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

Abstract

The invention belongs to the technical field of precision manufacturing, and discloses a contour error estimation method of a three-axis numerically controlled machine tool. The method includes the following steps: (a) planning an ideal machining reference trajectory, storing the three-dimensional coordinates of each machining point after the interpolation of the reference trajectory, monitoring and storing the three-dimensional coordinates of each machining point on the actual machining trajectory in each adoption cycle; (b) Obtain the reference position point closest to the actual processing point on the reference trajectory; (c) According to the different positional relationship between the nearest reference position point and its adjacent points, different methods are used according to different situations for the required contour. error is estimated. Through the present invention, the estimation process does not need the parameter information and curvature information of the ideal machining parameter trajectory, which is suitable for the case of large curvature in the machining process, with low realization difficulty, small calculation amount, short time consumption, real-time performance and wide application range.

Description

A Contour Error Estimation Method for Three-axis CNC Machine Tool

technical field

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

Background technique

In recent years, with the rapid development of the manufacturing industry, the processing parts are becoming more and more precise and complex, which makes the processing requirements of CNC machine tools in the field of precision manufacturing gradually develop towards high precision. The so-called high precision generally refers to high contour machining accuracy. The machining accuracy level of CNC machine tools directly reflects the technical level of national equipment manufacturing.

In order to reduce the contour error in the NC machining process and improve the contour accuracy of the workpiece surface to be machined, a common method is to design a corresponding contour error controller based on the contour error information to achieve contour control with high machining accuracy. The existing estimation method Generally, it is necessary to refer to the curvature, differential and other information of the trajectory or use an iterative method to estimate the contour error. This method will limit the versatility of the estimation method, and there is a problem that the calculation is too large and the real-time performance is not strong. Because the high-precision contour error estimation is Therefore, how to quickly and effectively estimate the contour error in the NC machining process and how to establish a mathematical model for NC machining contour error estimation is a major problem to be solved urgently.

SUMMARY OF THE 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 CNC machine tool. The positional relationship between adjacent points determines the method of error estimation, thereby solving the technical problem of error estimation of three-axis contour machining in three-dimensional space.

In order to achieve the above object, according to the present invention, a method for estimating a contour error of a three-axis CNC machine tool is provided, characterized in that the method comprises the following steps:

(a) For the object to be processed, plan the processing path of the three-axis CNC machine tool tool and obtain an ideal processing reference trajectory, interpolate the reference trajectory and store the three-dimensional coordinates of each processing point after interpolation, and the tool follows the reference. The object to be processed is processed by the trajectory, and the actual processing trajectory of the tool is monitored at the same time, and the three-dimensional coordinates of each processing point on the actual processing trajectory are stored;

(b) For the current actual machining point Pa of the tool, find the reference point _{Pr+k corresponding} to the actual machining point in the reference trajectory, and calculate the distance between the actual machining point and a point near the reference point, The point corresponding to the minimum value of the distance is the reference position point _Pr+kj closest to the actual machining point on the reference track;

(c) The points adjacent to the nearest reference position point _Pr+kj on the reference track are Pr _+kj-1 and Pr _+k-j+1 , according to the following different situations, respectively The required contour error is estimated:

(c1) When the _Pr+kj-1 , _Pr+kj and Pr _+k-j+1 are not on the same straight line,

该交点

与所述实际加工点P_a的距离为待估算的轮廓误差

Construct a circle according to the _Pr+kj-1 , _Pr+kj and Pr _+k-j+1 , and determine the radius of the circle and the coordinates of the center O ₀ ; place the actual machining point at the location of the circle The plane ⊙O ₀ is projected, and its projection point P' _a is obtained; the connecting line between the center O ₀ of the circle and the projection point P _a ' is connected with _Pr+kj-1 and Pr _+k- on the circle The arcs between _j+1 intersect, and the intersection point is

the intersection

The distance from the actual machining point _Pa is the contour error to be estimated

(c2) When the _Pr+kj-1 , _Pr+kj and Pr _+k-j+1 are on the same straight line,

A straight line is constructed according to the _Pr+kj-1 , _Pr+kj and Pr _+k-j+1 , and the projection point of the actual processing point on the straight line is obtained, and the projection point is the same as the actual processing point. The distance between points _Pa is the contour error to be estimated

(c3) When the reference position point _Pr+kj is the end point of both ends on the reference track,

The distance between the reference position point P _r+kj and the actual machining point P _a is the contour error to be estimated

Further preferably, in step (b), the nearest reference position point _Pr+kj is preferably calculated according to the following expression,

Among them, Pa is the coordinate of the actual processing point Pa in the formula, Pr+ _{k +i is} the coordinate of the point Pr+k+ _i near the reference point in the formula, and i is the positive and negative along the reference trajectory Sampling point number in the forward or reverse direction, _Li is the distance between the actual processing point and the point near the reference point.

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

Wherein, O ₀ is the coordinate of the center of the circle in the formula, _Pr+kj-1 is the coordinate of the point _Pr+kj-1 in the formula, and R is the radius of the circle.

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

Wherein, P' _a is the coordinate of the projection point in the formula, and P _a is the coordinate of the actual processing point in the formula.

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

1. In the present invention, by using the discrete points on the ideal processing parameter trajectory, the estimation process does not require the parameter information and curvature information of the ideal processing parameter trajectory, but only needs to use the coordinates of the discrete points to reduce the complexity of the estimation, the difficulty is low, and the scope of application wide;

2. In the present invention, the arc is determined by three adjacent points, thereby reflecting the change of the ideal path curve, and estimating the curvature of the trajectory between the ideal processing parameters, thereby reducing the sensitivity to the curvature change of the trajectory, which is suitable for the processing process In the case of large curvature;

3. The contour error estimation method for three-axis numerical control machining provided by the present invention can accurately estimate the size of the contour error in the three-axis numerical control machining process, and in the estimation process, only the distance to the actual machining point after the interpolation of the tool path is required. The reference position point and the actual processing point position do not need other additional information, the calculation amount is small, the time is short, and it is real-time;

4. The invention is simple and easy to implement, can accurately and quickly estimate the size of the contour error in the CNC machining process, and has universality, which is suitable for various types of three-dimensional space tool paths, and has a great effect on improving the machining accuracy of CNC machine tools. good application value.

Description of drawings

Fig. 1 is the implementation flow chart of the contour error estimation during the machining process of the three-axis numerical control machine tool (CNC) constructed according to the preferred embodiment of the present invention;

Fig. 2 is the contour error schematic diagram of the numerical control machining constructed according to the preferred embodiment of the present invention;

3 is a schematic diagram of a three-axis contour error estimation method constructed according to a preferred embodiment of the present invention;

4 is a schematic diagram of a three-axis contour error estimation method under special circumstances constructed according to a preferred embodiment of the present invention;

Figure 5(a) is a comparison diagram of the estimation accuracy of the overall contour error constructed according to the preferred embodiment of the present invention;

Fig. 5(b) is a comparison chart of the estimation accuracy of the contour error components of each axis constructed according to the preferred embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

Fig. 1 is the implementation flow chart of the contour error estimation in the three-axis numerical control machine tool (CNC) machining process constructed according to the preferred embodiment of the present invention, as shown in Fig. 1, the present invention constructs the contour error estimation model in the three-axis CNC machining process The method includes the following steps:

Store the tool reference position commands of X, Y and Z axes after interpolation of the reference trajectory during CNC machine tool processing into the memory of the CNC machine tool;

As shown in Figure 2, it is a schematic diagram of the contour error of CNC machining on the XY plane, where P _r is the tool reference position, P _a is the actual tool position corresponding to the tool reference position P _r , and e _x and e _y represent the CNC machining process. The tracking error of the tool in the X-axis and Y-axis directions respectively, ε represents the contour error of the tool during the CNC machining process. Obviously, it is clear from Fig. 2 that the contour 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 contour error in real time during the CNC machining process, people generally use the approximate estimation method in the process of actually solving the contour error, which can not only meet the accuracy requirements of the estimation, but also reduce the The computing load achieves the effect of real-time estimation.

In the CNC machining process, the tool reference position command is pre-stored in the memory of the CNC machine tool before the workpiece machining starts, that is to say, the tool reference position command is stored in the CNC machine tool memory. Rather than an additional step required by the present invention, this increases the utility and convenience of the present invention.

2. Use the encoder to measure the actual position of the tool corresponding to each sampling period in real time;

At present, most of the commercial three-axis CNC machine tools on the market have the function of real-time monitoring of the tool position through a position detection device, which includes an encoder, a grating ruler, and a laser interferometer. Compared with other position detection devices, the encoder is economical and the detection accuracy basically meets the actual processing requirements, so the encoder is most widely used in the position detection of CNC machine tools. Therefore, the actual position of the tool corresponding to each sampling period can be quickly and easily measured in real time by using the encoder.

3. Use the index method to find the reference position closest to the actual position of the tool;

FIG. 3 is a schematic diagram of a three-axis contour error estimation method constructed according to a preferred embodiment of the present invention. As shown in FIG. 3 , it is a schematic diagram of a three-axis contour error estimation method proposed by the present invention, wherein ... P _r+kj-1 , P _r+kj , P _r+k-j+1 ... are the tool reference position command points after the tool path has been interpolated, these points are pre-stored in the CNC system memory, so they are known; P _r+k is the tool reference position corresponding to the actual tool position P _a in the current sampling period, and the actual tool position P _a is obtained through the monitoring of the encoder. Ideally, we hope that P _r+k and P _a are coincident, but due to the problems of disturbance and bandwidth limitation in the motion control system in practice, errors inevitably exist. First, calculate the distance between the actual tool position _Pa and the point near the reference position _Pr+k :

所对应的参考位置即为所要获得的距离刀具实际位置最近的参考位置点。如图3所示，参考位置点P_r+k-j即为所找到的距离刀具实际位置最近的参考位置点。In formula (1), P _a =[x _a , y _a , z _a ] is the actual position of the tool, P _r+k+i =[x _r+k+i , y _r+k+i , z _{r+k+ i} ] is the position point near the tool reference position _Pr+k , and N is the index boundary set. The index boundary is set to reduce the amount of calculation and improve the estimation speed. The size of the index boundary is generally set between 50 and 100, so that both The index accuracy can be guaranteed, and the calculation amount can also be reduced. Then find the minimum value by comparing the distances obtained by formula (1)

The corresponding reference position is the closest reference position to the actual position of the tool to be obtained. As shown in Fig. 3, the reference position point _Pr+kj is the found reference position point closest to the actual position of the tool.

4. Use the stored reference position command and the actual measured tool position to use the proposed three-point arc approximation estimation method to estimate the contour error;

As shown in Figure 3, the reference position point _Pr+kj is the found reference position point closest to the actual position Pa of the tool, and _Pr+kj-1 and Pr _{+k-j+1 are} the _Pr+kj phase Reference location points on both sides of the neighbor.

First of all, assuming that the three points Pr _+kj-1 , _Pr+kj and Pr _+k-j+1 are not collinear, then according to the theorem of "Three points that are not on a straight line, there is only one plane" It can be known that three points _Pr+kj-1 , _Pr+kj and Pr _+k-j+1 which are not on the same straight line can uniquely determine a space plane, and three points that are not on the same straight line can determine a unique arc. Therefore, the plane determined by the three points _Pr+kj-1 , _Pr+kj and Pr _+k-j+1 which are not on the same straight line can be defined as the circular plane ⊙O ₀ , Pr _+kj-1 , P The center of the arc determined by the three points _r+kj and P _r+k-j+1 is O ₀ =[x ₀ , y ₀ , z ₀ ] ^T , the radius of the arc is R, and the center O ₀ =[x ₀ , y ₀ , z ₀ ] ^T and radius R are unknowns to be solved, and the solution method will be expanded in detail below.

Because the four points in the three-dimensional space P _r+kj-1 =[x _r+kj-1 , y _r+kj-1 , z _r+kj-1 ] ^T ,

P _r+kj =[x _r+kj ,y _r+kj ,z _r+kj ] ^T , P _r+k-j+1 =[x _r+k-j+1 ,y _r+k-j+1 ,z _r+k-j+1 ] ^T and O ₀ =[x ₀ ,y ₀ ,z ₀ ] ^T are coplanar, so the following formula can be obtained:

_Pr+kj-1 , _Pr+kj and Pr _+k-j+1 in formula (2) are known reference positions; formula (2) can be rewritten as the following equation:

A ₁ x ₀ +B ₁ y ₀ +C ₁ z ₀ +D ₁ =0 (3)

和

In formula (3)

and

According to the distance from the arc center O ₀ to the three points _Pr+kj-1 , _Pr+kj and Pr _+k-j+1 on the arc are equal to the arc radius R, the following two equations can be obtained :

( _Pr+k-j+1 -O ₀ ) ^T ( _Pr+k-j+1 -O ₀ )=( _Pr+kj -O ₀ ) ^T ( _Pr+kj -O ₀ ) (4)

( _Pr+k-j+1 -O ₀ ) ^T ( _Pr+k-j+1 -O ₀ )=( _Pr+kj-1 -O ₀ ) ^T ( _Pr+kj-1 -O ₀ ) (5)

Equations (4) and (5) can be written as the following equations, respectively:

A ₂ x ₀ +B ₂ y ₀ +C ₂ z ₀ +D ₂ =0 (6)

A ₃ x ₀ +B ₃ y ₀ +C ₃ z ₀ +D ₃ =0 (7)

In formula (4) and formula (5) [A ₂ B ₂ C ₂ ] ^T =2( _Pr+kj -Pr _+k-j+1 ),

D ₂ = _Pr+k-j+1 ^T · _Pr+k-j+1 -Pr _+kj ^T ·Pr _+kj , [A ₃ B ₃ C ₃ ] ^T =2( _{Pr+kj- 1} -Pr _+k-j+1 ), and

D ₃ = _Pr+k-j+1 ^T · _Pr+k-j+1 -Pr _+kj-1 ^T · _Pr+kj-1 .

Simultaneous formulas (3), (6) and (7) can be obtained as follows:

Therefore, the coordinates of the arc center O ₀ in the three-dimensional space can be obtained by the following formula (9):

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

Because the actual position P _a of the tool may not be coplanar with the circular plane ⊙O ₀ , projection processing is required. Assume that the actual tool position P _a =[x _a , y _a , z _a ] ^T is projected on the circular plane ⊙O ₀ to be P′ _a =[x′ _a , y′ _a , z′ _a ] ^T . The unit normal vector n of the circular plane ⊙O ₀ can be obtained by the following formula:

n=v ₁ ×v ₂ (13)

||·|| in Equation (11) and Equation (12) is the Euclidean norm, and “×” in Equation (13) represents the cross product between two vectors. When the unit normal vector n of the circular plane ⊙O ₀ is obtained by formula (13), the actual position of the tool P _a =[x _a , y _a , z _a ] The projection point P′ _a of ^T on the circular plane ⊙O ₀ can be passed through Obtained by the following formula:

为估算所得到的轮廓位置。三轴数控加工的轮廓误差的大小可以通过下式获得：As shown in Figure 3, the line connecting the arc center O ₀ and the projection point _P'a and the intersection of the arc P _r+k-j+1 P _r+kj-1

for the estimated contour position. The size of the contour error of three-axis CNC machining can be obtained by the following formula:

的坐标，轮廓误差大小的估算只需要求解出拟合圆弧的圆心O₀的坐标、圆弧半径R的大小以及刀具实际位置P_a＝[x_a,y_a,z_a]^T在圆平面⊙O₀的投影点P′_a的坐标即可。(15) ||·|| is the Euclidean norm. It can be seen from equation (15) that the estimated contour error does not need to solve the estimated contour position

To estimate the size of the contour error, it only needs to solve the coordinates of the center O ₀ of the fitted arc, the size of the arc radius R and the actual position of the tool P _a = [x _a , y _a , z _a ] ^T on the circular plane The coordinates of the projection point _P'a of ⊙O ₀ are sufficient.

When the three points P _r+kj-1 , P _r+kj and P _r+k-j+1 are collinear, the three points cannot determine a unique plane, and the above three-point arc estimation method is This situation cannot be handled, and in order to be able to handle this situation, the present invention adopts the method shown in FIG. 4 . The actual tool position P _a =[x _a ,y _a ,z _a ] ^T line segment is directly obtained by the projection method The projected point P' _a on . The method of calculating the projection point _P'a can be obtained by the following formula:

上的投影点P′_a的坐标。因此，此时三轴数控加工的轮廓误差的大小可以通过下式获得：In formula (16) ||·|| is the Euclidean norm. The actual tool position P _a =[x _a , y _a , z _a ] ^T line segment can be obtained by formula (16) and formula (17)

The coordinates of the projected point _P'a on . Therefore, the size of the contour error of the three-axis CNC machining can be obtained by the following formula:

The contour error when the three points Pr _+kj-1 , _Pr+kj and Pr _+k-j+1 are collinear can be estimated by equation (18).

When the reference position closest to the actual position of the tool found by the index method is located at the two end points of the reference position command, it is P ₁ or P _N (the subscripts 1 and N represent the reference position commands at the beginning and the end respectively). The size of the contour error of the axis CNC machining can be obtained by the following formula:

To sum up, it is a complete contour error estimation method for three-axis numerical control machining proposed by the present invention.

Fig. 5(a) is a comparison diagram of the estimation accuracy of the overall contour error constructed according to the preferred embodiment of the present invention, and Fig. 5(b) is the estimated accuracy of the contour error components of each axis constructed according to the preferred embodiment of the present invention As shown in Fig. 5(a) and Fig. 5(b), the estimation accuracy is reflected by the size 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. . It can be seen from Fig. 5 that both the estimation accuracy of the overall contour error and the estimation accuracy of the contour error components of each axis are within 2 × 10 ^-6 mm, that is, the estimation error of the proposed contour error estimation method is less than 2 × 10 mm. ^-3 μm, which far meets the precision requirements in the commercial CNC machining process. Therefore, through experiments, it can be concluded that the method proposed by the present invention can meet the contour error estimation of three-axis numerical control machining.

The invention proposes a contour error estimation method for three-axis numerical control machining. This method can estimate the size of the contour error in the three-axis numerical control machining process with high accuracy, and only the reference position and the tool path interpolation are required in the estimation process. The actual tool nose point position without any additional information. The invention 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 various types of three-dimensional space tool paths, and has a good effect on improving the machining accuracy of the numerical control machine tool. Value.

Those skilled in the art can easily understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, etc., All should be included within the protection scope of the present invention.

Claims (4)

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

(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 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

(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

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,

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.

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.

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