An on-machine measurement error prediction method considering positioning error of five-axis machine tools

Abstract

In order to improve the accuracy of on-machine measurement detection, the present invention discloses an on-machine measurement error prediction method considering the positioning error of a five-axis machine tool, including identifying the positioning error of a five-axis machine tool, calculating the feasible domain of measurement, establishing an on-machine measurement error prediction model, and predicting the distribution of on-machine measurement errors. In practical applications, the feasible measurement positions in the machine tool are converted into machine tool rotation axis angle combinations, and a measurement feasible area is constructed in a two-dimensional plane composed of the rotation axis angle combination. A model for the influence of positioning errors on on-machine measurement errors is established, and the distribution of measurement errors in the feasible area of ​​measurement is predicted based on this model, and finally the measurement position with the least influence of positioning errors is selected. By establishing and analyzing the distribution of the influence of machine tool positioning errors on on-machine measurement errors, the present invention can reduce on-machine measurement errors and improve the credibility of measurement results. The method has good stability and can be extended to on-machine measurement of other multi-axis machine tools, and has certain engineering application value.

Description

Technical Field

[0001] The invention belongs to the field of mechanical precision manufacturing and measurement, and specifically relates to an on-machine measurement error prediction method taking into account the positioning error of a five-axis machine tool. Background Art

[0002] On-machine measurement is a process method for realizing on-machine measurement of workpieces during the machining process by installing a probe on the spindle of a CNC machine tool, which converts the machine tool that undertakes the machining task into a carrier for on-machine measurement. Compared with the three-coordinate measurement commonly used in production workshops, on-machine measurement can avoid repeated clamping of workpieces and ensure the continuity of the measurement process and the machining process. It is a key technology for realizing adaptive machining and has broad application prospects in the production line. However, as a carrier for in-machine measurement, the machine tool will introduce many errors due to the movement of various mechanisms during the measurement process, which directly affects the accuracy of the machine tool, and thus the credibility of the on-machine measurement accuracy has been questioned.

[0003] It should be clearly emphasized that positioning error is the main factor affecting the accuracy of machine tools. In the factory and regular operation and maintenance inspection of machine tools, positioning accuracy is an important indicator to measure the overall working performance of machine tools. At present, the relevant equipment and methods for identifying positioning errors are given in the ISO standard, and many scholars have also conducted research on the identification and compensation of positioning errors. However, few scholars have conducted in-depth research on the accumulation of positioning errors of machine tools during on-machine measurement, and lack the prediction of on-machine measurement errors and optimization of measurement processes based on the distribution of positioning errors. In addition, due to the high flexibility of five-axis machine tools, the same point to be measured on the workpiece can often be measured at different positions in the machine tool, and the positioning errors introduced by measurements at different positions are different. At present, in the on-machine measurement planning, software is usually relied on to automatically select a feasible measurement position for measurement, and there is a lack of analysis on the degree of influence of positioning errors introduced by machine tools, resulting in the on-machine measurement accuracy being affected by the distribution of positioning errors, resulting in uncertainty in the on-machine measurement results.

[0004] Therefore, it is of great significance to develop a method to analyze the positioning error distribution of five-axis machine tools to predict on-machine measurement errors. Summary of the invention

[0005] In order to solve the above technical problems and improve the accuracy of on-machine measurement and detection, a prediction method for on-machine measurement error considering the positioning error of five-axis machine tools is proposed. The feasible measurement positions in the machine tool are converted into the combination of the rotation axis angles of the machine tool. The feasible measurement area is constructed in the two-dimensional plane composed of the rotation axis angle combination. The influence model of positioning error on on-machine measurement error is established, and the distribution of measurement error in the area is predicted based on the model, which can be used to select the measurement position with the least influence of positioning error. This method can effectively and accurately analyze the distribution of on-machine measurement errors of five-axis machine tools, thereby improving the accuracy and reliability of on-machine measurement.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a method for predicting on-machine measurement errors considering the positioning error of a five-axis machine tool, characterized in that it comprises the following steps:

[0007] Step 1: Identify the positioning error of the five-axis machine tool and fit the positioning error distribution;

[0008] Step 2: Under different five-axis machine tool rotation axis angle combinations, the position of the measured point and the direction of the external normal vector in the machine tool coordinate system CS M The measurement paths of the points to be measured are not unique. Due to the limitation of the machine tool structure, the rotation angle ranges of the B and C rotation axes are [B min ,B max ] and [C min ,C max ]. For a given combination of rotation axis angles, the position of the point to be measured and the direction of the external normal vector in the machine tool coordinate system CS M After the detection distance is specified, the measurement path of the point to be measured is uniquely determined. Therefore, the feasible measurement path is converted into the angle point set of the two rotation axes of the five-axis machine tool to form the measurement feasible domain of the point to be measured.

[0009] Specifically calculate the measurement feasible domain of the point q to be measured under two types of measurement path constraints, including:

[0010] Measurement path constraint condition 1: Ensure that the area below the equator of the probe ruby ​​ball touches the measured point q, that is The measurement feasible domain when is in the probe coordinate system CS R The external normal vector N of the next test point q R The z-direction component of

[0011] Measurement path constraint condition 2: Ensure that the measurement path is within the machine tool motion range and the probe positioning point theoretical position p M and the theoretical position q of the point to be measured M At the same time, it is located within the probe reachable area Θ, that is, q M ∈Θ and p M The measurement feasible domain when ∈Θ;

[0012] Step 3: In the machine coordinate system CS M Next, establish the final measurement result of the point to be measured q With the theoretical position q M The on-machine measurement error prediction model err;

[0013] Step 4: Combine the positioning error distribution obtained in step 1 and the measurement feasible domain of the measured point q obtained in step 2, calculate the positioning error corresponding to each angle combination (B, C) of the two rotation axes B and C in the measurement feasible domain, and substitute the positioning error and the angle combination into the measurement error prediction model err established in step 3 to predict the measurement error distribution corresponding to all angle combinations (B, C) of the two rotation axes B and C in the measurement feasible domain.

[0014] Furthermore, in step 1, the specific process of identifying the positioning error of the five-axis machine tool and fitting the positioning error distribution is as follows:

[0015] Step 1.1: Use a laser interferometer in the machine tool to identify the discrete position positioning error σ of the three linear axes X, Y, and Z by changing the positions of the beam splitter, reflector, and interferometer x-y-z =[σ x ,σ y ,σ z ]′, by installing a rotary axis calibration device to identify the angular positioning error σ of the two rotary axes B and C B-C =[σ B ,σ C ]′;

[0016] Step 1.2: Based on the positioning error of the discrete positions and angles identified in step 1.1, use spline curves to fit the positioning error measurement results of the X, Y, Z, and B axes, and use spline surfaces to fit the positioning error measurement results of the C axis to form the positioning error distribution within the travel range of each axis.

[0017] Furthermore, in step 2, calculate The process of measuring the feasible domain when is:

[0018] Step 2.1-1: Establish the probe coordinate system CS at the center of the probe ruby ​​sphere R Finally, based on the machine tool structure,

[0019] Establish the probe coordinate system CS at the center of the probe ruby ​​sphere R , based on the machine tool structure, establish the workpiece coordinate system CS W To the probe coordinate system CS R The transformation matrix R is:

[0020]

[0021] In the formula, italic B and C are the angles of the rotation axes of B and C;

[0022] Step 2.1-2: Set the probe coordinate system CS R The external normal vector of the next test point q Workpiece coordinate system CS W The external normal vector of the next test point q The angle combination of the B and C rotation axes is (B, C). The relationship between the three is constructed by the transformation matrix R, which can be expressed by the mathematical model as follows:

[0023]

[0024] Step 2.1-3: For a certain point to be measured, one of the conditions for the feasible domain of the measurement path is to ensure that the area below the equator of the probe ruby ​​sphere touches the point to be measured. In machine measurement, the probe is required to touch the point to be measured in the opposite direction of the external normal vector of the point to be measured. Under the condition that the angle combination of the B and C rotation axes (B, C) is known, in the probe coordinate system CS R The outer normal vector The direction is determined, and the touch position of the probe on the ruby ​​ball is obtained, that is, the condition that the probe touches the point to be measured in the area below the equator of the ruby ​​ball To represent the measurement feasible domain, it can be further expressed as:

[0025]

[0026] In the formula [B min ,B max ] and [C min ,C max ] are the rotation angle ranges of B and C rotation axes respectively.

[0027] Furthermore, in step 2, q is calculated M ∈Θ and p M The process of measuring the feasible domain when ∈Θ is:

[0028] Step 2.2-1: Based on the machine tool structure, establish the workpiece coordinate system CS W To machine coordinate system CS M The transformation matrix M is:

[0029]

[0030] In the formula, italic B and C are the angles of the rotation axes of B and C, [δx p ,δy p ,δz p ] is the spindle point in the machine tool coordinate system CS M The coordinates in [δx w ,δy w ,δz w ] is the workpiece coordinate system CS W The origin is in the machine coordinate system CS M The coordinates in ;

[0031] Step 2.2-2: For a certain point to be measured, one of the conditions for the feasible domain of the measurement path is to ensure that the measurement path is within the machine tool motion range. During the on-machine measurement process, the probe needs to be moved to the positioning point first, and then move in the opposite direction of the normal vector of the point to be measured until the probe is triggered. The distance from the positioning point to the point to be measured is called the detection distance l. Calculate the probe positioning point in the workpiece coordinate system CS W The position p in W :

[0032] p W =q W +l·N W ,

[0033] Where q W The point q to be measured is in the workpiece coordinate system CS W Theoretical position below.

[0034] Step 2.2-3: Assume that the points to be measured q are located in the machine tool coordinate system CS M Theoretical position In the workpiece coordinate system CS W Position in The relationship between the two is constructed by the transformation matrix M, which can be expressed by a mathematical model:

[0035]

[0036] Step 2.2-4: Set the probe positioning points in the machine tool coordinate system CS M Theoretical position under In the workpiece coordinate system CS W Position in The relationship between the two is constructed by the transformation matrix M, which can be expressed by a mathematical model:

[0037]

[0038] Step 2.2-5: The area that the probe can reach in the machine tool spindle motion space is called the probe reachable area, denoted by Θ. M The probe positioning point theoretical position p M and the theoretical position q of the point to be measured M At the same time, when it is located within the reachable area Θ of the probe, the measurement path can be guaranteed to be within the motion range of the machine tool, that is, q M ∈Θ and p M ∈Θ to represent the measurement feasible domain. Combining steps 2.3-2 and 2.3-3, q M ∈Θ and p M ∈Θ is further expressed as:

[0039]

[0040] In the formula [x min ,x max ],[y min ,y max ],[z min ,z max ] are the travel ranges of the three linear axes of the machine tool X, Y, and Z.

[0041] Furthermore, in step 3, the final measurement result of the measured point q is established. With the theoretical position q M The specific process of the on-machine measurement error prediction model err is as follows:

[0042] Step 3.1: Consider the outer surface of the workpiece as a combination of a series of small planes, use the point to be measured q to represent the center point of the small plane, and use the outer normal vector of the point to be measured q to represent the center point of the small plane. represents the plane normal vector of the tiny plane;

[0043] Step 3.2: After the workpiece is clamped and aligned, without the influence of positioning error, the transformation matrix M and the point to be measured q are used in the workpiece coordinate system CS. W The direction of the external normal vector N W Establish the machine tool coordinate system CS of the point to be measured q M The theoretical external normal vector N M for:

[0044]

[0045] Calculate the detection positioning point in the machine tool coordinate system CS M The theoretical position p M , p M =q M +l·N M , where l is the same as above; further calculate the theoretical position h of the center point of the probe ruby ​​ball when the probe touches the workpiece M ,h M =q M -r·N M , where r is the radius of the probe ruby ​​ball;

[0046] Step 3.3: After the workpiece is clamped and aligned, under the condition of positioning error, the discrete position positioning error σ of the three linear axes X, Y, and Z identified in step 1.1 is combined x-y-z =[σ x ,σ y ,σ z ]′ and the angular positioning error of the two rotation axes B and C σ B-C =[σ B ,σ C ]′, calculated in the machine tool coordinate system CS M The actual position of the detection point for:

[0047]

[0048] Calculate the measured point q in the machine tool coordinate system CS M The actual location of for:

[0049]

[0050] Further calculate the measured point q in the machine tool coordinate system CS M The actual external normal vector for:

[0051]

[0052] Step 3.4: When measuring, the probe will be located from the actual position of the probe positioning point Starting from the theoretical position q of the point to be measured M Approach, calculate in the machine coordinate system CS M The actual probe approach direction D in is:

[0053]

[0054] Step 3.5: Combined with Step 3.3 and Step 3.4, the actual position of the probe ruby ​​sphere center when the probe touches the workpiece surface and triggers the probe for:

[0055]

[0056] The recorded position of the probe ruby ​​sphere center under the influence of the positioning errors of the three linear axes X, Y, and Z for:

[0057]

[0058] In the formula h σ x-y-z =[ h σ x , h σ y , h σ z ]'for Positioning error of the linear axis at .

[0059] Step 3.6: Record the position of the probe ruby ​​sphere center calculated in step 3.5 Based on the measurement point q in the machine tool coordinate system CS M The final measurement result is for:

[0060]

[0061] Step 3.7: In the machine coordinate system CS M Calculate the final measurement result of the point to be measured q and the theoretical position q of the point to be measured M The absolute error of the distance As a prediction model for on-machine measurement error, combined with the results of step 3.5 and step 3.6, err can be further expressed as:

[0062]

[0063] Beneficial Effects

[0064] The beneficial effects of the present invention are:

[0065] 1. Convert the feasible measurement positions of the points to be measured into feasible combinations of rotation axis angles, and transform the measurement path optimization problem into a planning problem of a two-dimensional plane point set;

[0066] 2. The feasible conditions for the measurement path of a single point to be measured are established, and the constraints of the position of the point to be measured and the direction of its external normal vector on the angle combination of the machine tool rotation axis are given;

[0067] 3. With the purpose of reducing the influence of machine tool positioning error and improving on-machine measurement accuracy during detection, on-machine measurement error prediction and measurement path optimization are carried out to reduce on-machine measurement error and improve the credibility of measurement results;

[0068] 4. This method has good stability and can be applied to on-machine measurement of other multi-axis machine tools, and has certain engineering application value.

[0069] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0071] Figure 1 Positioning error distribution of each axis of a five-axis machine tool;

[0072] Figure 2 Measuring feasibility diagrams;

[0073] Figure 3 The impact of positioning error on on-machine measurement;

[0074] Figure 4 On-machine measurement process under the influence of positioning error;

[0075] Figure 5On-machine measurement error distribution prediction diagram;

[0076] Figure 6 Distribution of points to be tested on the standard block;

[0077] Figure 7 (a) Comparison of experimental measurement error and prediction result of test point 1 in Example 1; (b) Comparison of experimental measurement error and prediction result of test point 2 in Example 1; (c) Comparison of experimental measurement error and prediction result of test point 3 in Example 1 DETAILED DESCRIPTION

[0078] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0079] Step 1: In order to analyze the impact of positioning error on measurement error, it is necessary to identify the positioning error of each axis of the five-axis machine tool. Use a laser interferometer to measure the linear axis positioning error by changing the position of the beam splitter, reflector, and interferometer, and measure the rotation axis positioning error by adding a rotary axis calibration device. Based on the positioning errors of discrete positions and angles obtained by measurement, use spline curves to fit the positioning error measurement results of the X, Y, Z, and B axes, and use spline surfaces to fit the positioning error measurement results of the C axis to obtain the positioning error distribution within the travel range of each axis, such as Figure 1 shown.

[0080] Step 2: Calculate the measurement feasible region.

[0081] The specific implementation method of the above step 2 is:

[0082] Step 2.1: Under different five-axis machine tool rotation axis angle combinations, the position and external normal vector direction of the test point are different in the machine tool coordinate system, making the measurement path of the test point non-unique. For a given rotation axis angle combination, the position and external normal vector direction of the test point are uniquely determined in the machine tool coordinate system. Therefore, after specifying the detection distance, the measurement path of the test point is uniquely determined. Therefore, the feasible measurement position can be converted into a set of angle points of the two rotation axes of the five-axis machine tool to form the measurement feasible domain of the test point. Establish the probe coordinate system CS at the center point of the probe ruby ​​sphere R , based on the machine tool structure, the transformation matrix R from the workpiece coordinate system to the probe coordinate system is established as:

[0083]

[0084] The external normal vector of the point to be measured in the probe coordinate system is established by the transformation matrix R External normal vector of the point to be measured in the workpiece coordinate system The relationship with the rotation angle (B, C) is as follows:

[0085]

[0086] In order to ensure that the area below the equator of the probe ruby ​​ball touches the test point, Obtain the rotation axis angle constraint condition 1 of the measurement feasible domain shown in formula (3).

[0087]

[0088] In the formula [B min ,B max ] and [C min ,C max ] are the rotation angle ranges of B and C rotation axes respectively.

[0089] Step 2.2: Based on the machine tool structure, establish the workpiece coordinate system CS W To machine coordinate system CS M The transformation matrix M is:

[0090]

[0091] In the formula [δx p ,δy p ,δz p ] is the spindle point in the machine tool coordinate system CS M The coordinates in [δx w ,δy w ,δz w ] is the workpiece coordinate system CS W The origin is in the machine coordinate system CS M The coordinates in .

[0092] During the on-machine measurement process, the probe needs to be moved to the positioning point first, and then move in the opposite direction of the normal vector of the point to be measured until the probe is triggered. The distance from the probe positioning point to the point to be measured is called the detection distance l. Calculate the probe positioning point in the workpiece coordinate system CS W The position p in W :

[0093] p W =q W +l·N W (5)

[0094] where q W is the position of the point to be measured in the workpiece coordinate system.

[0095] Then in the machine tool coordinate system CS M Calculate the theoretical position q of the point to be measured M , let its coordinates be but:

[0096]

[0097] Similarly, in the machine tool coordinate system CS M Calculate the theoretical position of the probe positioning point p M , let its coordinates be but:

[0098]

[0099] Step 2.3: The area that the probe can reach in the machine tool spindle motion space is called the probe reachable area, denoted by Θ. This area is in the machine tool coordinate system CS M The inside is a cube. The travel ranges of the three linear axes of the machine tool are [x min ,x max ],[y min ,y max ],[z min ,z max ]. When q M ∈Θ and p M When ∈Θ, the measurement path can be guaranteed to be within the machine tool motion range. The second rotation axis angle constraint condition of the measurement feasible domain is obtained as shown in formula (8).

[0100]

[0101] Where B∈[B min ,B max ],C∈[C min ,C max ]. The set of angle points of the two rotation axes of the five-axis machine tool that satisfies the two constraints at the same time is the measurement feasible graph, such as Figure 2 shown.

[0102] Step 3: In the machine coordinate system CS M Next, establish the final measurement result of the point to be measured q With the theoretical position q M The on-machine measurement error prediction model err.

[0103] The specific implementation method of the above step 3 is:

[0104] Step 3.1: Based on the differential idea, the outer surface of the workpiece is regarded as a combination of a series of small planes. The center point of the small plane is represented by the point q to be measured, and the outer normal vector N of the point q to be measured is represented by W represents the plane normal vector of the tiny plane;

[0105] Step 3.2: After the workpiece is clamped and aligned, without the influence of positioning error, the transformation matrix M and the point to be measured q are used in the workpiece coordinate system CS. W The direction of the external normal vector NW Establish the machine tool coordinate system CS of the point to be measured q M The theoretical external normal vector N M for:

[0106]

[0107] Further, calculate the detection positioning point in the machine tool coordinate system CS M The theoretical position p M :

[0108] p M =q M +l·N M (10)

[0109] Furthermore, the theoretical position h of the center of the probe ruby ​​ball when the probe touches the workpiece is calculated. M :

[0110] h M =q M -r·N M (11)

[0111] Where r is the radius of the probe ruby ​​sphere.

[0112] Step 3.3: After the workpiece is clamped and aligned, under the condition of positioning error, the discrete position positioning error σ of the three linear axes X, Y, and Z is considered x-y-z =[σ x ,σ y ,σ z ]′ and the angular positioning error of the two rotation axes B and C σ B-C =[σ B ,σ C ]′, in the machine tool coordinate system CS M The actual position of the detection point for:

[0113]

[0114] In addition, due to the angular positioning error (σ B ,σ C ), the actual measurement angle of the turntable will change to (B+σ B ,C+σ C ), workpiece coordinate system CS W In the machine tool coordinate system CS M The position in the theoretical measurement angle combination will change. W Theoretical Auxiliary Coordinate System The workpiece coordinate system CS at this time W Actual workpiece coordinate system The influence of positioning error is as follows: Figure 3 shown.

[0115] Furthermore, the point to be measured q is in the machine tool coordinate system CS M The actual location of for:

[0116]

[0117] Furthermore, the point to be measured q is in the machine tool coordinate system CS M The actual external normal vector for:

[0118]

[0119] Step 3.4: Since the positioning error cannot be recognized by the CNC system, the probe will be measured from the actual position of the probe positioning point. Starting from the theoretical measurement point q M Close, such as Figure 4 As shown, then in the machine tool coordinate system CS M The actual probe approach direction D in is:

[0120]

[0121] Furthermore, the actual position of the probe ruby ​​sphere center when the probe touches the workpiece surface and the probe is triggered

[0122]

[0123] The recorded position of the probe ruby ​​sphere center under the influence of the positioning errors of the three linear axes X, Y, and Z for:

[0124]

[0125] in h σ x-y-z =[ h σ x , h σ y , h σ z ]'for Positioning error of the linear axis at .

[0126] Step 3.5: Since the radius compensation direction is still the opposite direction of the theoretical direction of the normal vector outside the test point, the recorded position of the probe ruby ​​sphere center calculated in step 4.4 is considered. Based on the measurement point q in the machine tool coordinate system CS M The final measurement result is for:

[0127]

[0128] Step 3.6: Combine the results of step 3.4 and step 3.5, and in the machine tool coordinate system CS M Calculate the final measurement result of the point to be measured q and the theoretical position q of the point to be measured M The absolute error of the distance between the two is used as the prediction model err of the on-machine measurement error:

[0129]

[0130] Step 4: The positioning error distribution obtained in step 1 can obtain the positioning error of each axis of the machine tool under any position and turntable rotation angle. Through step 2, the measurement feasible domain of the point to be measured can be obtained. Each angle combination in the feasible domain corresponds to the position of the point to be measured in the machine tool under a turntable rotation angle combination. Based on the distribution of positioning error, the positioning error of each axis corresponding to any angle combination in the feasible domain can be obtained. Substituting the positioning error and angle combination into the measurement error prediction model proposed in step 3, the measurement error corresponding to any angle combination in the feasible domain can be predicted. By predicting the positioning errors of all angle combinations in the feasible domain, the on-machine measurement error distribution prediction diagram can be obtained, as shown in Figure 5 shown.

[0131] The following is an example of on-machine measurement of three measurement points on a standard block:

[0132] The on-machine measurement system in the present invention is the Beijing Jingdiao JD50 system, the probe used is the OMP40 trigger probe of Renishaw Company, and the standard block size used is 35×8×70mm.

[0133] Embodiment 1: There are 3 test points distributed on the standard block, such as Figure 6 The corresponding coordinates are shown in Table 1.

[0134] Table 1 Coordinate measuring machine test results of the test points

[0135]

[0136] According to the travel range and positioning error distribution of each axis of the machine tool, the on-machine measurement error prediction model in this application is used to obtain the measurement error distribution of the three points to be measured. The sampling angles of the B axis are B = -15°, -30°, -45°, -60°, -75°, -90°, and the sampling angles of the C axis are C = 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, 330°, for a total of 72 sampling angle combinations. According to the measurement error distribution of the three points to be measured, the predicted amount of the sampling angle measurement error within the feasible measurement domain is obtained. The three points to be measured are measured at the same sampling angle, and the measurement is repeated three times to obtain the actual measurement results of the measurement errors of the three points to be measured. The measurement error prediction results and the actual measurement results of the three points to be measured are shown in Tables 2 to 4 respectively.

[0137] Table 2 Prediction results and actual measurement results of measurement error at test point 1

[0138]

[0139]

[0140] Table 3 Prediction results and actual measurement results of measurement error at test point 2

[0141]

[0142]

[0143] Table 4 Prediction results and actual measurement results of measurement error at test point 3

[0144]

[0145]

[0146] The experimental measurement errors of the test points 1 to 3 in Example 1 are compared with the predicted results. Figure 7 As shown in (a) to 7(c), it can be seen that the on-machine measurement error prediction method in this application can better predict the measurement error distribution, and the prediction error is below 0.01 mm, which proves the practicality and effectiveness of this method.

Claims

1. A method for predicting on-machine measurement errors considering positioning errors of five-axis machine tools, characterized in that: Use the following steps: Step 1: Identify the positioning errors of the three linear axes X, Y, and Z and the two rotary axes B and C in the five-axis machine tool, and fit the positioning error distribution within the travel range of each axis; Step 2: Calculate the feasible measurement domain of the point q to be measured under two types of measurement path constraints: The first constraint of the measurement path is to ensure that the area below the equator of the probe ruby ​​ball touches the point to be measured q, that is The measurement feasible domain when is in the probe coordinate system CS R The external normal vector N of the next test point q R The z-direction component of The second constraint condition of the measurement path is to ensure that the measurement path is within the machine tool motion range and the probe positioning point theoretical position p M and the theoretical position q of the point to be measured M At the same time, it is located within the probe reachable area Θ, that is, q M ∈Θ and p M The measurement feasible domain when ∈Θ; Step 3: In the machine coordinate system CS M Next, establish the final measurement result of the point to be measured q With the theoretical position q M The on-machine measurement error prediction model err; Step 4: Combine the positioning error distribution obtained in step 1 and the measurement feasible domain of the measured point q obtained in step 2, calculate the positioning error corresponding to each angle combination (B, C) of the two rotation axes B and C in the measurement feasible domain, and substitute the positioning error and the angle combination into the measurement error prediction model err established in step 3 to predict the measurement error distribution corresponding to all angle combinations (B, C) of the two rotation axes B and C in the measurement feasible domain.

2. The on-machine measurement error prediction method considering the positioning error of a five-axis machine tool according to claim 1, characterized in that: In step 1, the specific process of identifying the positioning error of the five-axis machine tool and fitting the positioning error distribution is as follows: Step 1.1: Use a laser interferometer in the machine tool to identify the discrete position positioning error σ of the three linear axes X, Y, and Z by changing the positions of the beam splitter, reflector, and interferometer x-y-z =[σ x ,σ y ,σ z ]′, by installing a rotary axis calibration device to identify the angular positioning error σ of the two rotary axes B and C B-C =[σ B ,σ C ]′; Step 1.2: Based on the positioning error of the discrete positions and angles identified in step 1.1, use spline curves to fit the positioning error measurement results of the X, Y, Z, and B axes, and use spline surfaces to fit the positioning error measurement results of the C axis to form the positioning error distribution within the travel range of each axis.

3. The on-machine measurement error prediction method considering the positioning error of a five-axis machine tool according to claim 1, characterized in that: In step 2, calculate The process of measuring the feasible domain when is: Step 2.1-1: Establish the probe coordinate system CS at the center of the probe ruby ​​sphere R , based on the machine tool structure, establish the workpiece coordinate system CS W To the probe coordinate system CS R The transformation matrix R is: Step 2.1-2: Establish the probe coordinate system CS by the transformation matrix R R The external normal vector of the next test point q Workpiece coordinate system CS W The external normal vector of the next test point q Relationship with rotation angle (B, C): Step 2.1-3: To ensure that the area below the equator of the probe ruby ​​ball touches the test point, that is, When the measurement feasible domain is transformed, the angle constraint condition of B and C rotation axes is expressed as: In the formula [B min ,B max ] and [C min ,C max ] are the rotation angle ranges of B and C rotation axes respectively.

4. The on-machine measurement error prediction method considering the positioning error of a five-axis machine tool according to claim 1, characterized in that: In step 2, calculate q M ∈Θ and p M The process of measuring the feasible domain when ∈Θ is: Step 2.2-1: Based on the machine tool structure, establish the workpiece coordinate system CS W To machine coordinate system CS M The transformation matrix M is: In the formula [δx p ,δy p ,δz p ] is the spindle point in the machine tool coordinate system CS M The coordinates in [δx w ,δy w ,δz w ] is the workpiece coordinate system CS W The origin is in the machine coordinate system CS M The coordinates in ; Step 2.2-2: Calculate the probe positioning point in the workpiece coordinate system CS W The position p in W : p W =q W +l·N W , Where q W The point to be measured q is in the workpiece coordinate system CS W The theoretical position under the probe; l is the detection distance, that is, the distance from the probe positioning point to the point to be measured q; Step 2.2-3: Use the transformation matrix M to establish the coordinate system CS of the point to be measured q in the machine tool coordinate system M Theoretical position With the workpiece coordinate system CS W Position in The relationship between: Step 2.2-4: Establish the probe positioning point in the machine tool coordinate system CS using the transformation matrix M M Theoretical position under With the workpiece coordinate system CS W Position in The relationship between: Step 2.2-5: In the machine coordinate system CS M The probe positioning point theoretical position p M and the theoretical position q of the point to be measured M When the probe is located in the reachable area θ, the measurement path is guaranteed to be within the machine tool motion range, and the measurement feasible domain is converted into the second constraint condition of the B and C rotation axis angles, which is expressed as: In the formula [x min ,x max ],[y min ,y max ],[z min ,z max ] are the travel ranges of the three linear axes of the machine tool X, Y and Z.

5. The on-machine measurement error prediction method considering the positioning error of a five-axis machine tool according to claim 1, characterized in that: In step 3, the specific process of establishing the on-machine measurement error prediction model err is as follows: Step 3.1: Consider the outer surface of the workpiece as a combination of a series of small planes, use the point to be measured q to represent the center point of the small plane, and use the outer normal vector N of the point to be measured q to represent the center point of the small plane. W represents the plane normal vector of the tiny plane; Step 3.2: After the workpiece is clamped and aligned, without the influence of positioning error, the transformation matrix M and the point to be measured q are used in the workpiece coordinate system CS. W The direction of the external normal vector N W Establish the machine tool coordinate system CS of the point to be measured q M The theoretical external normal vector N M for: Calculate the detection positioning point in the machine tool coordinate system CS M The theoretical position p M :p M =q M +l·N M ; Further calculate the theoretical position h of the center point of the probe ruby ​​ball when the probe touches the workpiece M :h M =q M -r·N M , where r is the radius of the probe ruby ​​ball; Step 3.3: After the workpiece is clamped and aligned, under the condition of positioning error, consider the discrete position positioning error σ of the three linear axes X, Y, and Z x-y-z =[σ x ,σ y ,σ z ]′ and the angular positioning error of the two rotation axes B and C σ B-C =[σ B ,σ C ]′, in the machine tool coordinate system CS M The actual position of the detection point for: Calculate the measured point q in the machine tool coordinate system CS M The actual location of for: Further calculate the measured point q in the machine tool coordinate system CS M The actual external normal vector for: Step 3.4: When measuring, the probe will be located from the actual position of the probe positioning point Starting from the theoretical position q of the point to be measured M Approach, calculate in the machine coordinate system CS M The actual probe approach direction D in is: Step 3.5: Combined with Step 3.3 and Step 3.4, the actual position of the probe ruby ​​sphere center when the probe touches the workpiece surface and triggers the probe for: The recorded position of the probe ruby ​​sphere center under the influence of the positioning errors of the three linear axes X, Y, and Z for: In the formula h σ x-y-z =[ h σ x , h σ y , h σ z ]'for Linear axis positioning error at ; Step 3.6: Record the position of the probe ruby ​​sphere center calculated in step 3.5 Based on the measurement point q in the machine tool coordinate system CS M The final measurement result is for: Step 3.7: Combine the results of step 3.5 and step 3.6, and in the machine tool coordinate system CS M Calculate the final measurement result of the point to be measured q and the theoretical position q of the point to be measured M The absolute error of the distance between the two is used as the prediction model of the on-machine measurement error err:

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