CN103777570B - Mismachining tolerance quick detection compensation method based on nurbs surface - Google Patents

Abstract

The invention discloses a method for quickly detecting and compensating processing errors based on NURBS curved surfaces, including: 1) analyzing the designed NURBS curved surface, and selecting a series of feature points as the sequence P to be measured; 2) processing the designed NURBS curved surface with a machine tool surface, and then measure the points to be measured in the sequence to be measured P to obtain the measured sequence Q'; 3) Calculate the deviation between the measured sequence Q' and the sequence to be measured P, if the deviation is less than or equal to the machining accuracy, no adjustment is required; If the deviation is greater than the machining accuracy, adjust the measured sequence P according to the deviation to obtain the compensation sequence W; 4) Adjust the control point C according to the compensation sequence W to obtain the compensation surface, and process according to the compensation surface to obtain the error of the designed NURBS surface Smaller machining surfaces. The method of the invention can improve the detection efficiency of the machining accuracy of the free-form surface by the on-machine measurement method and can perform compensation processing on the free-form surface.

Description

A Fast Detection and Compensation Method for Machining Errors Based on NURBS Surface

technical field

The invention relates to the field of machine tool processing, in particular to a fast detection and compensation method for processing errors based on NURBS curved surfaces.

Background technique

With the development of industries such as aviation, automobiles and molds, free-form surfaces are more and more widely used in part design, and the processing of free-form surfaces has higher requirements for precision and efficiency. In order to improve the machining accuracy of free-form surfaces, it is generally necessary to measure, evaluate and compensate for machining errors. The characteristics of non-rotational symmetry, irregular shape, and irregular structure of free-form surfaces make the measurement of free-form surfaces very complicated. Rapid and precise measurement and evaluation of the machining error of free-form surfaces is of great significance for machining high-precision free-form surfaces.

The measurement of free-form surfaces can be mainly divided into two methods: off-line measurement and on-machine measurement. The off-line detection technology based on the three-coordinate measuring machine can be used to measure the accuracy of the free-form surface, but this measurement requires the workpiece to be moved, re-clamped and positioned. This process will bring a certain repositioning error and affect the accuracy of the measurement. . The on-machine measurement technology is to directly measure the CNC-machined parts on the CNC milling machine, which avoids the relocation error problem in the offline measurement method. There are two types of on-machine measurement: contact measurement and non-contact measurement. At present, there are many measurement principles that can measure the position of a point on a curved surface.

By measuring a series of points on the surface, the evaluation of the machining accuracy of the surface can be realized, and the error distribution of the processed surface can be obtained, so as to determine the error compensation strategy. At present, there are mainly the following types of measurement schemes for free-form surface machining errors: 1. Plan the detection path for the measured surface, then measure the points on the surface one by one, and compare and analyze the detection results with the ideal CAD model of the part to find each Measure the deviation of the points to obtain the processing error of the curved surface. Its representative patent is "on-line detection method for surface processing accuracy of complex parts" CN201210266355.6; 2. Design the measurement path according to the processing path, measure the points on the surface point by point, and real-time Collect the surface error data of the measuring points to realize the acquisition of the surface error data of the entire workpiece surface. Its representative patent is "In-situ measurement method of free-form surface based on processing machine tools" CN201010530776.6; 3. Measure the profile of the characteristic section of the curved surface , to obtain the error between the measured profile points of each characteristic section of the curved surface and the corresponding real profile points, which is used to detect the accuracy of the curved surface. Its representative patent is "a detection method for blades with complex curved surfaces" CN201310021045.2.

Method 1 can obtain the machining error of the surface by measuring a large number of points on the surface, and then comparing it with the ideal CAD model. However, due to the large number of measured points, the measurement efficiency of the entire surface will be relatively low. Method 2 is similar to method 1, except that the surface shape error data is obtained directly in each measurement, which avoids the later data processing and error analysis of massive measurement data, and can improve the measurement efficiency to a certain extent, but there are still disadvantages of method 1. A large number of measurement points makes the measurement inefficient. Method 3 chooses to measure the characteristic line of the curved surface. This method requires a small number of measurement points, but it can only test whether the accuracy meets the requirements, and cannot measure the specific processing error of the curved surface.

The NURBS surface can accurately represent complex free-form surfaces. The shape of the surface is determined by the control points, weight factors and node vectors. The original surface can be adjusted by changing the node vectors, control points and weight factors.

Contents of the invention

In order to improve the detection efficiency of the machining accuracy of the free-form surface by the on-machine measurement method and perform compensation processing on the free-form surface, the present invention provides a fast detection and compensation method for machining errors based on NURBS curved surfaces.

A method for fast detection and compensation of machining errors based on NURBS surfaces, comprising the following steps:

1) Analyze the node vector UV and control point C information of the designed NURBS surface, and select a series of feature points on the designed NURBS surface as the sequence P to be measured;

2) Process the surface with a machine tool according to the node vector UV and control point C of the designed NURBS surface, and then use the measuring head to measure the points to be measured in the sequence P to be measured to obtain the measured sequence Q';

3) Calculate the deviation between the measured sequence Q' and the measured sequence P, if the deviation is less than or equal to the machining accuracy, no adjustment is required;

If there is a deviation greater than the machining accuracy, adjust the sequence P to be measured according to the deviation to obtain the compensation sequence W;

4) Adjust the control point C according to the compensation sequence W to obtain the compensation surface, and process it according to the compensation surface to obtain a processed surface with a smaller error with the designed NURBS surface.

In step 1), as a preference, the sequence P to be measured includes the points on the surface corresponding to the node vector UV at the node and the basic feature points on the surface, and the basic feature points are the extreme points of the surface and the maximum and minimum curvature point. The above points have greater control over the NURBS surface, that is, they have a greater impact on the NURBS surface. The above points are selected as the sequence P to be measured, and finally the compensation sequence W is obtained by adjusting the sequence P to be measured, so that a more accurate compensation surface can be obtained. Finally, the processed surface with smaller error is obtained.

In step 2), use the measuring head to measure the points to be measured in the sequence P to be measured, including: unloading the processing tool, installing the contact measuring head on the spindle of the machine tool, during measurement, the X-axis and Y-axis coordinates are the same as the points to be measured The points to be measured in the sequence P are consistent, and the Z-axis coordinate value is obtained. The Z-axis coordinate value needs to eliminate the deviation x, Where R is the radius of the measuring ball in the contact measuring head, θ is the slope of the main direction of the measuring point, that is, θ is the angle formed by the tangent of the surface at the intersection of the measuring ball and the curved surface in the contact measuring head and the horizontal direction.

In step 3), the deviation between the measured sequence Q' and the measured sequence P is calculated, and the measured sequence P is adjusted according to the deviation to obtain the compensation sequence W, which specifically includes: calculating the measured points in the measured sequence Q' and the measured sequence The error between the Z-axis coordinates of the point to be measured corresponding to P is subtracted from the sequence P to be measured to obtain the compensation sequence W.

In step 4), the control point C is adjusted according to the compensation sequence W to obtain the compensation surface, which specifically includes: setting the machining accuracy eps, and calculating the deviation sequence D' according to the compensation sequence W and the sequence P to be measured, if the deviation sequence D' If the absolute value of each error in the deviation sequence D' is less than or equal to eps, the surface does not need to be adjusted; if at least one error d' in the deviation sequence D' has an absolute value greater than eps, the surface needs to be adjusted; The corresponding control point C is adjusted, and the amount of adjustment of the corresponding control point C of d' is passed through - calculation, where w _i,j is the weight factor associated with the control point C, N _i,k (u) and N _j,l (v) are the canonical B-spline basis of degree k in direction u and degree l in direction v respectively, ε _{i , j} is the vector adjusted by the control point C corresponding to d', q is the three-dimensional coordinate of the point to be measured corresponding to d' on the surface, and q is the three-dimensional coordinate of the measured point on the surface corresponding to d'. After the control point C is adjusted, re-measure according to the new measurement sequence and deviation sequence of the surface, calculate the deviation again, and then adjust again until the surface adjustment is completed.

Compared with prior art, the present invention has following advantage:

The NURBS surface-based processing error rapid detection and compensation method of the present invention can quickly measure, evaluate and compensate the machining accuracy of the free-form surface on the machine, and the biggest feature is that the compensation surface can be quickly obtained by measuring the feature points on the surface , to complete the detection, evaluation and compensation of the machining accuracy of the free-form surface. High-efficiency measurement greatly improves the applicability of on-machine measurement in actual processing. The method proposed by the invention is not limited to the contact measuring head, but also applicable to most other forms of on-machine measuring equipment, and has broad application prospects.

Description of drawings

Fig. 1 is the schematic diagram of the steps of the NURBS surface-based machining error rapid detection and compensation method of the present invention;

Fig. 2 is a structural representation of a NURBS surface and the points to be measured selected after analyzing the surface;

Fig. 3 is the structural representation of the measurement deviation x caused by the curvature of the measuring point on the curved surface in the present invention;

Fig. 4 is the structural representation of design surface and processing surface;

Fig. 5 is the machining error distribution diagram between the design curved surface and the processed curved surface;

Fig. 6 is a structural schematic diagram of the design curved surface and the compensation curved surface.

detailed description

Example 1

The present invention will be further described below in conjunction with accompanying drawings and examples.

As shown in Figure 1, for the present invention based on NURBS curved surface machining error rapid detection and compensation method, comprising the following steps:

1) Analyze the node vector UV and control point C information of the designed NURBS surface, and select a series of feature points on the designed NURBS surface as the sequence P to be measured;

The sequence P to be tested includes the points on the surface corresponding to the node vector UV at the node and the basic feature points on the surface. The basic feature points are the extreme points of the surface and the maximum and minimum points of curvature;

2) Process the surface with a computer-aided machine tool according to the node vector UV and control point C of the designed NURBS surface, and then use the measuring head to measure the points to be measured in the sequence P to be measured to obtain the measured sequence Q';

Use the measuring head to measure the point to be measured in the sequence P to be measured, including: remove the processing tool, install the contact measuring head on the spindle of the machine tool, during measurement, the X-axis and Y-axis coordinates are the same as those in the sequence P to be measured The points are consistent, and the Z-axis coordinate value is obtained. The Z-axis coordinate value needs to eliminate the deviation x, Where R is the radius of the measuring ball in the contact measuring head, θ is the slope of the main direction of the measuring point, that is, θ is the angle formed by the tangent of the surface at the intersection of the measuring ball 2 and the actual contact point 4 in the contact measuring head and the horizontal direction;

3) Calculate the error between the measured point in the measured sequence Q' and the Z-axis coordinate of the measured point corresponding to the measured sequence P, subtract the error from the measured sequence P to obtain the compensation sequence W, if the deviation is less than or equal to the machining accuracy, No adjustment is required;

If there is a deviation greater than the machining accuracy, adjust the sequence P to be measured according to the deviation to obtain the compensation sequence W;

4) Adjust the control point C according to the compensation sequence W to obtain a compensation surface, and process according to the compensation surface to obtain a processed surface with a smaller error with the designed NURBS surface;

Adjust the control point C according to the compensation sequence W to obtain the compensation surface, which specifically includes: setting the machining accuracy eps, calculating the deviation sequence D' according to the compensation sequence W and the sequence P to be measured, if the absolute value of each error in the deviation sequence D' are less than or equal to eps, the surface does not need to be adjusted; if at least one error d' in the deviation sequence D' has an absolute value greater than eps, the surface needs to be adjusted; then the control point C of the point p to be measured corresponding to d' on the surface To adjust, the amount adjusted by the control point C is passed calculation, where w _i,j is the weight factor associated with the control point C, N _i,k (u) and N _j,l (v) are the canonical B-spline basis of degree k in direction u and degree l in direction v respectively, ε _{i , j} is the vector adjusted by the control point C, q is the three-dimensional coordinates of the point to be measured corresponding to d' on the surface, and q is the three-dimensional coordinates of the measured point on the surface corresponding to d'.

As shown in Figure 2, it is a NURBS surface of 3×3 times, with a size of 100mm×100mm, and a total of 49 control points C. The node vector u={0,0,0,0,0.2674,0.5,0.7401, 1,1,1,1}, v={0,0,0,0,0.2753,0.5,0.7536,1,1,1,1}, control point C={(0,0,20),(0 ,17,20),...,(100,100,20)}. The required machining accuracy is 0.02mm.

The 121 points on the surface are the selected sequence P to be measured, P={(2.0084,3.5678,20.0063),(1.9917,15.3949,20.0812),…,(95.4523,97.3105,18.0836)}, and its corresponding uv parameters As follows: u=v={0.02, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.98}.

According to the node vector UV and control point C of the designed NURBS surface, use computer-aided machine tools to process the surface. After the free-form surface is processed, remove the processing tool and install the contact measuring head (Renishaw RMP600) on the spindle of the machine tool. As shown in Figure 3, the touch-type measuring head includes a measuring ball 2 and a stylus 1 connected to the measuring ball 2. When the touch-type measuring head is activated, the length of the stylus 1 and the radius of the measuring ball 2 are calibrated first, and then the sequence P to be measured is calibrated. Measure and get the measured sequence Q, Q={(2.0084,3.5678,20.0227),(1.9917,15.3949,20.0947),...,(95.4523,97.3105,18.6855)}, process the measured data in the measured sequence Q, eliminate the The measurement deviation x caused by the curvature of the measuring point surface 3, the corrected measured sequence Q' is obtained, and the deviation is passed Calculation, where R is the radius of the measuring ball 2 in the contact measuring head, θ is the slope of the main direction of the measuring point, that is, the angle formed by the tangent of the surface at the intersection of the measuring ball 2 and the actual contact point 4 in the contact measuring head and the horizontal direction 6.5 is the theoretical position of the point to be measured, and the Z-axis coordinate value needs to subtract the deviation x, that is

Q'={(2.0084, 3.5678, 20.0226), (1.9917, 15.3949, 20.0914), ..., (95.4523, 97.3105, 18.1205)}.

As shown in FIG. 4 , it is a structural schematic diagram of the design curved surface 7 , the control points 8 of the design curved surface, the processed curved surface 9 and the control points 10 of the processed curved surface.

Record the control point C after the hth (h=1, 2, 3...) adjustment operation on the point to be measured as C _h ={c _h1 ,c _h2 ,...,c _hM }, M is the number of control points, this In the embodiment, M is 49, and the corresponding measurement sequence Ph = _{{ ph1,ph2,...,phN } on} the obtained curved surface, N is the number of sequences P to be measured, and N is 121 in this embodiment, The maximum value in the deviation sequence D _h ={d _h1 ,d _h2 ,…,d _hN }, D’ _h ={d’ _h1 ,d’ _h2 ,…,d’ _hN } at the measuring point is d _kmax , d’ _kmax .

Input the design surface information, the sequence P to be measured and the sequence Q' to be measured into the computer, set the processing accuracy eps=0.003mm, and the program calculates the deviation sequence D according to the sequence Q' to be measured and the sequence P to be measured, and the distribution of processing errors is shown in the figure As shown in Figure 5, it can be seen from Figure 5 that the machining accuracy of some areas of the curved surface does not meet the required machining accuracy of 0.003mm, and error compensation is required. D＝{d ₁ ,d ₂ ,...,d ₁₂₁ }＝{0.0163,0.0102,...,0.0369}, d _max ＝d ₁₂₁ ＝0.0369＞eps, compare the size of the items in D with the machining accuracy eps, such as in D If all items are less than or equal to the machining accuracy eps, the design surface information input to the machine tool can achieve the desired machining accuracy without adjustment. When one of the items in D is greater than eps, that is, the above situation, d _max =d ₁₂₁ =0.0369>eps=0.003, then it is necessary to first correspond to the sequence P to be measured corresponding to d ₁₂₁ on the curved surface The control point C of the point to be measured p ₁₂₁ is adjusted.

Calculate the error between the measured points in the measured sequence Q' and the Z-axis coordinates of the measured points corresponding to the measured sequence P, and obtain the deviation sequence D', D'={0.0162,0.0102,...,0.0369}, in the measured sequence P subtracts this error to obtain the compensation sequence W, which is as follows:

W = {(2.0084, 3.5678, 19.990), (1.9917, 15.3949, 20.071), ..., (95.4523, 97.3105, 18.0467)}.

Input the design surface information, the sequence P to be measured and the sequence W to be measured into the computer, set the machining accuracy as eps'=0.003mm, and calculate the deviation sequence D' according to the compensation sequence W and the sequence P to be measured, D'={0.0162 ,0.0102,...,0.0369}, d' _max ＝d' ₁₂₁ ＝0.0369＞eps', compare the size of each item in D' with the processing precision eps', when a certain item d' in D' is greater than eps', then the Adjust the control point C on the surface corresponding to the point p to be measured corresponding to d', and the adjusted amount of the control point C is passed calculation, where w _i,j is the weight factor associated with the control point, N _i,k (u) and N _j,l (v) are the canonical B-spline basis of u to k degree and v to l degree respectively, ε _{i, j} is the vector adjusted by the control point C, q is the three-dimensional coordinate of the point to be measured, and q is the three-dimensional coordinate of the actual measuring point corresponding to the point to be measured.

Calculate the measurement sequence P' _h and the deviation sequence D' _h on the surface. If d' _kmax is less than eps', the surface adjustment is completed, and the obtained surface is the compensation surface. Since d' _max =d' ₁₂₁ =0.0369>eps', therefore, the control point C of the point to be measured p ₁₂₁ corresponding to d' ₁₂₁ on the curved surface must be adjusted first, and the adjusted amount of the control point C is passed calculation, where w _i,j is the weight factor associated with the control point, N _i,k (u) and N _j,l (v) are the canonical B-spline basis of u to k degree and v to l degree respectively, ε _{i, j} is the vector adjusted by the control point C, q is the three-dimensional coordinates of the point p ₁₂₁ to be measured, and q is the three-dimensional coordinates of the actual measuring point q ₁₂₁ corresponding to the point p ₁₂₁ to be measured. Each adjustment measurement sequence and deviation sequence are as follows:

1st:

C' ₁ = {(0,0,19.9867),(0,17,19.9907),...,(100,100,19.9306)};

P' ₁ = {(2.0084,3.5678,20.0028),(1.9917,15.3949,20.0727),...,(95.4523,97.3105,18.0637)};

D' ₁ ={0.0127,0.0053,...,0.0176}, d' _1max =d' _1,71 =0.0231>eps';

2nd:

C' ₂ ＝{(0,0,19.9822),(0,17,19.9903),...,(100,100,19.9069)};

P' ₂ ＝{(2.0084,3.5678,19.9992),(1.9917,15.3949,20.0731),...,(95.4523,97.3105,18.0568)};

D' ₂ ={0.0093,0.0054,...,0.0101}, d' _2max =d' _2,46 =0.0171>eps';

…………

…………

…………

15th time:

C' ₁₅ ＝{(0,0,19.9763),(0,17,19.9874),...,(100,100,19.9355)};

P' ₁₅ ＝{(2.0084,3.5678,19.9927),(1.9917,15.3949,20.0744),...,(95.4523,97.3105,18.0496)};

D' ₁₅ ={0.0026,0.0034,...,0.0029}, d' _15max =d' _15,15 =0.0074>eps';

16th time:

C' ₁₆ ＝{(0,0,19.9759),(0,17,19.9857),...,(100,100,19.9338)};

P' ₁₆ ＝{(2.0084,3.5678,19.9925),(1.9917,15.3949,20.0735),...,(95.4523,97.3105,18.0482)};

D' ₁₆ ={0.0024,0.0025,...,0.0015}, d' _16max =d' _16,11 =0.0027<eps';

The compensation curved surface 11 is obtained, as shown in Figure 6, which is the design curved surface 12 and the compensation curved surface 11, wherein the design curved surface 7 and the design curved surface 12 are the same curved surface, both of which are the curved surfaces that have just been designed, and the workpiece is compensated according to the compensation curved surface 11. , the processing error between the obtained processed curved surface and the designed curved surface 12 is less than or equal to the processing accuracy eps=0.003 mm, which meets the processing requirements and improves the processing accuracy of the designed curved surface.

Claims (6)

1. A method for fast detection and compensation of machining errors based on NURBS curved surface, characterized in that, comprising the following steps: 1) Analyze the node vector UV and control point C information of the designed NURBS surface, and select a series of feature points on the designed NURBS surface as the sequence P to be measured; 2) Process the surface with a machine tool according to the node vector UV and control point C of the designed NURBS surface, and then use the measuring head to measure the points to be measured in the sequence P to be measured to obtain the measured sequence Q'; 3) Calculate the deviation between the measured sequence Q' and the measured sequence P, if the deviation is less than or equal to the machining accuracy, no adjustment is required; If there is a deviation greater than the machining accuracy, adjust the sequence P to be measured according to the deviation to obtain the compensation sequence W; 4) Adjust the control point C according to the compensation sequence W to obtain a compensation surface, and process according to the compensation surface to obtain a processed surface with a smaller error with the designed NURBS surface; Adjust the control point C according to the compensation sequence W to obtain the compensation surface, which specifically includes: setting the machining accuracy eps, calculating the deviation sequence D' according to the compensation sequence W and the sequence P to be measured, if the absolute value of each error in the deviation sequence D' If they are all less than or equal to eps, the surface does not need to be adjusted; if at least one error d' in the deviation sequence D' has an absolute value greater than eps, the surface needs to be adjusted; then the control point C on the surface corresponding to d' in the deviation sequence D' To adjust, the amount of adjustment of the control point C corresponding to d' is passed calculation, where w _i,j is the weight factor associated with the control point C, N _i,k (u) and N _j,l (v) are the canonical B-spline basis of degree k in direction u and degree l in direction v respectively, ε _{i , j} is the vector adjusted by the control point C corresponding to d', p is the three-dimensional coordinate of the point to be measured corresponding to d' on the surface, and q is the three-dimensional coordinate of the measured point on the surface corresponding to d'. 2. The method for fast detection and compensation of machining errors based on NURBS curved surfaces according to claim 1, wherein in step 1), the sequence P to be measured includes points and curved surfaces on the corresponding curved surface of node vector UV at the node place The basic feature points on . 3. The method for quickly detecting and compensating processing errors based on NURBS curved surfaces according to claim 2, wherein the basic feature points are the extreme points of the curved surface and the maximum and minimum points of curvature. 4. The method for fast detection and compensation of machining errors based on NURBS curved surfaces according to claim 1, wherein in step 2), measuring the points to be measured in the sequence P to be measured with a measuring head includes: unloading the machining tool , install the contact measuring head on the spindle of the machine tool. When measuring, the X-axis and Y-axis coordinates are consistent with the points to be measured in the sequence P to be measured, and the Z-axis coordinate value is obtained. The Z-axis coordinate value needs to eliminate the deviation x, Where R is the radius of the measuring ball in the contact measuring head, and θ is the slope of the main direction of the measuring point. 5. The method for quickly detecting and compensating processing errors based on NURBS curved surfaces according to claim 4, wherein said θ is the angle formed by the tangent to the curved surface at the intersection of the measuring ball and the curved surface in the contact measuring head and the horizontal direction . 6. The method for fast detection and compensation of processing errors based on NURBS curved surfaces according to claim 1, wherein in step 3), the deviation between the measured sequence Q' and the sequence P to be measured is calculated, and the sequence P to be measured is calculated according to the deviation Make adjustments to obtain the compensation sequence W, which specifically includes: calculating the error between the measured point in the measured sequence Q' and the Z-axis coordinate of the point to be measured corresponding to the sequence to be measured P, and subtracting the error from the sequence to be measured P to obtain compensation Sequence W.