CN107544430B

CN107544430B - Contour error estimation method of three-axis numerical control machine tool

Info

Publication number: CN107544430B
Application number: CN201710853232.5A
Authority: CN
Inventors: 杨明; 杨吉祥; 丁汉; 黄翔
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Priority date: 2017-09-20
Filing date: 2017-09-20
Publication date: 2020-02-14
Anticipated expiration: 2037-09-20
Also published as: CN107544430A

Abstract

The invention belongs to the technical field of precision manufacturing, and discloses a contour error estimation method of a three-axis numerical control machine tool. The method comprises the following steps: (a) planning an ideal machining reference track, storing three-dimensional coordinates of each machining point of the interpolated reference track, and monitoring and storing the three-dimensional coordinates of each machining point on the actual machining track in each adopted period; (b) acquiring a reference position point which is closest to an actual processing point on a reference track; (c) and estimating the required contour error by adopting different methods according to different situations according to different position relations between the nearest reference position point and the adjacent points. The invention does not need the parameter information and curvature information of ideal processing parameter track in the estimation process, is suitable for the condition of larger curvature in the processing process, and has the advantages of low realization difficulty, small calculated amount, short time, real-time property and wide application range.

Description

Contour error estimation method of three-axis numerical control machine tool

Technical Field

The invention belongs to the technical field of precision manufacturing, and particularly relates to a contour error estimation method of a three-axis numerical control machine tool.

Background

In recent years, with the rapid development of manufacturing industry, the precision and complexity of machined parts are becoming more and more precise, so that the machining requirements of numerically controlled machine tools in the field of precision manufacturing are gradually developing towards high precision. The high precision generally refers to high profile processing precision. The machining precision level of the numerical control machine directly reflects the technical level of national equipment manufacturing.

In order to reduce the profile error in the numerical control machining process and further improve the profile accuracy of the surface of a machined workpiece, a common method is to design a corresponding profile error controller based on profile error information to realize profile control with high machining accuracy, the existing estimation method generally needs to refer to information such as curvature and differential of a track or estimate the profile error by adopting an iterative method, the generality of the estimation method is limited, and the problem of poor real-time performance caused by over-calculation exists.

Disclosure of Invention

In view of the above defects or improvement requirements of the prior art, the present invention provides a contour error estimation method for a three-axis numerical control machine tool, which solves the technical problem of three-axis contour machining error estimation in a three-dimensional space by finding a point closest to a current machining point in an ideal path of a tool and then determining an error estimation mode according to a position relationship between the point and an adjacent point.

To achieve the above object, according to the present invention, there is provided a contour error estimation method of a three-axis numerical control machine tool, comprising the steps of:

(a) planning a machining path of a cutter of a three-axis numerical control machine tool and obtaining an ideal machining reference track aiming at an object to be machined, interpolating the reference track and storing three-dimensional coordinates of each machining point after interpolation, machining the object to be machined by the cutter according to the reference track, monitoring an actual machining track of the cutter and storing the three-dimensional coordinates of each machining point on the actual machining track;

(b) for the current actual machining point P of the tool_aFinding a reference point P corresponding to the actual processing point in the reference track_r+kCalculating the distance between the actual processing point and a point near the reference point, wherein the point corresponding to the minimum value of the distance is the reference position point P closest to the actual processing point on the reference track_r+k-j；

(c) On the reference track and the nearest reference position point P_r+k-jAdjacent point is P_r+k-j-1And P_r+k-j+1The required profile error is estimated separately from the following different cases:

(c1) when said P is_r+k-j-1、P_r+k-jAnd P_r+k-j+1When the two are not on the same straight line,

according to said P_r+k-j-1、P_r+k-jAnd P_r+k-j+1Constructing a circle, and determining the radius and center O of the circle₀Coordinates of the actual machining point on the plane ⊙ O of the circle₀Projecting to obtain its projected point P'_a(ii) a The center of the circle O₀And the projection point P_a' with a line connecting to said circle P_r+k-j-1And P_r+k-j+1The arc between them is crossed, the intersection point is

The point of intersection

And the actual machining point P_aIs the profile error to be estimated

(c2) When said P is_r+k-j-1、P_r+k-jAnd P_r+k-j+1When the two parts are on the same straight line,

according to said P_r+k-j-1、P_r+k-jAnd P_r+k-j+1Constructing a straight line, and acquiring the projection point of the actual processing point on the straight line, wherein the projection point and the actual processing point P_aThe distance between them being the profile error to be estimated

(c3) When the reference position point P_r+k-jAs end points of both ends of the reference track,

the reference position point P_r+k-jAnd the actual machining point P_aThe distance between them being the profile error to be estimated

Further preferably, in step (b), the nearest reference position point P is calculated preferably according to the following expression_r+k-j，

Wherein, P_aIn the formula, the actual processing point P_aCoordinate of (A), P_r+k+iIn which is a point P in the vicinity of the reference point_r+k+iI is the number of sample points in the forward or reverse direction along the reference trajectory, L_iIs the distance of the actual machining point from a point near the reference point.

Further preferably, in step (c1), the radius of the circle is preferably performed according to the following expression,

wherein, O₀In which is the coordinate of the center of the circle, P_r+k-j-1In the formula is point P_r+k-j-1R is the radius of the circle.

Further preferably, in step (c1), the contour error is preferably performed according to the following expression,

wherein, P'_aIn which is the coordinate of the projection point, P_aIn the formula, the coordinates of the actual machining point are shown.

In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:

1. by utilizing the discrete points on the ideal processing parameter track, the parameter information and curvature information of the ideal processing parameter track are not needed in the estimation process, and only the coordinates of the discrete points are needed, so that the estimation complexity is reduced, the difficulty is low, and the application range is wide;

2. in the invention, the arc is determined by three adjacent points, so that the change of an ideal path curve is reflected, and the curvature of the track of the ideal processing parameter is estimated, thereby reducing the sensitivity to the curvature change of the track and being suitable for the condition of larger curvature in the processing process;

3. the contour error estimation method for the three-axis numerical control machining, provided by the invention, can be used for estimating the size of the contour error in the three-axis numerical control machining process with high precision, and in the estimation process, only the reference position point and the actual machining point position which are closest to the actual machining point after the tool track interpolation are needed, and other additional information is not needed, so that the calculated amount is small, the time consumption is short, and the real-time performance is realized;

4. the method is simple and easy to implement, can accurately and quickly estimate the size of the contour error in the numerical control machining process, has universality, is suitable for cutter tracks of various types of three-dimensional spaces, and has good application value for improving the machining precision of the numerical control machine.

Drawings

FIG. 1 is a flow chart of an implementation of contour error estimation during three-axis numerically controlled (CNC) machining constructed in accordance with a preferred embodiment of the present invention;

FIG. 2 is a schematic illustration of contour error for a numerically controlled process constructed in accordance with a preferred embodiment of the present invention;

FIG. 3 is a schematic diagram of a three-axis contour error estimation method constructed in accordance with a preferred embodiment of the present invention;

FIG. 4 is a schematic diagram of a three-axis contour error estimation method for a special case constructed in accordance with a preferred embodiment of the present invention;

FIG. 5(a) is a graph of estimated accuracy versus total profile error constructed in accordance with a preferred embodiment of the present invention;

fig. 5(b) is a graph of estimated accuracy versus profile error component for various axes constructed in accordance with a preferred embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

Fig. 1 is a flow chart showing the implementation of contour error estimation in a three-axis numerically controlled (CNC) machining process according to a preferred embodiment of the present invention, and as shown in fig. 1, the method for constructing a contour error estimation model in a three-axis CNC machining process according to the present invention includes the steps of:

x, Y and a Z-axis tool reference position command of a reference track during machining of the numerical control machine tool after interpolation is stored in a memory of the numerical control machine tool;

FIG. 2 is a schematic diagram of the profile error of the NC machining in the X-Y plane, where P is_rFor reference position of tool, P_aIs referred to as a tool reference position P_rCorresponding actual position of the tool, e_xAnd e_yAnd the tracking error of the cutter in the X-axis direction and the tracking error of the cutter in the Y-axis direction in the numerical control machining process are respectively represented, and epsilon represents the contour error of the cutter in the numerical control machining process. It is clear from fig. 2 that the profile error is defined as the shortest normal distance from the actual position of the tool to the reference trajectory of the tool.

Because it is very difficult to accurately calculate the true value of the profile error in real time in the numerical control machining process, people generally adopt an approximate estimation method in the actual process of solving the profile error, so that the estimation accuracy requirement can be met, and the calculation load can be reduced to achieve the effect of real-time estimation.

In the numerical control machining process, the cutter reference position command is pre-stored in the memory of the numerical control machine tool before the workpiece machining is started, namely the cutter reference position command is stored in the memory of the numerical control machine tool and is the original process of the numerical control machining, but not the steps additionally required by the invention, so the practicability and the convenience of the invention are improved.

2. Measuring the actual position of the cutter corresponding to each sampling period in real time by using an encoder;

at present, most of commercial three-axis numerical control machines on the market have the function of monitoring the position of a cutter in real time through a position detection device, and the position detection device comprises an encoder, a grating ruler, a laser interferometer and the like. Compared with other position detection devices, the encoder has the characteristics of economy and detection precision basically meeting the actual processing requirements, so that the encoder is most widely applied to position detection of the numerical control machine tool. Therefore, the encoder can be used for quickly and conveniently measuring the actual position of the tool corresponding to each sampling period in real time.

3. Finding a reference position closest to the actual position of the cutter by an index method;

FIG. 3 is a schematic diagram of a triaxial contour error estimation method constructed according to a preferred embodiment of the present invention, and FIG. 3 is a schematic diagram of a triaxial contour error estimation method proposed by the present invention, wherein … P_r+k-j-1,P_r+k-j,P_r+k-j+1… are tool reference position command points of the tool track after interpolation processing, and these points are prestored in the memory of the numerical control system and are known; p_r+kIs the current sampling period and the actual position P of the cutter_aCorresponding reference position of tool, actual position of tool P_aObtained by encoder monitoring. Ideally we want P_r+kAnd P_aAlthough the motion control systems are overlapped, the motion control systems in actual situations have problems such as disturbance and bandwidth limitation, so that errors are inevitable. First, the actual positions P of the cutting tools are calculated respectively_aAnd a reference position P_r+kDistance of nearby points:

p in formula (1)_a＝[x_a,y_a,z_a]As the actual position of the tool, P_r+k+i＝[x_r+k+i,y_r+k+i,z_r+k+i]For reference position P of the tool_r+kNearby location points, N is the set index boundaryThe index boundary is set to reduce the calculation amount and improve the estimation speed, and the size of the index boundary is generally set to be 50-100, so that the index precision can be ensured, and the calculation amount can be reduced. Then, the minimum value is found out by comparing the distances obtained by the formula (1)

The corresponding reference position is the reference position point which is closest to the actual position of the cutter and is to be obtained. As shown in fig. 3, the reference position point P_r+k-jI.e. the reference position point found closest to the actual position of the tool.

4. Carrying out contour error estimation by using the stored reference position command and the actually measured cutter position by using the proposed three-point arc approximation estimation method;

as shown in fig. 3, the reference position point P_r+k-jFor the found distance from the actual position P of the tool_aNearest reference position point, P_r+k-j-1And P_r+k-j+1Is P_r+k-jReference position points on two adjacent sides.

First, suppose P_r+k-j-1、P_r+k-jAnd P_r+k-j+1The three points are not collinear, and then the theorem that three points P which are not on the same straight line are found according to the theorem that three points which are not on the same straight line are crossed and only one plane is arranged_r+k-j-1、P_r+k-jAnd P_r+k-j+1A spatial plane can be uniquely determined, and three points which are not on the same straight line can determine a unique circular arc. Therefore, three points P not on the same straight line can be made_r+k-j-1、P_r+k-jAnd P_r+k-j+1The determined plane is a circular plane ⊙ O₀，P_r+k-j-1、P_r+k-jAnd P_r+k-j+1The circle center of the arc determined by the three points is O₀＝[x₀,y₀,z₀]^TThe radius of the circular arc is R and the center of the circle is O₀＝[x₀,y₀,z₀]^TAnd radius R is the unknown to be solved for, the solution of which will be developed in detail below.

Because of four points P in three-dimensional space_r+k-j-1＝[x_r+k-j-1,y_r+k-j-1,z_r+k-j-1]^T、

P_r+k-j＝[x_r+k-j,y_r+k-j,z_r+k-j]^T、P_r+k-j+1＝[x_r+k-j+1,y_r+k-j+1,z_r+k-j+1]^TAnd O₀＝[x₀,y₀,z₀]^TAre coplanar, and therefore the following formula can be derived:

p in formula (2)_r+k-j-1、P_r+k-jAnd P_r+k-j+1Is a known reference position; equation (2) can be rewritten as follows:

A₁x₀+B₁y₀+C₁z₀+D₁＝0 (3)

in the formula (3)

And

and according to the circle center O of the arc₀To three points P on the arc_r+k-j-1、P_r+k-jAnd P_r+k-j+1Are equal to the arc radius R, the following two equations can be obtained:

(P_r+k-j+1-O₀)^T(P_r+k-j+1-O₀)＝(P_r+k-j-O₀)^T(P_r+k-j-O₀) (4)

(P_r+k-j+1-O₀)^T(P_r+k-j+1-O₀)＝(P_r+k-j-1-O₀)^T(P_r+k-j-1-O₀) (5)

equations (4) and (5) can be written as follows:

A₂x₀+B₂y₀+C₂z₀+D₂＝0 (6)

A₃x₀+B₃y₀+C₃z₀+D₃＝0 (7)

in the formulae (4) and (5) [ A ]₂B₂C₂]^T＝2(P_r+k-j-P_r+k-j+1)、

D₂＝P_r+k-j+1 ^T·P_r+k-j+1-P_r+k-j ^T·P_r+k-j、[A₃B₃C₃]^T＝2(P_r+k-j-1-P_r+k-j+1) And, and

D₃＝P_r+k-j+1 ^T·P_r+k-j+1-P_r+k-j-1 ^T·P_r+k-j-1。

the simultaneous equations (3), (6) and (7) can give the following formula:

thus, the center O of the arc in three-dimensional space₀Can be obtained by the following formula (9):

therefore, the radius of the circular arc can also be easily obtained by the following formula (10):

because of the actual position P of the tool_aPossibly with the circular plane ⊙ O₀Not coplanar and therefore subjected to a projection process. Assuming the actual position P of the tool_a＝[x_a,y_a,z_a]^TAt the circular plane ⊙ O₀Is P'_a＝[x′_a,y′_a,z′_a]^TCircular plane ⊙ O₀The unit normal vector n of (a) can be obtained by:

n＝v₁×v₂(13)

in the formulae (11) and (12), | · | is an euclidean norm, and "×" in the formula (13) represents a cross product between two vectors, when the circle plane ⊙ O₀The unit normal vector n is obtained by the equation (13), and the actual position P of the tool_a＝[x_a,y_a,z_a]^TAt the circular plane ⊙ O₀Projected point P 'of'_aCan be obtained by the following formula:

as shown in fig. 3, the center O of the arc₀And projection point P'_aIs connected with the arc P_r+k-j+1P_r+k-j-1Point of intersection of

To estimate the resulting contour position. The size of the contour error of the triaxial numerical control machining can be obtained by the following formula:

(15) where | | · | | is the euclidean norm. As can be seen from equation (15), estimating the magnitude of the contour error does not require solving for the estimated contour position

The estimation of the error magnitude of the contour only needs to solve the center O of the fitting circular arc₀Coordinate of (d), size of arc radius R and actual position P of tool_a＝[x_a,y_a,z_a]^TAt the circular plane ⊙ O₀Projected point P 'of'_aThe coordinates of (2) are just required.

When P is present_r+k-j-1、P_r+k-jAnd P_r+k-j+1In order to be able to deal with the situation where the three points are collinear, where the three points cannot define a unique plane, the above-described three-point arc estimation method cannot deal with this situation, the present invention uses the method shown in fig. 4. Directly determining the actual position P of the tool by projection_a＝[x_a,y_a,z_a]^TOn line segmentProjected point P 'on'_a. Calculating projection point P'_aCan be obtained by the following formula:

in the formula (16), | | · | | is the euclidean norm. The actual position P of the tool can be obtained by the equations (16) and (17)_a＝[x_a,y_a,z_a]^TOn line segment

Projected point P 'on'_aThe coordinates of (a). Therefore, the size of the contour error of the three-axis numerical control machining at this time can be obtained by the following formula:

when P can be estimated by the formula (18)_r+k-j-1、P_r+k-jAnd P_r+k-j+1Contour error when these three points are collinear.

When the reference position which is closest to the actual position of the tool and is found by the index method is positioned at the reference positionWhen two endpoints of the command are set, namely P₁Or P_N(subscripts 1 and N denote the reference position commands at the head and tail ends, respectively), the size of the contour error of the three-axis numerical control machining at this time can be obtained by the following formula:

in summary, the method for estimating contour error in three-axis numerical control machining is provided by the present invention.

Fig. 5(a) is a graph showing the comparison of the estimated accuracy of the total contour error constructed according to the preferred embodiment of the present invention, and fig. 5(b) is a graph showing the comparison of the estimated accuracy of the contour error components of the respective axes constructed according to the preferred embodiment of the present invention, as shown in fig. 5(a) and 5(b), the estimated accuracy is reflected by the magnitude of the estimated deviation, which is obtained by subtracting the actual value of the contour error from the estimation method proposed by the present invention. As can be seen from FIG. 5, the estimation accuracy of the contour error components of both the entire contour error and the respective axes is 2X 10^-6mm or less, i.e. the estimation error of the proposed contour error estimation method is less than 2 x 10^-3And the micrometer is far enough to meet the precision requirement in the commercial numerical control machining process. Therefore, experiments can show that the method provided by the invention can meet the contour error estimation of three-axis numerical control machining.

The invention provides a contour error estimation method for three-axis numerical control machining, which can estimate the size of a contour error in the three-axis numerical control machining process with high precision, and only needs a reference position and an actual tool nose point position after tool track interpolation in the estimation process without other additional information. The method is simple and easy to implement, can accurately and quickly estimate the size of the contour error in the numerical control machining process, has universality, is suitable for cutter tracks of various types of three-dimensional spaces, and has good application value for improving the machining precision of the numerical control machine.

It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims

1. A contour error estimation method of a three-axis numerical control machine tool is characterized by comprising the following steps:

according to said P_r+k-j-1、P_r+k-jAnd P_r+k-j+1Constructing a circle, and determining the radius and center O of the circle₀Coordinates of the actual machining point on the plane ⊙ O of the circle₀Projecting to obtain its projected point P'_a(ii) a The center of the circle O₀And projection point P'_aIs connected to the circle P_r+k-j-1And P_r+k-j+1The arc between them is crossed, the intersection point is

The point of intersection

And the actual machining point P_aIs the profile error to be estimated

2. The contour error estimation method of a three-axis numerical control machine tool according to claim 1, wherein in the step (b), the nearest reference position point P is calculated according to the following expression_r+k-j，

Wherein, P_aIn the formula, the actual processing point P_aCoordinate of (A), P_r+k+iIn which is a point P in the vicinity of the reference point_r+k+iI is along the reference trackNumber of sample points in the forward or reverse direction of the trace, L_iIs the distance of the actual machining point from a point near the reference point.

3. The contour error estimation method of a three-axis numerical control machine tool according to claim 1, wherein, in the step (c1), the radius of the circle is performed according to the following expression,

4. The contour error estimation method of a three-axis numerical control machine tool according to claim 1, wherein, in the step (c1), the contour error is performed according to the following expression,

wherein, P'_aIn which is the coordinate of the projection point, P_aIn the formula, the coordinates of the actual machining point are shown, and R is the radius of the circle.