JP2014075031A - Geometrical error identification method and numerical control method, numerical control device, and machining center using the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To accurately identify geometrical errors of rotation axes of a machine structure including two rotation axes, with less measurement points.SOLUTION: A geometrical error identification method identifies a geometrical error of a machine structure including two rotation axes combined at a prescribed angle. Two rotation axes are rotated once or more by a prescribed angle to move a measurement object point of the machine structure to at least three different positions separated from the origin of the machine structure. A difference vector D between a machine coordinate vector at movement destinations of the measurement object point and a logical machine coordinate vector not including an influence of geometrical errors is calculated. When geometrical errors of two rotation axes are denoted as unknown numbers and a vector representing an influence of the geometrical errors at the plurality of movement destinations is denoted as an error vector E, the difference vector D is represented by a linear regression equation with the error vector E as an explanatory variable and the difference vector D as a dependent variable. A regression coefficient is calculated by minimizing the deviation of the linear regression equation, and the geometrical error is identified by the regression coefficient.

Description

  The present invention relates to a geometric error identification method for a machine tool such as a machining center, a numerical control method using the geometric error identification method, a numerical control device, and a machining center.

  As a machining center, a 3-axis machining center and a 5-axis machining center are known. The 5-axis machining center is obtained by adding two rotation axes to the three linear axes of the 3-axis machining center. There are many types and models of this 5-axis machining center (hereinafter, the machining center is abbreviated as “MC”). (Upper and lower) linear three axes plus C axis (table rotation) and A axis (tilt) rotation two axes, C axis (table rotation) and B axis (spindle head) rotation two axes Are often used.

  The 5-axis MC can process a three-dimensional complicated shape such as an impeller and a blade, but has a problem that it is difficult to maintain and manage the machining accuracy because it has more axes than the 3-axis MC. If there is a geometric error between the five axes (an error that originally exists in the machine main body), a machining error occurs in the workpiece even if the workpiece or tool mounting state is precisely adjusted as follows.

  The geometric error includes, for example, the parallelism between the A and C rotation axes and the X, Y, and Z translation axes, the mismatch of the rotation centers between the A and C rotation axes, and the like, and is generated when the 5-axis MC is manufactured and assembled. . This geometric error may be manifested as a workpiece machining error with an error difference or twice as large. For this reason, it is required to accurately identify the geometric error and input it as machine information so as to compensate for the geometric error when creating the NC program.

  Conventionally, as a technique for identifying a geometric error of a 5-axis MC or correcting a coordinate system of an NC program based on the error, there is one described in Patent Documents 1-6, for example.

  In the technique of Patent Document 1, the C-axis member is rotated around the C-axis while the B ′ axis is fixed, and the position of the spindle tip at each predetermined turning angle is measured. The turning plane is determined, and the NC program coordinate system is changed to compensate for the geometric error by using the normal vector of the turning plane as a vector in the C-axis direction.

  The technique of Patent Document 2 is an improvement of the technique of Patent Document 1, and even if the spindle rotation center is deviated / inclined from its original position, a machining error caused by the center is compensated.

  In the technique of Patent Document 3, a deformation error estimated value, a positioning error estimated value, and a thermal displacement estimated value are taken into a geometric error as a part of a geometric error, and a geometric error compensation value is calculated by a geometric error compensation calculating means. This is reflected in the servo command value.

  The technique of Patent Document 4 creates an error map and corrects errors with high accuracy.

  In the technique of Patent Document 5, when measuring the tilt error and the position error of the rotary shaft, a plurality of jigs to be measured are arranged on the rotary table, thereby reducing the number of times the rotary table is positioned and shortening the measurement time. Yes.

  In the technique of Patent Document 6, jigs to be measured are arranged at 12 intervals on the circumference of the rotary table, each position of the jig to be measured is measured, and a circle passing through each position is approximated by an arc approximation method. Thus, the geometric error between the rotation axis and the translation axis is identified.

JP 2001-269839 A JP 2004-272887 A JP 2009-104317 A JP 2012-79358 A JP 2005-61834 A JP 2011-38902 A

  However, in any of the patent document techniques, if geometric errors are to be identified with high accuracy, the number of measurement points increases and it takes a long time to measure. It takes time to attach the jig to be measured, and there is a problem that productivity is lowered in all cases.

  Therefore, an object of the present invention is to provide a method for accurately identifying a geometric error of a rotating shaft with a small number of measurement points, and to provide a numerical control method, a numerical control device, and a machining center using the geometric error identification method. is there.

  In order to solve the above problems, the present invention provides a geometric error identification method for identifying a geometric error of a mechanical structure including two rotational axes combined at a predetermined angle, and the geometric error identification method includes: By rotating the two rotation axes at a predetermined angle at least once with respect to the origin, the measured point of the mechanical structure is moved to at least three different positions apart from the origin, and the measured point The difference vector D between the machine coordinate vector at a plurality of movement destinations and the theoretical machine coordinate vector not including the influence of the geometric error at the plurality of movement destinations is calculated, and the difference vector D is calculated for the two rotation axes. When a vector representing the influence of the geometric error at a plurality of destinations is defined as an error vector E with the geometric error as an unknown, the error vector E is used as an explanatory variable, and the difference vector D is defined as a dependent variable. Expressed in linear regression equation for the deviation of the linear regression equation to calculate the regression coefficients by minimizing a geometric error identification method, wherein from the regression coefficient that was set to identify the geometric errors. The “machine coordinate vector” is an abbreviation of a position vector representing machine coordinates.

  As described above, the present invention estimates the regression coefficient by minimizing the deviation of the linear regression equation having the error vector E as the explanatory variable and the difference vector D as the dependent variable, and identifies the geometric error from the regression coefficient. As a result, the geometric error of the two rotation axes can be obtained with high accuracy and in a short time with a small number of measurement points.

It is the schematic of 5 axis | shaft MC and its numerical control apparatus. It is a conceptual diagram around the C-axis and the A-axis of the 5-axis MC. It is a flowchart which calculates the center coordinate of the movement destination of a reference | standard sphere. It is a flowchart which shows embodiment of the geometric error identification method of this invention.

  Hereinafter, an embodiment in which the geometric error identifying method according to the present invention is applied to a geometric error identifying method for two rotational axes (A axis and C axis) of a 5-axis MC as a mechanical structure will be described.

(Outline of 5-axis MC)
FIG. 1 shows a main part around the main axis of the 5-axis MC and a numerical control device (block diagram) 10 for controlling the 5-axis MC. In the figure, 1 is a frame, 2 is a main shaft, 3 is a table, 4 is a trunnion, and 5 is a saddle. The configuration itself of the numerical control device 10 is the same as that of the conventional numerical control device, but software for correcting geometric errors is stored in the ROM.

  The processor CPU of the numerical controller 10 reads a system program stored in the ROM via the bus and controls the entire apparatus. Temporary calculation data and display data are stored in the RAM. Various data input by the operator via the display / MDI unit 20 are also stored in the RAM. In the figure, reference numerals 31 to 36 denote motors, and 37 denotes a position coder. There are a total of six motors 31 to 36 for X-axis translation, Y-axis translation, Z-axis translation, A-axis rotation, C-axis rotation, and main axis.

(Principle of geometric error identification method)
FIG. 2 schematically shows the 5-axis MC around the C-axis and the A-axis. By rotating the C axis and the A axis at least once at a predetermined rotation angle, the measurement point on the table 3 is moved to at least three different positions apart from the origin of the 5-axis MC machine coordinate system. Then, in order to obtain geometric error data (components in the X, Y, and Z directions of an error vector E described later), the moving position of the measurement point on the table 3 is measured by the machine coordinate system.

  The table 3 can rotate about the C axis and can tilt about the A axis. In this embodiment, the measurement point on the table 3 is given by a reference sphere 6 fixed to the C-axis table 3 as shown in FIG. The center coordinate of the reference sphere 6 is the point to be measured. The origin is set at the initial position of the table 3. Although this initial position is arbitrary, it is usually horizontal and has a rotation angle of 0 ° around the C axis.

  The “predetermined rotation angle” of the C-axis and the A-axis when the C-axis and the A-axis are rotated at a predetermined rotation angle at least once each is arbitrary, and the 5-axis MC display / MDI unit 20 sends the numerical control device 10 Set. In this movement, the C axis and A axis are always rotated once. When the reference sphere 6 is moved, both the C axis and the A axis may be rotated by one movement, or only one of them may be rotated.

  The geometric error identification method of the present invention is a difference vector D between a machine coordinate vector at the center of a reference sphere 6 as a measured point and a theoretical machine coordinate vector at the center of the reference sphere 6 that does not include the influence of the geometric error. Is calculated. When the difference vector D is defined as an error vector E, the error vector E being an explanatory variable when the geometric error of two rotation axes (C axis and A axis) is an unknown and a vector representing the influence of the geometric error at a plurality of destinations is used. As a linear regression equation with the difference vector D as a dependent variable. A regression coefficient is calculated by minimizing the deviation of the linear regression equation, and a geometric error is identified from the regression coefficient. This is the principle of the geometric error identification method of the present invention.

As shown in Table 1, the geometric error of the two rotation axes (C axis and A axis) is composed of _four rotation errors δ _{1 to} δ ₄ and four translation errors δ _{5 to} δ ₈ .

  In the geometric error identification method of the present invention, when the center sphere is measured at each moving position by moving the reference sphere 6 by two rotational axes, the three components of the error vector E in the X, Y, and Z directions at each measurement point. Therefore, if measurement is performed three times at three moving positions, data necessary for identifying eight geometric errors as unknowns can be obtained.

(Measurement of measured points)
The measurement of the measurement point is performed by measuring the position (machine coordinate position) of the reference sphere 6 as the measurement jig with the touch sensor 7 as shown in FIGS. The touch sensor 7 is used by being attached to the main shaft 2. The reference sphere 6 is fixed at an arbitrary position on the table 3 that rotates about the A axis as shown in FIG. 2A, and the main shaft 2 is operated as shown in FIG. The probes 7 a of the touch sensor 7 are brought into contact with at least four places on the surface of the sphere 6.

  FIG. 2B shows a state in which the probe 7a is in contact with the reference sphere 6 five times. The broken line in the figure is the movement locus of the probe 7a. From the position (machine coordinate position) of the main shaft 2 at the time of contact, the center coordinates of the reference sphere 6 are calculated with five axes MC. The position measurement sensor may be a non-contact sensor such as a laser sensor other than the touch sensor.

The reference sphere 6 is measured first at the initial position (origin position) of the table 3 as shown in FIG. The obtained measurement data is the machine coordinate vector at the initial position. After measurement at this initial position, the table 3 is tilted at an arbitrary angle in an arbitrary direction as shown in FIG. 2D, and the center coordinate P _j of the reference sphere 6 is measured by the touch sensor 7 in this state. The direction and angle of rotation of the table 3 are arbitrary, but the direction and angle are managed by the 5-axis MC numerical controller 10. In addition to tilting the table 3, the center coordinate P _j of the reference sphere 6 may be measured by rotating the table 3 at an arbitrary angle around the C axis at the same time, or in any direction around the C axis without tilting the table 3. The center coordinate P _j of the reference sphere 6 may be measured by rotating it at an arbitrary angle.

  In this way, the second measurement is performed by arbitrarily moving the reference sphere 6. A first machine coordinate vector at the first movement position is obtained from the obtained measurement data. Similarly, the table 3 is rotated by an arbitrary amount in an arbitrary direction, the third measurement and the fourth measurement are performed at positions excluding the initial position and the measured position, the second machine coordinate vector at the second movement position, and the third A third machine coordinate vector at the moving position is obtained. The first to third machine coordinate vectors obtained in this way are measurement values having the influence of geometric errors. Note that the measurement points do not need to be set at equal intervals, and may be measured at any measurement point where the influence of the geometric error is considered to be somewhat large in order to improve accuracy.

(Theoretical machine coordinate vector not affected by geometric error and machine coordinate vector affected by geometric error)
As shown in FIGS. 2C and 2D, an arbitrary position on the table 3 can be represented by a workpiece coordinate system vector Pw and a machine coordinate system vector Pm. The work coordinate system is a coordinate system set on a table, and the machine coordinate system is a coordinate system constituted by three straight axes (X, Y, Z) of five axes MC.
Since the geometric error identification method of the present invention expresses the error in machine coordinates, the motion of the two rotation axes including the geometric error is described by a coordinate rotation matrix.
Here, the workpiece coordinate system vector Pw and the machine coordinate system vector Pm can be expressed by the following equations (1) and (2).

Further, when the coordinate rotation matrix representing the rotation of the A axis is M _A and the coordinate rotation matrix representing the rotation of the C axis is M _C , the following expressions (3) and (4) are respectively expressed.

Coordinate transformation matrix representing the effect of eight geometric errors of the δ ₁ ~δ ₈ are respectively the following formulas (5), represented by (6).
Here, Me _A is a coordinate conversion matrix of geometric errors related to the A axis, and Me _C is a coordinate conversion matrix of geometric errors related to the C axis.

The theoretical machine coordinate vector Pm ₀ when there is no geometric error influence and the machine coordinate vector Pm when the geometric error influences are expressed by the following equations (7) and (8), respectively.

Here, assuming that the machine coordinate vector when one geometric error δ _i affects is Pm _i , for example, the machine coordinate vector when only δ ₁ affects is Pm ₁ , the Pm ₁ is expressed by the following equation (9). expressed.
Here, Me _A is as follows.

(Identification of geometric errors)
A workpiece coordinate vector Pw is obtained from the center coordinates of the reference sphere 6 at the initial angle (usually 0 °). Using this work coordinate vector Pw, the theoretical machine coordinate vector Pm _0j of the reference sphere 6 at the j-th measurement point and the machine coordinate vector Pm _ij when the geometric error δ _i affects are expressed by the equations (7) and (8). Are expressed by the following equations (11) and (12).
[Equation 11]
Pm _0j = M _A , M _C , Pw (11)
[Equation 12]
Pm _ij = Me _A · M _A · Me _A ^-1 · Me _C · M _C · Me _C ^-1 · Pw (12)

Thus, the difference vector D _j between the machine coordinate vector P _j representing the center position of the reference sphere 6 and the theoretical machine coordinate vector P _{0j at} the j-th measurement point is expressed by the following equation (13).

An error vector E _ij representing the influence of the geometric error δ _{i at} the j-th measurement point is expressed by the following equation (14).

  Difference vector D_jIs a dependent variable, an error vector E representing the effect of geometric error_ijAs an explanatory variable, it is expressed by a linear regression equation of the following equation (15).
[Equation 15]
  D_j= K₁・ E_1j+ K₂・ E_2j+ ... + K_i・ E_ij+ Ε (15)
  Regression coefficient K_1,K₂..K is the effect of geometric error E_ijIs an unknown variable representing the weight of. The last ε is the deviation.
  When one geometric error is a unit geometric error (0.001 rad for a rotation error, 0.001 mm for a translation error), the influence in three directions of X, Y, and Z is calculated, and the 3 Get direction data. Similarly, for other geometric errors, data in three directions are obtained for each measurement point.

Thereby, the relationship of following Formula (16) is obtained.

For equation (16), the regression coefficients K _1, K ₂ ·· K _i are determined (estimated) by minimizing the deviation ε. Here, the regression coefficients K _1, K ₂ ... _Ki are determined using the least square method, but the method for minimizing the deviation ε is not limited to the least square method. And identify the geometric error from the regression coefficients _{K 1, K 2 ·· K i} . In this embodiment, as described above, the unit geometric error of the _four rotation errors δ _{1 to} δ ₄ is 0.001 rad, and the unit geometric error of the four translation errors δ _{5 to} δ ₈ is 0.001 mm. As shown in Table 2, the geometric error is obtained by multiplying the regression coefficient by the unit geometric error. The unit geometric error may be an arbitrary size, but if the unit geometric error is significantly larger or smaller than the actual geometric error, the calculation error increases. For this reason, the unit geometric error should be aligned with the actual geometric error in order.

When determining the regression coefficient, an appropriate test (for example, t test) may be performed as necessary to determine its significance. In the example of Table 2, a result of determination coefficient R ² = 0.988 (R: correlation coefficient) is obtained, and 98.8% of the difference vector D can be explained using a linear regression equation.

Thus, the percentage of error in the difference vector D can be explained by a linear regression equation can be known from the coefficient of determination R ^2. If the coefficient of determination R ² is smaller than a predetermined threshold (e.g., 0.8) may be carried out measures such as again determined by increasing the measurement points. Finally, a translation error of 0.001 mm and a rotation error of 0.001 rad set as reference sizes are multiplied by the regression coefficient. This multiplied value is the identified geometric error.

(Flow chart of geometric error identification method)
The geometric error identification method described above is shown in FIG. 3 and FIG. The contents of this flowchart are stored in the ROM of the numerical controller 10 shown in FIG. FIG. 3 is a flowchart from when the reference sphere 6 is moved j times from the origin to calculation of the center coordinate P _j at the j-th destination. In S1, j = 0 is set, and in S2, the two rotation axes are positioned at predetermined set angles (θ _A = A _j , θ _C = C _j ). S3 center coordinates P _j of the reference sphere 6 is measured, the center coordinates P _j of the reference sphere 6 is stored in memory in S4.

In S5, it is determined whether or not the measurement points of all the center coordinates P _j from the first movement to the _j- th movement of the reference sphere 6 have been calculated, and all the measurement points of the center coordinates P _j have been calculated. If not, j = j + 1 is set in S6, and the process returns to S2. In S2, the two rotation axes are positioned at predetermined set angles (θ _A = A _j , θ _C = C _j ) for the next movement of the measured point (center of the reference sphere 6). If it is determined in S5 that all the measurement points of the central coordinates P _j up to the j-th movement have been calculated, the flow is ended.

FIG. 4 is a flowchart until the geometric error is identified based on the measurement data of the measurement points described above. First, the workpiece coordinate vector Pw is calculated from the center coordinates of the reference sphere 6 at the initial angles (C-axis rotation angle = 0 °, A-axis rotation angle = 0 °) in S1, and j = 0 is set in S2. . S3 in the calculated theoretical machine coordinate vector Pm _oj, the difference vector D _j are calculated in S4. It is determined whether or not all measurement points have been calculated in S5. If all measurement points have not yet been calculated, j = j + 1 is set in S6, and the process returns to S3. If it is determined that all measurement points have been calculated in S5, i = 1 is set in S7, and j = 0 is set in S8.

Next, a theoretical machine coordinate vector Pm _oj is calculated in S9, and a machine coordinate vector Pm _ij is calculated in S10. Next, an error vector E _ij representing the influence of the geometric error is calculated in S11, and it is determined whether or not all measurement points have been calculated in S12. If all the measurement points have not been calculated, j = j + 1 is set in S13, and the process returns to S9. If it is determined in S12 that all measurement points have been calculated, it is determined in S14 whether or not the influence of all geometric errors has been calculated. When the influence of all geometric errors is not calculated, i = i + 1 is set in S15, and the process returns to S8.

If it is determined in S14 that the influence of all geometric errors has been calculated, regression coefficients K ₁ ... K _i are determined by the least square method in S16. The coefficient of determination R ² in S17 whether greater than a predetermined threshold (e.g., 0.8) is determined. If the coefficient of determination R ² is equal to or less than a predetermined threshold value, adds the measurement point at S18, remeasurement is performed at S19. Additional measurement points may be added one position in S18, but in accordance with the difference between the coefficient of determination R ² magnitude and a predetermined threshold value, may be added two or more positions of the measuring points at once.

  Although the geometric error identification method has been described above, the present invention is not limited to the above-described embodiment, and various modifications can be made. For example, the present invention can be applied to general mechanical structures including two rotating shafts. The application target is not limited to the 5-axis MC. Further, the angle of the two rotation axes is not limited to 90 °, and the present invention can be applied to a combination angle other than 90 degrees by appropriately changing the coordinate rotation matrix corresponding to the angle. That is, in the case of a combination angle other than 90 degrees, a machine coordinate vector can be expressed by inserting a coordinate rotation matrix corresponding to the angle at which the two axes intersect between coordinate rotation matrices representing the motion of each axis. .

1: Frame 2: Spindle 3: Table 4: Trunnion 5: Saddle 10: Numerical control device

Claims (8)

A geometric error identification method for identifying a geometric error of a mechanical structure including two rotational axes combined at a predetermined angle, the geometric error identification method comprising:
Using the origin of the machine structure as a reference, the measurement point of the machine structure is moved to at least three different positions apart from the origin by rotating the two rotation axes at a predetermined angle at least once. ,
A difference vector D between a machine coordinate vector at a plurality of destinations of the measurement point and a theoretical machine coordinate vector not including the influence of geometric errors at the plurality of destinations is calculated, and the difference vector D is A linear regression equation using the error vector E as an explanatory variable and the difference vector D as a dependent variable, where an error vector E is a vector representing the influence of the geometric error at a plurality of destinations with the geometric error of the two rotation axes as an unknown. A geometric error identification method, wherein a regression coefficient is calculated by minimizing a deviation of the linear regression equation, and the geometric error is identified from the regression coefficient.   The geometric error identification method according to claim 1, wherein a combination angle of the two rotation axes is 90 °.   3. The geometric error according to claim 1, wherein the mechanical structure is a machining center, and the two rotation axes are a C axis for rotating a work mounting table and an A axis for tilting the table. Identification method.   4. The geometric error according to claim 3, wherein a reference sphere is arranged at the measurement point of the mechanical structure, and a center machine coordinate of the reference sphere is measured by a touch sensor attached to a spindle head of a machining center. Identification method.   5. A numerical control method for a machining center, wherein the geometric error identification method according to claim 1 is used.   A numerical control apparatus for a machining center, wherein the numerical control method according to claim 5 is used.   A machining center having the numerical control device according to claim 6.   8. The machining center according to claim 7, wherein the NC program is modified based on the geometric error identified by the geometric error identification method according to claim 3 or 4.