CN111967097B - Geometric error global sensitivity analysis method for numerical control machine tool - Google Patents
Geometric error global sensitivity analysis method for numerical control machine tool Download PDFInfo
- Publication number
- CN111967097B CN111967097B CN202010625505.2A CN202010625505A CN111967097B CN 111967097 B CN111967097 B CN 111967097B CN 202010625505 A CN202010625505 A CN 202010625505A CN 111967097 B CN111967097 B CN 111967097B
- Authority
- CN
- China
- Prior art keywords
- error
- machine tool
- geometric
- errors
- geometric error
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 38
- 238000010206 sensitivity analysis Methods 0.000 title claims abstract description 12
- 238000006073 displacement reaction Methods 0.000 claims abstract description 44
- 230000003993 interaction Effects 0.000 claims abstract description 18
- 230000008878 coupling Effects 0.000 claims abstract description 4
- 238000010168 coupling process Methods 0.000 claims abstract description 4
- 238000005859 coupling reaction Methods 0.000 claims abstract description 4
- 238000003754 machining Methods 0.000 claims description 52
- 230000035945 sensitivity Effects 0.000 claims description 39
- 239000011159 matrix material Substances 0.000 claims description 35
- 238000005259 measurement Methods 0.000 claims description 20
- 230000008859 change Effects 0.000 claims description 15
- 230000008569 process Effects 0.000 claims description 14
- 238000010219 correlation analysis Methods 0.000 claims description 13
- 238000004364 calculation method Methods 0.000 claims description 11
- 238000004458 analytical method Methods 0.000 claims description 7
- 230000009466 transformation Effects 0.000 claims description 4
- 230000003068 static effect Effects 0.000 claims description 3
- 238000012886 linear function Methods 0.000 claims 1
- 238000012545 processing Methods 0.000 abstract description 7
- 238000013461 design Methods 0.000 abstract description 5
- 238000012482 interaction analysis Methods 0.000 abstract description 2
- 238000004519 manufacturing process Methods 0.000 description 6
- 239000013598 vector Substances 0.000 description 6
- 238000012360 testing method Methods 0.000 description 4
- 238000010205 computational analysis Methods 0.000 description 2
- 230000001419 dependent effect Effects 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000005299 abrasion Methods 0.000 description 1
- 238000005520 cutting process Methods 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 230000002068 genetic effect Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Abstract
The invention discloses a geometric error global sensitivity analysis method of a numerical control machine tool, and belongs to the field of machine tool precision design. In particular to a numerical control machine tool space error modeling method, geometric error and motion displacement fitting and geometric error mutual coupling interaction analysis. Establishing a machine tool geometric error model through a multi-body system, and performing deviation guide on geometric errors by processing precision; establishing a geometric error-motion travel fitting function, and deriving a motion travel by using the geometric error; while analyzing complex interactions between geometric errors. The method can be used for identifying the critical geometric errors of the machine tool by comprehensively considering the first three factors, and the geometric error sensitivity analysis result can provide references for the design, assembly and processing of the machine tool.
Description
Technical Field
The invention relates to a geometric error global sensitivity analysis method of a numerical control machine tool, and belongs to the field of machine tool precision design.
Background
The state of development of the machine industry, one of the main marks of the national degree of industrialization, is receiving increasing attention. The numerical control machine tool as an important carrier for the development of the modern industry plays a decisive role in the working performance. The performance of the machine tool is mainly characterized in that whether the quality of a processed product meets the precision requirement of a user or not. The precision of the machine tool is mainly expressed as follows: machining precision, positioning precision and repeated positioning precision, wherein the machining precision of the machine tool is a main parameter for evaluating the working performance of the machine tool and a final target. And is affected by various factors, such as the axial extension of the spindle due to heat generated in the long-time use process of the spindle of the machine tool, or the phenomenon of 'thermal head lifting' at the front end of the spindle can directly affect the precision of the machine tool. In addition, the machining accuracy of the machine tool is lowered by the applied cutting force, the pressed deformation of the guide rail, the manufacturing error of the parts themselves, complicated artifacts, and the like. Among many factors, the geometric error and thermal error of the machine tool account for about 50-70% of the total error, and the individual machining error accounts for about 40%, so that the geometric error of the machine tool is researched and reduced, and the machining precision of the machine tool can be effectively improved.
Machine tool geometry errors are of various types according to the different manifestations, and mainly include positioning errors, straightness errors, roll errors, pitch errors, yaw errors, perpendicularity and parallelism errors between motion axes, and the like. The interaction of these errors with each other affects the machining accuracy of the machine tool. How to identify key geometric error items that have a great influence on machining accuracy, and to effectively control them are key problems in improving machining accuracy of machine tools.
To solve this problem, three aspects need to be considered:
first: and establishing a machine tool geometric error model. By simplifying the machine tool structure, analyzing the relative motion of each motion axis of the machine tool, establishing the topological structure of the machine tool, and constructing a geometric error model of the machine tool by using a homogeneous change matrix according to a multi-body system theory so as to represent the nonlinear relation between the machining precision and the geometric error;
second,: a functional relationship between geometric error and displacement is established. Due to the increasing abrasion of the screw rod and the guide rail and the deviation during manufacturing and assembling, the geometric error is generated when the support and guide moving parts realize linear movement, and the generated geometric error value also fluctuates along with the change of the movement stroke. Therefore, the research on the change rule of geometric errors along with the stroke of the moving part is necessary. According to the characteristic that the size of the geometrical error changes along with displacement in the geometrical error measurement process, fitting a nonlinear function relation between the geometrical error of the machine tool and the displacement from measurement data, so as to study the fluctuation of the geometrical error along with the displacement;
third,: the interactions between the geometric errors are analyzed. Geometric errors are important reasons for reducing the machining precision of the numerical control machine tool, and the correlation of the geometric errors objectively exists. Often, improving one error value will result in a change in another or more error values associated with the error value. In the actual machining process, therefore, the geometric errors do not solely affect the machining accuracy of the machine tool, but rather affect the machining accuracy of the machine tool jointly by interaction with one another. The study of complex correlations between geometric errors is the basis for the optimal design and production manufacturing of machine tools. The most used in the correlation analysis of the prior variables is a simple correlation coefficient, but only the linear correlation degree between two variables can be measured. For a highly nonlinear system of machine tools, the interaction between geometric errors is complex, nonlinear.
The invention mainly builds a machine tool geometric error global sensitivity analysis model by comprehensively considering three aspects of a machine tool geometric error model, error fluctuation along with displacement and error coupling, and identifies critical geometric errors affecting machining precision through sensitivity coefficients of error items, thereby providing references for manufacturing and assembling of the machine tool.
Disclosure of Invention
The invention provides a novel method for analyzing the global sensitivity of geometric errors of a numerical control machine, and particularly relates to a method for modeling the spatial errors of the numerical control machine, geometric errors and motion displacement fitting and geometric error interaction analysis.
To achieve the above object, the following works are mainly performed:
1) By analyzing the relative motion between three motion axes of a main motion component X, Y, Z in a four-axis numerical control machine tool, according to a multi-body system theory, establishing a machine tool motion error homogeneous transformation matrix, further establishing a machine tool geometric error model, representing a nonlinear function relation between machining precision and geometric error, and performing deviation derivation on the geometric error by the machining precision to obtain the local influence of the geometric error on the machining precision;
2) According to the characteristic that the value of the geometric error changes along with the displacement change of the moving part during geometric error measurement, analyzing the image characteristics of the geometric error, providing a geometric error-displacement fitting function which mainly comprises a Fourier series, and deriving the geometric error from the motion travel to obtain the fluctuation of the geometric error along with the displacement change;
3) According to complex interaction among geometric errors, providing a second-order bias correlation coefficient based on a pearson product difference to perform coupling analysis on the geometric errors;
4) In order to comprehensively consider the influence degree of the geometric error on the machining precision of the machine tool, the results of the first three items are multiplied in sequence, and the result is used as the sensitivity of the geometric error.
Through the steps, a novel overall sensitivity analysis method for geometric errors of the numerical control machine tool is invented, so that the purpose of identifying key geometric errors of the machine tool is achieved, and the geometric error sensitivity analysis result can provide references for design, assembly and machining of the machine tool. Fig. 1 is a flowchart of the present invention, and the specific steps are as follows.
Step 1, establishing a machine tool motion characteristic matrix and a geometric error model
Step 1.1 analyzing the topology of a machine tool
According to the theory of a multi-body system, each component part of the machine tool is as follows: the machine tool body, the upright post, the workbench, the ram, the spindle box, the cutter and the like, and the workpiece can be simplified into a plurality of arbitrary classical bodies. The topological structure is in a twisted pair mode, a lathe bed fixed on a foundation and a stand column fixedly connected on the lathe bed and still are used as an inertial body, the reference sign is a B0 body, a ram is a B1 body, and the serial numbers of B2, B2 and … Bj … Bn are sequentially arranged along the directions far away from the B0 body and the B1 body according to the structural mode of the machine tool, wherein n is the number of typical bodies of the machine tool. And establishing a topological structure of the machine tool according to the relative movement and the labels among the parts of the machine tool.
Step 1.2, establishing a motion characteristic matrix of the machine tool
And establishing a right-hand rectangular Cartesian coordinate system which is fixedly connected with the machine tool body B0 and other bodies, wherein the coordinate system on each body is a sub-coordinate system, and corresponding axes on each sub-coordinate system are parallel to each other.
By the multi-body system theory and the generalized coordinate system set, the motion between adjacent bodies of the selected machine tool can be described by using a 4 x 4 homogeneous coordinate transformation matrix, wherein the workbench is fixedly connected with the workpiece and is stationary, so that the B axis is considered to be free of errors. Table 1 gives the signs of all geometrical errors of the machine tool and their physical significance. Table 2 shows the ideal motion characteristic matrix and the error matrix when the machine tool has error relative motion.
Table 1 sign and physical meaning of geometrical errors
Table 2 machine tool motion error feature matrix
Wherein:
p represents rest; s represents motion;
t represents typical body B j Relative to B i Is a motion feature matrix of the ideal;
DeltaT represents typical body B j Relative to B i Is a motion error feature matrix of (1);
I 4x4 meaning that when the error is relatively small, it is negligible as an identity matrix;
other physical meanings of the errors are listed in table 1.
Step 1.3, establishing a machine tool geometric error model
Let the coordinates of the tool forming point in the tool coordinate system be:
P t ＝(p tx p ty p tz 1) T (1)
let the coordinates of the workpiece forming point in the workpiece coordinate system be:
P w ＝(p wx p wy p wz 1) T (2)
when the machine tool works in an ideal state without errors, the ideal coordinates of the workpiece forming point in the tool coordinate system are as follows:
in actual cases, the actual coordinates of the workpiece forming point in the tool coordinate system are:
P tactual ＝( E T 03 ) -1E T 04 P w (4)
wherein:
the total error matrix of the machine tool is as follows:
wherein E is a machine tool comprehensive volume error model.
From (5), accuracy and geometry errors, movement axis positions and P are mainly known w In relation, a general volumetric error model of the machine tool can thus be established.
E＝E(G，P w ，H) (6)
Wherein:
E＝[E x ，E y ，E z ，0] T representing the volumetric error vectors in 3 directions of the machine tool;
H＝[x，y，z，1] T wherein x, y and z represent position vectors of a feeding shaft of the machine tool in three directions;
G＝[g 1 ，g 2 ，…，g 18 ] T representing a vector consisting of 18 geometrical errors of the machine tool and let δx x ，δy x ，δz x ，εα x ，εβ x ，εγ x ，δx y ，δy y ，δz y ，εα y ，εβ y ，εγ y ，δx z ，δy z ，δz z ，εα z ，εβ z ，εγ z ＝g 1 ，g 2 ，…，g 18 ；
Step 2 geometric error measurement data and Displacement fitting
Step 2.1 measuring geometrical errors of the machine tool
When the influence of geometrical errors on a machine tool is studied in an important way, P w And H assuming no error, should be set to a known constant and the static turntable is kept from rotating while the error is measured, taking into account only 18 position-dependent geometric errors along the X, Y, Z directions. And selecting the same measuring range on each axis, setting measuring points at certain intervals, enabling the motion axis to run 2 times in the forward and reverse directions of motion respectively, measuring 4 times by using a 6D laser interferometer, and recording geometric error data at different positions.
Step 2.2 geometric error and measurement Point location fitting
Generally, a polynomial fitting is adopted for a fitting function of a single geometric error and stroke displacement of a moving part, but model orders need to be estimated in the fitting process, and the model preset error may be caused by the estimated orders. The invention provides a fitting means based on Fourier series by exploring the internal relation between the surface curve of the guide rail and the straightness error and the angle error on the basis of looking up a large amount of documents. The example proves that the following Fourier series is used for performing expansion fitting on the geometric error and the displacement, the fitting degree is high, and the residual error is small.
F(u)＝a 0 +a 1 cos(wu)+b 1 sin(wu)+a 2 cos(2wu)+b 2 sin(2wu)+a 3 cos(3wu)+b 3 sin(3wu)+…+a l cos(lwu)+b l sin(lwu)(l＝1，2，…) (7)
Wherein a is 0 ，a 1 ，b 1 …a l ，b l And w is a coefficient of the fitting function, l is an order of the Fourier series; besides the Fourier series, a sine function is used for fitting, and the sine function is in the form of:
S(u)＝p 1 sin(c 1 u+d 1 )+p 2 sin(c 2 u+d 2 )+…+p m sin(c m u+d m )(m＝1，2，…) (8)
wherein p is 1 ，c 1 ，d 1 …p m ，c m ，d m The coefficient of the sine function fitting, m is the order of the sine function; u is the measuring point position, namely the movement stroke.
Step 3 geometric error correlation analysis
The pearson product-difference correlation coefficient is a widely used measure of the correlation between successive random variables. The partial correlation coefficient quantifies the correlation of two variables (e.g., genetic activity) on one or more other variables. The invention provides a method for analyzing nonlinear correlation among machine tool geometric errors by utilizing a second-order partial correlation coefficient of a Pearson product difference. After simple correlation analysis, i.e., pearson 0-order partial correlation analysis, is performed on the error, a second-order partial correlation coefficient is calculated as shown in the following formula.
(i, j=1, 2, …,18 and i+.j)
(i, j, k=1, 2, …,18 and are mutually unequal in pairs)
(i, j, k, l=1, 2, …,18 and are not equal to each other in pairs)
Wherein the method comprises the steps ofIs the pearson 0-order partial correlation coefficient; />Is the pearson 1-order partial correlation coefficient; />Is the pearson 2 nd order partial correlation coefficient. The pearson 1-order partial correlation coefficient represents the correlation of any two errors over a third, different error, and the pearson 2-order partial correlation coefficient represents the correlation of any two errors over the remaining two errors that are different from them. For 0 th order correlation calculation, e.g. +.>And->The result is the same, the 0-order bias correlation can be written into an 18×18 symmetric matrix, but when the 1-order bias correlation and the 2-order bias correlation are calculated, infinity appears when errors are the same, and in order to ensure that the calculation result can still be written into the 18×18 matrix so as to clearly display the correlation relationship among the errors, the following is provided:
(1) When 1-or 2-order partial correlation coefficients having the same two errors (i.e., i=k) are calculated, the result is set to 1 processing with reference to 0-order partial correlation.
(2) After calculating the 1-order partial correlation, 2448 groups of data are obtained, for simplifying the calculation, the average value of each condition is calculated, then the calculated result is written into an 18×18 matrix according to the 0-order calculation result, and then the 2-order partial correlation coefficient is calculated according to the 1-order partial correlation formula.
Direct interactions and potential correlations between errors can be obtained by computational analysis.
Step 4 machine tool geometric error global sensitivity analysis
Step 4.1 local influence of geometrical errors on machining precision
And (3) according to the machine tool geometric error model established in the step (1.4), obtaining a nonlinear function relation between the machine tool machining precision and the geometric error. In order to measure the local influence of single errors on the machining precision of a machine tool, the geometrical errors are offset by adopting the machining precision. Then the error δx is analyzed x (＝g 1 ) The influence on the machining precision in the X direction when slight changes occur is as follows:
g is given in equation 12 1 After partial derivative is taken, the average of the error measurement data is taken. Similarly, g can be obtained 1 The influence on the machining precision in the y and z directions is written in a matrix form as follows:
similarly, it can be found thatThe geometric error pair processing precision of the rest 17 items relative to the position is 3
The degree of local influence in the individual directions.
Step 4.2 study of the volatility of geometric errors with Displacement
In order to study the change trend of geometric errors along with displacement, according to the fitting function of the errors and the motion displacement in the step 2.2, the invention adopts the fitting function to derive the displacement, and the like is expressed in g 1 For example, useSymbol g 1 Fitting a function to the measurement point displacement
Where n is the number of measurement points, u t And (3) for measuring the point displacement, the above fitting function derives the displacement and then brings the displacement into the test point and calculates the average value, so that the fluctuation influence of the change of the travel of the moving part on the geometric error is obtained. The same steps can be adopted to calculateAnd the fluctuation of the geometric errors related to the positions of the remaining 17 items along with the displacement.
Step 4.3 machine tool geometric error bias correlation analysis
After the second-order partial correlation coefficient of the geometric error under each condition calculated by the step 3 is calculated, the average value of each condition is calculated, the result is still written into an 18×18 matrix, the average value of each row is calculated, the result is taken as the correlation degree and interaction of the geometric error represented by the row and the whole of the rest errors, and the result is used as a symbolA second order partial correlation coefficient representing a single error.
Step 4.4 machine tool geometric error global sensitivity formula
Comprehensively considering the analysis results of the steps 4.1-4.3, calculating the global sensitivity of the geometric error to the machining precision of the machine tool in a form of sequential multiplication, and taking the error g as the error g 1 For example, use symbol f x (g 1 )，f y (g 1 )，f z (g 1 ) Representing the global sensitivity coefficient of the error pair X, Y, Z,3 directions, i.e
Error g 1 The global sensitivity coefficient for the whole process space is expressed as
Repeating the steps to obtain the global sensitivity coefficients of the machine tool 18 items of geometric errors X, Y, Z and 3 directions, namely
Will be any error g i The global sensitivity coefficient for the whole process space is expressed as
Second order partial correlation coefficientLargely explaining the interaction of this error with other errors, +.>The large coefficient indicates that the error fluctuates greatly with displacement change, < >>The larger the global sensitivity coefficient is, the larger the influence of the error on the whole machining precision of the machine tool is, the more strict control should be performed, and the machining precision of the machine tool is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of the structure and typical body numbering of the machine tool.
Fig. 3 is a topological structure diagram of a machine tool.
FIG. 4 shows the geometric error δx x -u-fitting and residual map.
FIG. 5 is a geometric error δy x -u-fitting and residual map.
FIG. 6 shows the geometric error εβ x -u-fitting and residual map.
Fig. 7 shows the geometric error second order bias correlation coefficient.
Fig. 8 is a global sensitivity coefficient graph of various errors versus X-direction machining accuracy.
Fig. 9 is a graph of global sensitivity coefficients for various errors versus Y-direction machining accuracy.
Fig. 10 is a global sensitivity coefficient graph of various errors versus Z-direction machining accuracy.
FIG. 11 is a graph of global sensitivity coefficients based on errors over the entire working space of the machine tool.
Detailed Description
The invention takes a four-axis horizontal machining center as an example to verify the global sensitivity analysis method of the geometric errors of the numerical control machine tool.
The method specifically comprises the following steps:
step 1, establishing a machine tool motion characteristic matrix and a geometric error model
Step 1.1 analyzing the topology of a machine tool
According to the theory of a multi-body system, each component part of the machine tool is as follows: the machine tool body, the upright post, the workbench, the ram, the spindle box, the cutter and the like, and the workpiece can be simplified into a plurality of arbitrary classical bodies. The topological structure is in a twisted pair mode, a lathe bed fixed on a foundation and a stand column fixedly connected on the lathe bed and still are used as an inertial body, the reference sign is a B0 body, a ram is a B1 body, and the serial numbers of B2, B2 and … Bj … Bn are sequentially arranged along the directions far away from the B0 body and the B1 body according to the structural mode of the machine tool, wherein n is the number of typical bodies of the machine tool. And establishing a topological structure of the machine tool according to the relative movement and the labels among the parts of the machine tool. The structure of the machine tool and the numbering of the typical bodies are shown in fig. 2. Fig. 3 shows a topology of a machine tool.
Step 1.2, establishing a motion characteristic matrix of the machine tool
And establishing a right-hand rectangular Cartesian coordinate system which is fixedly connected with the machine tool body B0 and other bodies, wherein the coordinate system on each body is a sub-coordinate system, and corresponding axes on each sub-coordinate system are parallel to each other.
By the multi-body system theory and the generalized coordinate system set, the motion between adjacent bodies of the selected machine tool can be described by using a 4 x 4 homogeneous coordinate transformation matrix, wherein the workbench is fixedly connected with the workpiece and is stationary, so that the B axis is considered to be free of errors. Table 1 gives the signs of all geometrical errors of the machine tool and their physical significance. Table 2 shows the ideal motion characteristic matrix and the error matrix when the machine tool has error relative motion.
Table 1 sign and physical meaning of geometrical errors
Table 2 machine tool motion error feature matrix
Wherein:
p represents rest; s represents motion;
t represents typical body B j Relative to B i Is a motion feature matrix of the ideal;
DeltaT represents typical body B j Relative to B i Is a motion error feature matrix of (1);
I 4x4 meaning that when the error is relatively small, it is negligible as an identity matrix;
other physical meanings of the errors are listed in table 1.
Step 1.3, establishing a machine tool geometric error model
Let the coordinates of the tool forming point in the tool coordinate system be:
P t ＝(p tx p ty p tz 1) T (1)
let the coordinates of the workpiece forming point in the workpiece coordinate system be:
P w ＝(p wx p wy p wz 1) T (2)
when the machine tool works in an ideal state without errors, the ideal coordinates of the workpiece forming point in the tool coordinate system are as follows:
in actual cases, the actual coordinates of the workpiece forming point in the tool coordinate system are:
P tactual ＝( E T 03 ) -1E T 04 P w (4)
wherein:
the total error matrix of the machine tool is as follows:
wherein E is a machine tool comprehensive volume error model.
From (5), accuracy and geometry errors, movement axis positions and P are mainly known w In relation, a general volumetric error model of the machine tool can thus be established.
E＝E(G，P w ，H) (6)
Wherein:
E＝[E x ，E y ，E z ，0] T representing the volumetric error vectors in 3 directions of the machine tool;
h= [ x, y, z,1] t, where x, y, z represent position vectors of the machine tool feed axis in three directions;
G＝[g 1 ，g 2 ，…，g 18 ] T representing a vector consisting of 18 geometrical errors of the machine tool and let δx x ，δy x ，δz x ，εα x ，εβ x ，εγ x ，δx y ，δy y ，δz y ，εα y ，εβ y ，εγ y ，δx z ，δy z ，δz z ，εα z ，εβ z ，εγ z ＝g 1 ，g 2 ，…，g 18 ；
Step 2 geometric error measurement data and Displacement fitting
Step 2.1 measuring geometrical errors of the machine tool
When the influence of geometrical errors on a machine tool is studied in an important way, P w And H assuming no error, should be set to a known constant and the static turntable is kept from rotating while the error is measured, taking into account only the 18 position-dependent geometric errors along the X, Y, Z,3 directions. Under the condition of ensuring that the test instrument does not interfere with the motion axis of the machine tool, the same measuring range of 800mm is selected on each axis, one measuring point is set every 80mm by taking a 50mm position as a starting point, and the total number of the test points is 11. And the motion axis runs 2 times in the forward and backward directions of motion respectively, each point is measured 4 times by using a 6D laser interferometer, and geometric error data at different positions are recorded. The data mean values are recorded and calculated as shown in tables 3-6.
Table 3X shaft geometry error measurement (mm)
Table 4Y shaft geometry error measurement (mm)
Table 5Z shaft geometry error measurement (mm)
TABLE 6 measurement of errors between units (mm)
Step 2.2 geometric error and measurement Point location fitting
Generally, a polynomial fitting is adopted for a fitting function of a single geometric error and stroke displacement of a moving part, but model orders need to be estimated in the fitting process, and the model preset error may be caused by the estimated orders. The invention provides a fitting means based on Fourier series by exploring the internal relation between the surface curve of the guide rail and the straightness error and the angle error on the basis of looking up a large amount of documents. The example proves that the following Fourier series is used for performing expansion fitting on the geometric error and the displacement, the fitting degree is high, and the residual error is small.
F(u)＝a 0 +a 1 cos(wu)+b 1 sin(wu)+a 2 cos(2wu)+b 2 sin(2wu)+a 3 cos(3wu)+b 3 sin(3wu)+…+a l cos(lwu)+b l sin(lwu)(l＝1，2，…) (7)
Wherein a is 0 ，a 1 ，b 1 …a l ，b l And w is a coefficient of the fitting function, l is an order of the Fourier series; besides the Fourier series, a sine function is used for fitting, and the sine function is in the form of:
S(u)＝p 1 sin(c 1 u+d 1 )+p 2 sin(c 2 u+d 2 )+…+p m sin(c m u+d m )(m＝1，2，…) (8)
wherein p is 1 ，c 1 ，d 1 …p m ，c m ，d m The coefficient of the sine function fitting, m is the order of the sine function; u is the measuring point position, namely the movement stroke. The geometric error and measurement point location fitting results are shown in table 7. Fig. 4-6 are graphs of partial geometric errors as a function of displacement.
Table 7 geometric error and Displacement fitting function table
/>
/>
Wherein R-square (determining coefficient) represents the fitting quality through the change of data, the normal value range is [0,1], the closer to 1, the stronger the interpretation ability of the equation variable to the function is indicated, and the model is better for the data fitting. As can be seen from the table, most of the determination systems are above 0.98, some of the determination systems are very close to 1, the fitting result shows that the Fourier series and the sine series are selected to fit the functional relation between the geometric error and the displacement, the fitting degree is high, the residual error is small, and the relation between the geometric error and the displacement can be displayed more clearly.
Step 3 geometric error correlation analysis
The pearson product-difference correlation coefficient is a widely used measure of the correlation between successive random variables. The partial correlation coefficient quantifies the correlation of two variables over one or more other variables. The invention provides a method for analyzing nonlinear correlation among machine tool geometric errors by utilizing a second-order partial correlation coefficient of a Pearson product difference. After simple correlation analysis, i.e., pearson 0-order partial correlation analysis, is performed on the error, a second-order partial correlation coefficient is calculated as shown in the following formula.
(i, j=1, 2, …,18 and i+.j)
(i, j, k=1, 2, …,18 and are mutually unequal in pairs)
(i, j, k, l=1, 2, …,18 and are not equal to each other in pairs)
Wherein the method comprises the steps ofIs the pearson 0-order partial correlation coefficient; />Is the pearson 1-order partial correlation coefficient; />Is the pearson 2 nd order partial correlation coefficient. The pearson 1-order partial correlation coefficient represents the correlation of any two errors over a third, different error, and the pearson 2-order partial correlation coefficient represents the correlation of any two errors over the remaining two errors that are different from them. For 0 th order correlation calculation, e.g. +.>And->The result is the same, the 0-order bias correlation can be written into an 18×18 symmetric matrix, but when the 1-order bias correlation and the 2-order bias correlation are calculated, infinity appears when errors are the same, and in order to ensure that the calculation result can still be written into the 18×18 matrix so as to clearly display the correlation relationship among the errors, the following is provided:
(3) When 1-or 2-order partial correlation coefficients having the same two errors (i.e., i=k) are calculated, the result is infinite, and the 1-order partial correlation is referred to as 1 processing.
(4) After calculating the 1-order partial correlation, 2448 groups of data are obtained, for simplifying the calculation, the data are averaged for each case and then are written into an 18×18 matrix according to a 0-order calculation result form, and then the 2-order partial correlation coefficient is calculated according to a 1-order partial correlation formula.
Direct interactions and potential correlations between errors can be obtained by computational analysis.
Step 4 machine tool geometric error global sensitivity analysis
Step 4.1 local influence of geometrical errors on machining precision
And (3) according to the machine tool geometric error model established in the step (1.4), obtaining a nonlinear function relation between the machine tool machining precision and the geometric error. In order to measure the local influence of single errors on the machining precision of a machine tool, the geometrical errors are offset by adopting the machining precision. Then the error δx is analyzed x (＝g 1 ) The influence on the machining precision in the X direction when slight changes occur is as follows:
g is given in equation 12 1 After partial derivative is taken, the average of the error measurement data is taken. Similarly, g can be obtained 1 The influence on the machining precision in the Y, Z direction is written in a matrix form as follows:
similarly, it can be found thatThe residual 17 items of geometric errors related to positions have local influence on the machining precision in 3 directions.
Step 4.2 study of the volatility of geometric errors with Displacement
In order to study the change trend of geometric errors along with displacement, according to the fitting function of the errors and the motion displacement in the step 2.2, the invention adopts the fitting function to derive the displacement, and the like is expressed in g 1 For example, useSymbol g 1 Fitting a function to the measurement point displacement
Where n is the number of measurement points, u t And (3) for measuring the point displacement, the above fitting function derives the displacement and then brings the displacement into the test point and calculates the average value, so that the fluctuation influence of the change of the travel of the moving part on the geometric error is obtained. The same steps can be adopted to calculateAnd the fluctuation of the geometric errors related to the positions of the remaining 17 items along with the displacement.
Step 4.3 machine tool geometric error bias correlation analysis
After the second-order partial correlation coefficient of the geometric error under each condition calculated by the step 3 is calculated, the average value of each condition is calculated, the result is still written into an 18×18 matrix, the average value of each row is calculated, the result is taken as the correlation degree and interaction of the geometric error represented by the row and the whole of the rest errors, and the result is used as a symbolA second order partial correlation coefficient representing a single error. Fig. 7 shows the geometric error second-order partial correlation coefficient represented by an 18×18 matrix. Wherein the sequence numbers 1,2, …,18 correspond to the geometric errors g 1 ，g 2 ，…，g 18 。
Step 4.4 machine tool geometric error global sensitivity formula
Comprehensively considering the analysis results of the steps 4.1-4.3, calculating the global sensitivity of the geometric error to the machining precision of the machine tool in a form of sequential multiplication, and taking the error g as the error g 1 For example, use symbol f x (g 1 )，f y (g 1 )，f z (g 1 ) Representing the global sensitivity coefficient of the error pair X, Y, Z,3 directions, i.e
/>
Error g 1 The global sensitivity coefficient for the whole process space is expressed as
Table 8 shows the geometric error g 1 Global sensitivity coefficient analysis results in three directions X, Y, Z and across the process space.
TABLE 8 geometric error g 1 Global sensitivity coefficient
Repeating the steps to obtain the global sensitivity coefficients of the machine tool 18 items of geometric errors X, Y, Z and 3 directions, namely
Will be any error g i The global sensitivity coefficient for the whole process space is expressed as
The global sensitivity coefficients for each geometrical error pair X, Y, Z in three directions and over the whole process space can be obtained by calculation, and the calculation results are shown in tables 9 to 12. For visual display of the results, bar graph representations are made, as shown in fig. 8-11.
Table 9 global sensitivity coefficient table of various errors versus X-direction machining accuracy
Global sensitivity coefficient table of each error of table 10 to Y-direction processing precision
Global sensitivity coefficient table of each error of table 11 to Z-direction processing precision
Table 12 global sensitivity coefficient table based on errors over the entire working space of the machine tool
Analysis result description
When the critical geometric errors affecting the machining precision of the machine tool are identified through the global sensitivity coefficients, signs of the coefficients are ignored, and absolute influences of the geometric errors on the machining precision of the numerical control machine tool are analyzed and compared to obtain the following conclusion:
(1) For the X direction, geometric error εγ x ，δx x ，εβ x Has a larger global sensitivity coefficient, which indicates that epsilon gamma is generated when the moving part moves along the X axis x ，δx x And εβ x The three geometric errors and other errors pass through each otherThe interaction has a great influence on the machining precision of the machine tool.
(2) For the Y-direction, geometric error δy y ，εα y ，δz z The global sensitivity coefficient of (2) is larger, which indicates that when the moving part moves along the Y axis, delta Y y ，εα y And δz z The three geometric errors and other errors have great influence on the machining precision of the machine tool through mutual interaction.
(3) Geometric error εβ for Z-direction x ，εβ z ，εα y Has a larger global sensitivity coefficient, which indicates epsilon beta when the moving part moves along the Z axis x ，εβ z And εα y The three geometric errors and other errors have great influence on the machining precision of the machine tool through mutual interaction.
(4) Geometric error epsilon gamma for the whole working space of the machine tool x ，εβ x ，δy y ，δx x ，εβ z And εα y The global sensitivity coefficient of the method is larger and accounts for about 74.6% of the total, the method has decisive influence on the machining precision of the numerical control machine tool, and the method is strictly controlled when the links of machine tool manufacture, assembly and the like are carried out, so that the machining quality of the product is fundamentally improved.
Claims (3)
1. A geometric error global sensitivity analysis method of a numerical control machine tool is characterized in that: the analysis method comprises the steps of,
1) By analyzing the relative motion among three motion axes of a moving part X, Y, Z in a four-axis numerical control machine tool, according to a multi-body system theory, a machine tool motion error homogeneous transformation matrix is established, and further, a non-linear function relation between machining precision and geometric errors is established by a machine tool geometric error model representation, and deviation of the machining precision to the geometric errors is conducted, so that the local influence of the geometric errors on the machining precision is obtained;
2) Analyzing the geometric error measurement image characteristics according to the change of the geometric error measurement value along with the change of the displacement of the moving part, providing a geometric error-displacement fitting function mainly based on Fourier series, and deriving a motion stroke by using the geometric error to obtain the fluctuation of the geometric error along with the change of the displacement;
3) According to complex interaction among geometric errors, providing a second-order bias correlation coefficient based on a pearson product difference to perform coupling analysis on the geometric errors;
4) In order to comprehensively consider the influence degree of the geometric error on the machining precision of the machine tool, the results are multiplied in sequence and then used as the global sensitivity of the geometric error;
the process of measuring the geometrical error of the machine tool is as follows, P w And H is assumed to be free of errors, is set to be a known constant, and keeps the static pressure turntable from rotating when the errors are measured, and only 18 geometric errors related to positions along X, Y, Z directions are considered; selecting the same measuring range on each axis, setting measuring points at certain intervals, enabling the motion axis to run 2 times in the forward and backward directions of motion respectively, measuring 4 times by using a 6D laser interferometer, and recording geometric error data at different positions;
performing expansion fitting on the geometric error and the displacement by using a Fourier series;
F(u)＝a 0 +a 1 cos(wu)+b 1 sin(wu)+a 2 cos(2wu)+b 2 sin(2wu)+a 3 cos(3wu)+b 3 sin(3wu)+…+a l cos(lwu)+b l sin (lwu), wherein l=1, 2, …;
wherein a is 0 ，a 1 ，b 1 ，a 2 ，b 2 ，a 3 ，b 3 ，…，a l ，b l And w is a coefficient of the fitting function, l is an order of the Fourier series; besides the Fourier series, a sine function is used for fitting, and the sine function is in the form of:
S(u)＝p 1 sin(c 1 u+d 1 )+p 2 sin(c 2 u+d 2 )+…+p m sin(c m u+d m ) Wherein m=1, 2, …; wherein p is 1 ，c 1 ，d 1 …p m ，c m ，d m Fitting coefficients for a sine function, m being the order of the sine function; u is the measuring point position, namely the movement stroke.
2. The method for analyzing the geometric error global sensitivity of the numerical control machine tool according to claim 1, wherein the method comprises the following steps: the geometric error correlation analysis process is as follows,
analyzing nonlinear correlation among geometric errors of the machine tool by using a second-order partial correlation coefficient of the pearson product difference; and after performing simple correlation analysis, namely pearson 0-order partial correlation analysis on the errors, performing second-order partial correlation coefficient calculation.
3. The method for analyzing the geometric error global sensitivity of the numerical control machine tool according to claim 1, wherein the method comprises the following steps: the machine tool geometry error bias correlation analysis process is as follows,
after the second-order partial correlation coefficient of the geometric error under each condition is calculated by the step 3, the average value of each condition is calculated, the result is still written into an 18 multiplied by 18 matrix, the average value of each row is calculated and used as the correlation degree and interaction of the geometric error represented by the row and the whole of the rest errors, and the correlation degree and interaction are used as symbolsA second order bias correlation coefficient representing a single error;
calculating the global sensitivity of the geometric error to the machining precision of the machine tool by adopting a form of multiplying in turn by the symbol f x (g 1 )，f y (g 1 )，f z (g 1 ) Representing the global sensitivity coefficients for the error pair X, Y, Z,3 directions,
will be any error g i The global sensitivity coefficient for the whole process space is expressed as
Second order partial correlation coefficientA larger number indicates a larger interaction between errors, < > and->The larger the coefficient is, the larger the fluctuation of the error with the displacement is, the +.>The greater the global sensitivity coefficient.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010625505.2A CN111967097B (en) | 2020-07-01 | 2020-07-01 | Geometric error global sensitivity analysis method for numerical control machine tool |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010625505.2A CN111967097B (en) | 2020-07-01 | 2020-07-01 | Geometric error global sensitivity analysis method for numerical control machine tool |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111967097A CN111967097A (en) | 2020-11-20 |
| CN111967097B true CN111967097B (en) | 2024-02-02 |
Family
ID=73361313
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010625505.2A Active CN111967097B (en) | 2020-07-01 | 2020-07-01 | Geometric error global sensitivity analysis method for numerical control machine tool |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111967097B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113932707B (en) * | 2021-08-29 | 2022-11-29 | 北京工业大学 | Method for compensating geometric error of three-coordinate measuring machine based on elastic network algorithm |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104007700A (en) * | 2014-05-29 | 2014-08-27 | 北京工业大学 | Three-axis numerical control machine tool key geometric error identification method based on global sensitivity analysis |
| CN110955979A (en) * | 2019-12-11 | 2020-04-03 | 北京工业大学 | Machine tool machining precision reliability sensitivity analysis method considering geometric error partial correlation |
-
2020
- 2020-07-01 CN CN202010625505.2A patent/CN111967097B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104007700A (en) * | 2014-05-29 | 2014-08-27 | 北京工业大学 | Three-axis numerical control machine tool key geometric error identification method based on global sensitivity analysis |
| CN110955979A (en) * | 2019-12-11 | 2020-04-03 | 北京工业大学 | Machine tool machining precision reliability sensitivity analysis method considering geometric error partial correlation |
Non-Patent Citations (3)
| Title |
|---|
| A method for identifying and predicting the geometric errors of a rotating axis;Jinwei Fan等;Research Square;第1-37页 * |
| Machining accuracy reliability analysis of multi-axis machine tool based on Monte Carlo simulation;Qiang Cheng等;J Intell Manuf(第29期);第191-209页 * |
| 数控机床几何误差相关性分析方法研究;郭世杰等;农业机械学报;第47卷(第10期);第383-389页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111967097A (en) | 2020-11-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Smith | Machine tool metrology: An industrial handbook | |
| Niu et al. | A machining accuracy improvement approach for a horizontal machining center based on analysis of geometric error characteristics | |
| Soori et al. | Dimensional and geometrical errors of three-axis CNC milling machines in a virtual machining system | |
| Chen et al. | A comprehensive error analysis method for the geometric error of multi-axis machine tool | |
| Ni | CNC machine accuracy enhancement through real-time error compensation | |
| Rahman et al. | Modeling, measurement and error compensation of multi-axis machine tools. Part I: theory | |
| Schwenke et al. | Geometric error measurement and compensation of machines—an update | |
| CN106141814B (en) | The detection of Digit Control Machine Tool translation shaft geometric error and discrimination method based on LaserTRACER | |
| JP4660779B2 (en) | Method for evaluating position error of moving device and method for improving moving accuracy based on the evaluation result | |
| CN109765848B (en) | Method for calculating geometric error contribution value of motion axis of five-axis machine tool and evaluating influence | |
| CN106774152B (en) | A kind of modeling method of numerically-controlled machine tool position correlation geometric error item | |
| CN1892175A (en) | Three-coordinate measuring machine-tool error compensation system and method | |
| CN103034166A (en) | Recognition method of critical geometrical error source of machine tool | |
| CN104007700A (en) | Three-axis numerical control machine tool key geometric error identification method based on global sensitivity analysis | |
| Yang et al. | Measurement of spindle thermal errors in machine tool using hemispherical ball bar test | |
| CN105631122B (en) | Thermal deformation simulation analysis and modeling method for machine tool large part | |
| CN104050316A (en) | Analysis method on basis of distribution characteristics of space machining error of numerical control machine tool | |
| Guo et al. | Geometric accuracy enhancement of five-axis machine tool based on error analysis | |
| CN110955979B (en) | Machine tool machining precision reliability sensitivity analysis method considering geometrical error bias correlation | |
| CN111967097B (en) | Geometric error global sensitivity analysis method for numerical control machine tool | |
| CN111666659A (en) | Modeling method for thermal error of complete machine tool | |
| Holub et al. | Effect of position of temperature sensors on the resulting volumetric accuracy of the machine tool | |
| Brecher et al. | Direct measurement of thermo-elastic errors of a machine tool | |
| Pu et al. | Modeling, identification, and measurement of geometric errors for a rotary axis of a machine tool using a new R-test | |
| CN113359609A (en) | Key geometric error optimization proportioning compensation method for five-axis numerical control machine tool |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |