the center of the sphere to the central axis of the sensor;

It is known that in the measurement coordinate system, the center coordinates of the sensing plane of the i-th sensor are (x _i-0 , y _i-0 , z _i-0 ), according to the point to

The distance formula of the plane and the Pythagorean theorem are combined with formula (4) and formula (2) to construct the following equations:

The coordinates of the sphere center point P in the measurement coordinate system can be obtained through this equation system.

Further, in the process of measuring the coordinates of the sphere center point P in the coordinate system by formula (4), in order to ensure the accuracy of the solution results, the following nonlinear equation system is built according to formula (4), and the solution of the equation system is the sphere. Center coordinates:

Let the objective function be:

The closer the value of the objective function is to zero, the more accurate the solution of the above nonlinear system of equations.

Further, in the process of solving the coordinates of the spherical center point P in the measurement coordinate system by formula (5), in order to ensure the accuracy of the solution results, the following nonlinear equation system is constructed according to formula (5), and the solution of the equation system is For the spherical center coordinates:

f _i (x,y,z)=(xx _i-0 ) ² +(yy _i-0 ) ² +(zz _i-0 ) ² -r _i ² -L _i ² =0 i=1,2,3 (9)

Let the objective function be:

The closer the value of the objective function is to zero, the more accurate the solution of the above nonlinear system of equations.

The beneficial effects of the present invention are: for the non-contact R-test five-axis CNC machine tool rotation axis error measuring instrument, the designed spherical coordinate calculation method can complete the accurate measurement of the three-dimensional displacement error of the machine tool spindle tool position point, and The measurement error caused by contact wear is avoided, and the measurement can be carried out under the condition of high-speed rotation of the spindle, with better measurement accuracy, range and stability.

Description of drawings

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

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

Detailed ways

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

Structure description of non-contact R-test measuring instrument using eddy current displacement sensor:

The structure model of the non-contact R-test measuring instrument using eddy current displacement sensor is shown in Figure 1, which mainly includes three 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 the axes of the three eddy current displacement sensors (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 bottom-end circle centers of the three sensors. point), 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 ball is shown in Figure 2. Let the distance from the center of the measuring ball to the sensing plane of the _i -th sensor be Li, the distance from the center of the ball to the center axis of the sensor is _ri , and the corresponding induced voltage is U _i . According to the induction principle and calibration experiment of the eddy current displacement sensor, it can be known that the induction voltage formula of the sensor is:

In the formula, U _i is the induced voltage value measured by the sensor; _ri is the distance from the center of the sphere to the sensor axis; _ki , _{mi , ni ,} qi are the characteristic parameters of the sensor induced voltage _, which can be passed through the sensor calibration test or factory delivery. Certificate obtained.

According to whether the induced voltage change caused by the radial deviation of the measuring sphere from the sensor axis in the measuring range can be ignored, the calculation of the spherical center coordinates of the measuring sphere 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, the influence of the sensor induced voltage characteristic parameters t and n on the induced voltage U is negligible, and the characteristic parameters t and n can be ignored. Simplify the sensor induced voltage characteristic curve equation as:

The simplified solution method for spherical center coordinates designed in this embodiment is as follows:

In the measurement coordinate system, the equations of the three sensor sensing planes are set as

a _i x+b _i y+c _i z+d _i =0 (i=1,2,3) (3)

According to the distance formula from the point to the plane, the following equations can be constructed by combining the formula:

Through the equation group (4), the coordinates of the sphere center point P in the measurement coordinate system can be obtained.

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, 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 result will be greatly affected. At this time, the sensor induced voltage characteristic curve is formula (1).

The exact solution method for the spherical center coordinates designed in this embodiment is as follows:

In the measurement coordinate system, the coordinates of the center of the sensing plane of the i-th sensor are known to be (x _i-0 , y _i-0 , z _i-0 ). According to the distance formula from point to plane and the Pythagorean theorem, the following equations can be constructed by combining equations (1) and (3):

Through the equation group (5), the coordinates of the sphere center point P in the measurement coordinate system can be obtained.

Numerical solution of differential evolution algorithm:

Since the induced voltage values in equations (4) and (5) are approximate values, conventional equation solving methods may not be able to obtain relatively accurate settlement results, or the settlement results may have multiple solutions. In order to ensure the accuracy of the solution result, the present invention transforms the solution of the equation system into the optimal value solution problem. Compared with the traditional optimization algorithm, the differential evolution algorithm has the characteristics of less calculation time and high robustness while ensuring the calculation accuracy, so the present invention adopts the differential evolution algorithm to solve the optimal value.

While using the differential evolution algorithm to solve, the algorithm solution of the spherical center coordinates is also divided into the following two cases:

1) Simplified solution of spherical center coordinates

According to the equation system (4), the following nonlinear equation system can be constructed, and the solution of the equation system is the spherical center coordinate.

Let the objective function be

Obviously, if the equation system (6) has a solution, the minimum value of the objective function (7) is zero. In the algorithm, the closer the value of the objective function (7) is to zero, the more accurate the solution of the corresponding system of equations (6).

The parameter settings of the differential evolution algorithm adopted in the present invention are shown in Table 1.

2) Exact solution of spherical center coordinates

According to the equation system (5), the following nonlinear equation system can be constructed, and the solution of the equation system is the spherical center coordinate.

f _i (x,y,z)=(xx _i-0 ) ² +(yy _i-0 ) ² +(zz _i-0 ) ² -r _i ² -L _i ² =0 (i=1,2, 3) (8)

Let the objective function be

Obviously, if the equation system (8) has a solution, the minimum value of the objective function (9) is zero. In the algorithm, the closer the value of the objective function (9) is to zero, the more accurate the solution of the corresponding equation system (8).

The parameter settings of the differential evolution algorithm adopted in the present invention are shown in Table 1.

Table 1 Differential evolution algorithm parameter settings

The present invention selects a 16U eddy current displacement sensor (with a range of 4mm) from Kaman Company, a standard measuring ball, and makes an R-test measuring instrument.

(1) Known calibration data

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 coefficients of the calibrated induction plane equations of each sensor are shown in Table 2.

Table 2 Sensor induction plane equation coefficients

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 calibrated induction plane equation coefficients of each sensor and the coordinates of the plane center are shown in Table 3 and Table 4.

Table 3. Coefficients of sensor induction plane equation when the induced voltage change is not negligible

Table 4. 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 induced voltages of each sensor at the three verification points are shown in Table 5. The theoretical coordinates of the three verification points in the measurement coordinate system are shown on the right side of Table 6. 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 is shown in Table 6. From the data comparison in Table 6, it can be found that the difference between the spherical center coordinates measured by this method and the theoretical coordinates is not greater than 0.0001mm.

Table 5 Induced voltage of each sensor at the verification point when the change in induced voltage is negligible (unit: V)

Table 6. Comparison between the calculated coordinate value and the theoretical coordinate value of the verification point 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 sphere center positions are taken as verification points, and the induced voltages of each sensor at the three verification points are shown in Table 7. The theoretical coordinates of the three verification points in the measurement coordinate system are shown on the right side of Table 8. 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 spherical center coordinates measured by this method and the theoretical coordinates is not greater than 0.00039mm.

Table 7 Induced voltage of each sensor at the verification point when the induced voltage change is not negligible (unit: V)

Table 8 Comparison of the calculated coordinate values of the verification points and the theoretical coordinate values when the induced voltage change is not negligible (unit: mm)

Claims (3)

1. A method for calculating the sphere center coordinate of a non-contact R-test measuring instrument by adopting an eddy current displacement sensor is characterized by comprising the following steps:

step 1: establishing a measurement coordinate system:

mounting a measuring ball on a machine tool main shaft, placing the bottom surface of a measuring instrument on a machine tool workbench, and moving the main shaft to enable the measuring ball to be approximately positioned at the central position of 3 eddy current displacement sensors; establishing a measurement coordinate system, wherein the distance between the origin of the measurement coordinate system and the sensing plane of the 3 sensors is basically consistent, and the XY coordinate plane is parallel to the reference plane;

step 2: calculating the measurement spherical center coordinate 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 induced voltage characteristic curve equation 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 coefficients of the characteristic curve equation of the induced voltage of the sensor are constants;

the equation for setting the sensing planes of 3 sensors under the measurement coordinate system is as follows:

a_ix+b_iy+c_iz+d_i＝0 i＝1,2,3 (2)

according to the distance formula from the point to the plane, the following equation system is constructed by combining the equation (1):

obtaining the coordinate of the center point P in the measuring coordinate system through the equation set;

b) when the induced voltage change 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 coefficients of the characteristic curve equation of the induced voltage of the sensor are constants; r is_iThe distance from the center of the sphere to the central axis of the sensor;

the center coordinate of the sensing plane of the ith sensor in the measuring coordinate system is known as (x)_i-0，y_i-0，z_i-0) According to the distance formula from the point to the plane and the Pythagorean theorem, the following equation set is constructed by combining the formula (4) and the formula (2):

the coordinates of the center point P in the measurement coordinate system are determined by the system of equations.

2. The method for calculating the coordinates of the center of sphere of the non-contact R-test measuring instrument using the eddy current displacement sensor according to claim 1, wherein in the process of solving the coordinates of the center point P in the measuring coordinate system by the equation (4), in order to ensure the accuracy of the solution result, the following non-linear equation set is established according to the equation (4), and the solution of the equation set is the coordinates of the center of sphere:

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-mentioned system of nonlinear equations.

3. The method for calculating the coordinates of the center of sphere of the non-contact R-test measuring instrument using the eddy current displacement sensor according to claim 1, wherein in the process of solving the coordinates of the center point P in the measurement coordinate system by the equation (5), in order to ensure the accuracy of the solution result, the following non-linear equation set is constructed according to the equation (5), and the solution of the equation set is the coordinates of the center of sphere:

f_i(x,y,z)＝(x-x_i-0)²+(y-y_i-0)²+(z-z_i-0)²-r_i ²-L_i ²＝0 i＝1,2,3 (9)

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-mentioned system of nonlinear equations.

Images