CN110489901B - Method for verifying modeling precision of space geometric error model of precision machine tool - Google Patents
Method for verifying modeling precision of space geometric error model of precision machine tool Download PDFInfo
- Publication number
- CN110489901B CN110489901B CN201910790030.XA CN201910790030A CN110489901B CN 110489901 B CN110489901 B CN 110489901B CN 201910790030 A CN201910790030 A CN 201910790030A CN 110489901 B CN110489901 B CN 110489901B
- Authority
- CN
- China
- Prior art keywords
- error
- numerical
- algorithm
- magnitude
- geometric
- 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 92
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 120
- 239000011159 matrix material Substances 0.000 claims abstract description 111
- 238000004364 calculation method Methods 0.000 claims abstract description 24
- 238000004088 simulation Methods 0.000 claims abstract description 18
- 238000004458 analytical method Methods 0.000 claims abstract description 14
- 230000008030 elimination Effects 0.000 claims abstract description 9
- 238000003379 elimination reaction Methods 0.000 claims abstract description 9
- 238000006073 displacement reaction Methods 0.000 claims description 40
- 238000006243 chemical reaction Methods 0.000 claims description 31
- 238000012512 characterization method Methods 0.000 claims description 22
- 230000009466 transformation Effects 0.000 claims description 13
- 238000003491 array Methods 0.000 claims description 12
- 230000006872 improvement Effects 0.000 claims description 8
- 230000008569 process Effects 0.000 claims description 8
- 238000005070 sampling Methods 0.000 claims description 7
- 230000008859 change Effects 0.000 claims description 6
- 238000009826 distribution Methods 0.000 claims description 6
- 238000012545 processing Methods 0.000 claims description 5
- 238000012795 verification Methods 0.000 abstract description 18
- 238000003672 processing method Methods 0.000 abstract description 4
- 238000005516 engineering process Methods 0.000 description 6
- 230000006870 function Effects 0.000 description 6
- 238000003754 machining Methods 0.000 description 4
- 230000003068 static effect Effects 0.000 description 4
- 238000002474 experimental method Methods 0.000 description 3
- 238000004519 manufacturing process Methods 0.000 description 2
- 230000009467 reduction Effects 0.000 description 2
- 238000000926 separation method Methods 0.000 description 2
- 238000011426 transformation method Methods 0.000 description 2
- DILISPNYIVRDBP-UHFFFAOYSA-N 2-[3-[2-(2-hydroxypropylamino)pyrimidin-4-yl]-2-naphthalen-2-ylimidazol-4-yl]acetonitrile Chemical compound OC(CNC1=NC=CC(=N1)N1C(=NC=C1CC#N)C1=CC2=CC=CC=C2C=C1)C DILISPNYIVRDBP-UHFFFAOYSA-N 0.000 description 1
- 230000000903 blocking effect Effects 0.000 description 1
- 230000000295 complement effect Effects 0.000 description 1
- 125000004122 cyclic group Chemical group 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000014509 gene expression Effects 0.000 description 1
- 239000004816 latex Substances 0.000 description 1
- 229920000126 latex Polymers 0.000 description 1
- 238000000465 moulding Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 238000007781 pre-processing Methods 0.000 description 1
- 230000002441 reversible effect Effects 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
Images
Landscapes
- Numerical Control (AREA)
Abstract
The invention discloses a method for checking the modeling precision of a space geometric error model of a precision machine tool, which is a numerical theory checking method for filling and judging the modeling precision accuracy of the space geometric error model containing parameters of the precision machine tool, and performs numerical simulation analog analysis on an iteration result by using a numerical algorithm, an iteration algorithm and a high-order infinitesimal elimination algorithm from the aspects of statistics and numerical simulation, thereby separating a theoretical calculation error caused by the iteration solving precision based on a small-error hypothesis theory and neglecting the high-order infinitesimal iteration solving precision; the numerical deviation magnitude corresponding to different processing methods in iterative solution of the feature matrix is quantized; the modeling precision is checked to ensure that the aim of accurate verification and guidance modeling is achieved on the basis of a certain numerical value magnitude. The method has the advantages of low cost, short period, high verification accuracy and the like, can be applied to the calibration of the modeling accuracy of the spatial geometric error model of the ultra-precise machine tool in an expanded way, and has good market application prospect and popularization value.
Description
Technical Field
The invention belongs to the technical field of precision machining and testing, and relates to a method for verifying the modeling precision of a space geometric error model of a precision machine tool.
Background
The precision and ultra-precision machining techniques are manufacturing techniques aimed at high precision, and not only become techniques that are mainly developed in various countries, but also become marks for measuring the manufacturing level of one country. The precision modeling technology of the precision and ultra-precision machine tool is one of effective ways for improving the precision and ultra-precision machining technology, is based on a multi-body system theory and a homogeneous coordinate transformation method, is based on a small error hypothesis theory and neglects high-order infinitesimal, and meanwhile improves and promotes the precision of the precision and ultra-precision machine tool in an error compensation mode by establishing a comprehensive space error model of the numerical control machine tool by means of different measuring instruments and corresponding measuring methods thereof, related methods of process improvement and the like. However, in the modeling technique, the spatial geometric error model containing the parameter quantity characterization error feature matrix is necessarily established. In addition, in the error analysis which uses the parameter-containing representation space geometric error model as the necessary condition, the improvement of the modeling precision and the reduction of the theoretical calculation error are more important.
The accuracy of the established space geometric error model is usually verified by adopting experimental methods such as different measuring instruments, corresponding measuring methods thereof, related methods of process improvement and the like, under the influence of objective factors such as environment, personnel, machine equipment precision and the like, the verification process has high cost, long period and poor stability, and the numerical deviation of the modeling precision is difficult to be directly and accurately verified by the experimental method due to higher numerical magnitude. In addition, for ultra-precision machining, the verification of the modeling precision of the space geometric error model is difficult to verify by adopting an experimental method. In addition, when the number of axes of the linkage shaft of the numerical control machine tool is more, the numerical deviation magnitude of the modeling precision is further increased and even is larger than the numerical magnitudes of the measured value of the instrument, the required value of the working condition and the measured value of the process improvement, namely, the modeling precision is further reduced, so that the generated modeling precision error can cause larger undetermined theoretical calculation error, certain influence is caused on the processing precision and the performance of the precise and ultra-precise machine tool, and the importance of verifying the modeling precision of the space geometric error model of the precise machine tool is reversely proved. However, the judgment of the accuracy of the theoretical modeling precision of the phenomenon lacks a corresponding theoretical verification method.
Based on the analysis, the theoretical modeling precision is particularly important in the precision machine tool precision modeling technology, if certain theoretical calculation errors exist, the numerical control machine tool modeling precision and the error analysis can generate larger uncertainty due to the 'linkage effect' of system errors, and meanwhile, certain blocking effect is caused on the related error analysis, especially on the multi-axis linkage precision and ultra-precision machine tools. How to theoretically verify the modeling precision of the space geometric error model of the precision machine tool is more urgent.
Disclosure of Invention
The invention provides a method for checking the modeling precision of a precision machine tool in order to fill up a numerical theory checking method for judging the accuracy of the modeling precision of a parametric representation space geometric error model of the precision machine tool, and provides a method for checking the modeling precision of the precision machine tool in the aspects of statistics and numerical simulation, wherein numerical simulation analog analysis is carried out on an iteration result through a numerical algorithm, an iteration algorithm and a high-order infinitesimal elimination algorithm, and a theoretical calculation error caused by the iteration solving precision based on a small-error hypothesis theory and neglecting the high-order infinitesimal iteration solving precision is separated; the numerical deviation magnitude corresponding to different processing methods in iterative solution of the feature matrix is quantized; the modeling precision is checked to ensure that the aim of accurate verification and guidance modeling is achieved on the basis of a certain numerical value magnitude. The method has the advantages of low cost, short period, high verification accuracy and the like, and can be extensively applied to verifying the modeling accuracy of the spatial geometric error model of the ultra-precise machine tool.
The specific technical scheme is as follows:
on the basis of revealing the modeling precision of the precise machine tool space geometric error model and the theoretical calculation error thereof, the invention provides a method for verifying the modeling precision of the precise machine tool space geometric error model, which is used for judging the modeling precision of the precise machine tool space geometric error model by combining relevant factors causing the reduction of the modeling precision of the precise machine tool and the increase of the theoretical calculation error thereof from the aspects of mathematical statistics and numerical simulation.
A method (first method) for verifying the accuracy of modeling a space geometric error model of a precision machine tool, comprising the steps of:
firstly, selecting at least five groups of one-dimensional random arrays by adopting a one-dimensional distribution sampling mode, and sequentially corresponding to geometric errors and geometric displacement related to a precision machine tool through unit magnitude conversion; the unit magnitude conversion is to carry out unit magnitude conversion in sequence through five groups of one-dimensional random arrays matched with the parameter-containing representation geometric error and geometric displacement term number of the precision machine tool, and convert the unit magnitude conversion into a numerical magnitude conforming to the actual working condition;
in the second step, the first step is that,under the condition of original iteration solving times of the space geometric error model, carrying out numerical simulation analog analysis on iteration results of a numerical algorithm, b iteration algorithm and c high-order infinitesimal elimination algorithm to respectively obtain numerical real solutions6Eij(a)6 error item elements in the high-order infinitesimal small error characteristic matrix are not omitted6Eij(b)The numerical value of (1) is solved and 6 error item elements in a high-order infinite small error feature matrix are eliminated6Eij(c)The numerical solution of'; the a numerical algorithm is obtained by directly substituting corresponding geometric errors and geometric displacement in a feature matrix through unit magnitude conversion of a random array and then iterating the values of the feature matrix6Eij(a)The numerical result of (1), namely the true value obtained by the 4x4 order characteristic matrix operation containing numerical elements; the b iterative algorithm is to obtain a characteristic matrix containing parameter representation geometric errors and geometric displacement in an iterative mode6Eij(b)Containing parameter characterization relations; the c high-order infinite truncation algorithm is obtained by different solving methods based on a small error hypothesis theory and neglecting high-order infinite small6Eij(c)' characterization relation containing parameter, said c algorithm comprises different high-order truncation infinite small algorithm c1…cn；
If the numerical magnitude between the c high-order infinite culling algorithm and the numerical solution of the a numerical algorithm or the b iterative algorithm has a deviation of spanning magnitude, the problems of modeling precision and theoretical calculation error exist, and the modeling method needs to be further corrected; otherwise, carrying out the third step;
thirdly, under the iterative algorithm of b, taking the numerical algorithm of a as a benchmark to obtain 6 error item elements in the feature matrix without truncating high-order infinite small errors6Eij(b)(a) Numerical simulation results of numerical deviation magnitude to verify that high-order infinite parametric-containing representation space geometric error model is not truncated6Eij(b)The accuracy of (2); meanwhile, under the c high-order infinite small-cut algorithm, 6 error item elements in a truncated high-order infinite small error characteristic matrix are obtained by taking the a numerical algorithm as the reference6Eij(c)' (a) simulation results of magnitude of numerical deviation, andperforming analog analysis, namely judging the numerical magnitude of the measured value of the instrument, the required value of the working condition and the actually measured value of the process improvement, and if the numerical magnitude is at the same level or lower than the numerical magnitude, selecting high-order infinite small cut algorithm modeling precision to meet the requirement of the working condition;
a method (second method) for verifying the accuracy of modeling a space geometric error model of a precision machine tool, comprising the steps of:
step one, adopting a multi-dimensional distribution sampling mode, taking parameter-containing characterization geometric errors and geometric displacement related to a precision machine tool as dimensions, selecting a group of one-dimensional random arrays, and sequentially corresponding to the geometric errors and the geometric displacement related to the precision machine tool through unit magnitude conversion; the unit magnitude conversion is to perform unit magnitude conversion in sequence through a one-dimensional random array matched with the parameter-containing representation geometric error and geometric displacement term number of the precision machine tool, and convert the unit magnitude conversion into a numerical magnitude in accordance with the actual working condition;
secondly, under the condition of the iteration times matched with the memory of the computer, firstly, for the a numerical algorithm and the b iterative algorithm, obtaining6Eij(a,b)The change rule between the numerical value field and the maximum magnitude thereof; then, for c high-order infinite small round off algorithm, obtaining6Eij(c)The change rule between the numerical value domain and the maximum magnitude thereof; finally, the a numerical algorithm is taken as a reference, and under the b iterative algorithm, the method is obtained6Eij(b)(a) The numerical value domain, the most value magnitude and the numerical value deviation of the iteration times corresponding to the most value magnitude are judged, if the deviation of the numerical value deviation magnitude is over the magnitude from the iteration result of the a numerical value algorithm, the space geometric error model represented by the parameter-containing quantity has the problems of modeling precision and theoretical calculation error, the modeling method needs to be further corrected, otherwise, the higher-order infinite small space geometric error model represented by the parameter-containing quantity is not omitted6Eij(b)Is accurate to perform the third step; the a numerical algorithm is obtained by directly substituting corresponding geometric errors and geometric displacement in a feature matrix through unit magnitude conversion of a random array and then iterating the values of the feature matrix6Eij(a)Is a numerical value knotThe result is the true value obtained by the 4x4 order feature matrix operation containing numerical value elements; the b iterative algorithm is to obtain a characteristic matrix containing parameter representation geometric errors and geometric displacement in an iterative mode6Eij(b)Containing parameter characterization relations; the c high-order infinite truncation algorithm is obtained by different solving methods based on a small error hypothesis theory and neglecting high-order infinite small6Eij(c)' characterization relation containing parameter;
thirdly, under the c high-order infinite small round elimination method, the a numerical algorithm is taken as a reference to obtain6Eij(c)' (a) numerical value domain, the most value magnitude and the numerical value deviation of the corresponding iteration times are judged, and if the numerical value magnitude is in the same level or lower than the numerical value magnitude, the modeling precision of the selected high-order infinite-small-cut algorithm meets the requirement of the working condition; finally, the algorithm a and the algorithm b are used as the reference in sequence, and under the algorithm b and the algorithm a, the method is obtained6Eij(b)(a)、6Eij(a)(b) The mean value of the numerical deviation in the range of the numerical field and the standard deviation thereof; under the c algorithm, obtain6Eij(c)'(a)、6Eij(c)' (b) mean deviation of values in the range of the numerical domain and their standard deviation, to quantify the errors of theoretical calculation in the separation and selective use of different process steps.
Further, the method for verifying the modeling precision of the space geometric error model of the precision machine tool relates to a method for representing geometric errors including relative corner errors delta by using parametersijRelative displacement error epsilonijWherein i is a linear motion shaft related to the precision machine tool, and j is the linear motion shaft and a rotating shaft related to the machine tool (the same below); the parameter-containing quantity represents the geometric displacement, including displacement x, y and z of X, Y, Z linear guide rail shaft and rotation quantity alpha, beta and gamma of A, B, C shaft rotating along X, Y, Z shaft; the characteristic error feature matrix containing parameter quantity, i.e. the transformation matrix of the tool coordinate system and the workpiece coordinate system containing geometric error terms, includes the error feature matrix E without high order infinitesimal truncationijEliminating the error characteristic matrix E with infinitesimal high orderij', setting an error characteristic matrix EijComprises the following steps:
in the formula etax,ηy,ηz,Px,Py,PzThe relative position error and the relative rotation angle error of the tool coordinate system and the workpiece coordinate system along the motion direction of the axis X, Y, Z of the precision machine tool after the characteristic matrix iteration are respectively obtained; the method comprises the steps of characterizing 6 error item elements in an error feature matrix by parameters, and recording 6 error item elements in the error feature matrix without truncation of high-order infinitesimal small errors6Eij(b)And satisfy
The 6 error term elements in the high-order infinite small error characteristic matrix are cut off and recorded as6Eij(c)', and satisfy
Wherein6Eij(a,b)Comprises6Eij(a)、6Eij(b)。
The method has the advantages that the method for checking the modeling precision of the precise machine tool in order to fill up the numerical theory checking method for judging the accuracy of the modeling precision of the parametric representation space geometric error model of the precise machine tool is provided from the aspects of statistics and numerical simulation, numerical simulation analog analysis is carried out on an iteration result through a numerical algorithm, an iteration algorithm and a high-order infinitesimal elimination algorithm, and the theoretical calculation error caused by the iteration solving precision based on a small-error hypothesis theory and neglecting the high-order infinitesimal iteration solving precision is separated; the numerical deviation magnitude corresponding to different processing methods in iterative solution of the feature matrix is quantized; the modeling precision is checked to ensure that the aim of accurate verification and guidance modeling is achieved on the basis of a certain numerical value magnitude. The method has the advantages of low cost, short period, high verification accuracy and the like, can be applied to the calibration of the modeling accuracy of the spatial geometric error model of the ultra-precise machine tool in an expanded way, and has good market application prospect and popularization value.
Drawings
FIG. 1 is a method for verifying the modeling accuracy of a spatial geometric error model of a precision machine tool.
The motion principle and the topological structure of the numerical control molding gear grinding machine SKMC-3000/20 are shown in figure 2.
In the figure: 0, a lathe bed; 1C axis (turntable table); 2, workpiece; 3X axis; 4Z axis; a 5A axis; a 6Y axis; 7 grinding wheel.
Detailed Description
Now, a five-linkage numerical control forming gear grinding machine SKMC-3000/20 is taken as an entity modeling object for illustration, as shown in fig. 2, according to a multi-body system theory and a homogeneous coordinate transformation method, based on a small error hypothesis theory and neglecting high order infinitesimal, a method for improving the precision of the precise machine space geometric error model modeling is utilized, and a method for verifying the precision of the precise machine space geometric error model modeling is provided for the problem of the modeling precision.
To facilitate the following expressions, the relevant definitions and associated assumptions are now made:
1. according to the theory of a multi-body system and homogeneous coordinate transformation, the homogeneous coordinate transformation matrix delta T of the forming gear grinding machine SKMC-3000/20 can be known27Equivalent to a homogeneous coordinate transformation matrix T of a grinding wheel coordinate system relative to a workpiece gear coordinate system under the ideal condition27Superimposing an error feature matrix E27And then:
E27＝ΔT27·(T27)-1 (2)
in the formula, the error feature matrix E with infinitesimal high order is not truncated27Can be expressed as:
based on the theory of small error hypothesis and neglecting the infinitesimal high order, the error feature matrix E27' may be expressed as:
2. the feature matrix without high-order infinite small errors left contains parameter variable representing 6 geometric error elements6E27(b)And satisfy
Parameter-contained 6 geometric error elements represented by parameters in high-order infinite small error feature matrix are omitted6E27(c)', and satisfy
3. Under the ideal state of each kinematic pair in the forming gear grinding machine SKMC-3000/20, a homogeneous coordinate transformation matrix T of a grinding wheel coordinate system relative to a workpiece gear coordinate system27Can be expressed as:
T27＝(T01s)-1·T03s·T34s·T45s·T56s (5)
under the condition that each kinematic pair in the forming gear grinding machine SKMC-3000/20 has an error state, a homogeneous coordinate transformation matrix delta T of a grinding wheel coordinate system relative to a workpiece gear coordinate system27Can be expressed as:
ΔT27＝(T01s·ΔT01s)-1·(T03s·ΔT03s)·(ΔT34p·T34s·ΔT34s)·(T45s·ΔT45s)·(ΔT56p·T56s·ΔT56s) (6)
4. the inverse matrix corresponding to the feature matrix under the ideal state is N-1Wherein N is1 -1＝(T01s)-1，N2 -1＝(T03s·T34s·T45s·T56s)-1，Tij -1＝((T01s)-1·(T03s·T34s·T45s·T56s))-1；
The inverse matrix corresponding to the characteristic matrix in the error state is R-1Let R1 -1＝(T01s·ΔT01s)-1，R2 -1＝((T03s·ΔT03s)·(ΔT34p·T34s·ΔT34s)·(T45s·ΔT45s)·(ΔT56p·T56s·ΔT56s))-1；
The a numerical algorithm is to directly substitute corresponding geometric errors and geometric displacement in a feature matrix through unit magnitude conversion of a random array, and then obtain the corresponding geometric errors and geometric displacement through iteration of feature matrix numerical values6E27(a)The numerical result is the true value obtained by the 4x4 order characteristic matrix operation containing numerical elements; b, iterative algorithm, namely obtaining a characteristic matrix containing parameter representation geometric errors and geometric displacement in an iterative mode6E27(b)Containing parameter characterization relations; c high order infinite truncation algorithm, which is obtained based on small error hypothesis theory and neglecting high order infinite small6E27(c)' characterization relation containing parameter;
6. for a common 8G memory computer, the maximum loop iteration number can reach 3x1017However, in order to perform subsequent data and image processing using Matlab, a part of the memory needs to be reserved, so the number of loop iterations involved in the feature matrix of the second verification method is set to 3 × 10 in the present example16(i.e., 43,046,721,107, the same below);
7. on the basis of the first checking method, in order to enable the first method to be more reasonable, the second checking method is provided, the purpose of mutual checking in different modes is achieved, meanwhile, the accuracy of the first method can be further verified, the use range and the accuracy of the precision machine tool space geometric error model modeling precision are expanded, and different checking methods can be selected according to the change of use conditions.
A method for improving the modeling precision of a space geometric error model of a precision machine tool comprises the following steps:
firstly, preprocessing an inverse matrix related to a feature matrix under different conditions;
under ideal state conditions, the inverse matrix N of the ideal characteristic matrix is due to the static and motion between bodies1 -1,N2 -1,T27 -1Without infinitesimal features, i.e. without relative rotation angle error (delta)ij) Relative displacement error (epsilon)ij) And perpendicularity error (S)xy,Szy,Szx) A characteristic of a parametric quantity, wherein i ═ x, y, z; j is x, y, z, a, c, firstly, the ideal characteristic matrix N of the inter-body motion of one branch of the topological structure1Obtaining N from the properties of the invertible matrix1 -1(ii) a Then obtaining an ideal inter-body static and motion characteristic matrix homogeneous coordinate transformation matrix (N) of the grinding wheel coordinate system relative to the workpiece gear coordinate system1 -1·N2) (i.e. T)27) (ii) a Finally, directly solving the whole (N)1 -1·N2)-1(i.e. T)27 -1)。
Under the condition of error state, homogeneous coordinate transformation of ideal characteristic matrix of interbody motion and interbody motion error characteristic matrix of one branch of topological structure
Existing in the presence of
Iteration of denominator polynomial terms and iteration of infinitesimal characteristics and high-order infinitesimal terms thereof exist, and the homogeneous coordinate transformation T of an ideal characteristic matrix of the interbody motion and an error characteristic matrix of the interbody motion of a C axis is firstly used01s·ΔT01sTo obtain R1Then directly obtain
Secondly, removing a denominator polynomial in the inverse matrix;
under the ideal state condition, the inverse matrix required by homogeneous coordinate transformation of the ideal feature matrix of static and moving between bodies contains
The removal of the denominator polynomial utilizes the property of a reversible matrix, namely, the elements except the diagonal are converted into plus and minus signs and then the positions are exchanged to obtain the product which does not contain the elements except the diagonal
An inverse matrix of the denominator polynomial;
for the condition of error state, the inverse matrix required by homogeneous coordinate transformation of static and moving error characteristic matrix between bodies contains
Removing the denominator polynomial, converting the denominator polynomial into a product form by utilizing an inverse number or adopting a method of manually removing the denominator;
finally, through Simplify function, realize
Removing and simplifying merging of polynomial containing denominator;
thirdly, 6 error item elements in the characteristic error feature matrix containing the parameter quantity obtained by the processing are converted6E27(b)The form of addition of the multiple products between each term in (a);
firstly, the error feature matrix E27Each error term element of6E27(b)The addition form of multiple products among each item in the character string representation is converted from mathematical representation to character string representation; secondly, removing spaces contained in the character string; then, sequentially dividing according to the signs of plus and minus through a Strsplit function, and respectively storing the number and the sign of each error item element; finally will be6E27(b)The mathematical characterization of the addition of the multiple products between each term in the string is converted into a string characterization of the form of the addition of the multiple products;
the fourth step, get every error term element to the third step6E27(b)The character string characterization relation in the form of the addition of the multiple products is used for judging and eliminating the infinitesimal high order;
firstly, according to the identification of the characteristic of the infinitesimal elements and the judgment of the index thereof, if the Cell contains a plurality of character strings, the Cell is of a high-order infinitesimal size; if the single character string is contained, no; then, the obtained Cell containing a plurality of character strings is divided according to the characters of the Cell, and the Cell is subjected to cyclic iteration through judgment of the characteristics of the micro-elements to obtain the Cell containing a plurality of character strings6E27(b)Each item of infinitesimal characteristic index contained in each error item element in the system is counted and superposed; thirdly, judging the index of the infinitesimal feature, and if the index of the infinitesimal feature is more than or equal to 2, discarding the item; if the exponent of the infinitesimal characteristic is less than 2, further judging whether the number of the signs is consistent with the number of the terms, if so, indicating that the first sign is a negative sign, and directly storing the signs in a one-to-one correspondence manner; if the first item is not consistent with the first item, the first item is a positive sign and is omitted, whether the first symbol is the first symbol or not is further judged, and if the first symbol is the first symbol, the number of the following items needs to be stored in the former symbol; then, the high order infinity will be dropped6E27(c)' separate terms in each error term element are taken together to give6E27(c)' a string representation of each error term element in the set; and finally, taking the character string representation form obtained by the Eval function as a Matlab solving command to carry out operation.
Based on the method, the problems of large calculated amount and high-order infinitesimal caused by relevant factors influencing the modeling precision, difficulty in accurate truncation, difficulty in guaranteeing the theoretical calculation precision and the like are effectively solved, and a space geometric error model with high-order infinitesimal truncation represented in a character string form is obtained by identifying according to the infinitesimal features, utilizing high-order infinitesimal judgment and loop iteration of truncation algorithm and combining with the statistical judgment of the infinitesimal features and indexes of the geometric error term; then carrying out Matlab solving operation through an Eval function; finally, the space geometric error model containing the parameter representation geometric error item after optimization is obtained by leading the space geometric error model into Mathtype in a Latex form6E27(c)'。
In conclusion, the five-linkage numerical control forming gear grinding machine SKMC-3000/20 is taken as an entity modeling object for illustration, and high-order-to-infinity truncation is obtainedSmall space geometric error model containing parameter quantity characterization geometric error term element6E27(c)The modeling accuracy of' is 10-8～10-10And the numerical deviation magnitude is equal to or more than the numerical deviation magnitude, wherein the numerical deviation magnitude of partial geometric error term elements completely conforms to the numerical iteration result.
An example of application of a method for verifying the modeling precision of a space geometric error model of a precision machine tool comprises two methods:
the first checking method has small calculation amount, but the generation of the random array has pseudo data and the reliability of the pseudo data needs to be improved, can be applied to the checking of the modeling precision of a space geometric error model containing parameter representation in the precision machine tool precision modeling technology, and comprises the following steps:
firstly, a one-dimensional distribution sampling mode is adopted, so that in order to avoid generating system errors of random arrays, five groups of one-dimensional random arrays are obtained by means of a Rand function, and are sequentially in one-to-one correspondence with 33 geometric errors and 5 geometric displacement quantities represented by parameters contained in a precision machine tool through unit magnitude conversion; the unit magnitude conversion is to carry out unit magnitude conversion in sequence through five groups of one-dimensional random arrays matched with the parameter-containing representation geometric error and geometric displacement term number of the precision machine tool, and convert the unit magnitude conversion into a numerical magnitude conforming to the actual working condition;
secondly, under the condition of original iterative solving times of the space geometric error model, carrying out numerical simulation analog analysis on iterative results of a numerical algorithm, b iterative algorithm and c high-order infinitesimal elimination algorithm to respectively obtain numerical real solutions6E27(a)6 error item elements in the high-order infinitesimal small error characteristic matrix are not omitted6E27(b)The numerical value of (1) is solved and 6 error item elements in a high-order infinite small error feature matrix are eliminated6E27(c)The numerical solution of'; the a numerical algorithm is obtained by directly substituting corresponding geometric errors and geometric displacement in a feature matrix through unit magnitude conversion of a random array and then iterating the values of the feature matrix6E27(a)The numerical result of (1), namely the true value obtained by the 4x4 order characteristic matrix operation containing numerical elements; the above-mentionedb, iterative algorithm, namely obtaining a characteristic matrix containing parameter representation geometric errors and geometric displacement in an iterative mode6E27(b)Containing parameter characterization relations; the c high-order infinite truncation algorithm is obtained by different solving methods based on a small error hypothesis theory and neglecting high-order infinite small6E27(c)' characterization relation containing parameter, the c algorithm comprises a method for improving the modeling precision of the space geometric error model of the precision machine tool;
if the numerical magnitude between the c high-order infinite culling algorithm and the numerical solution of the a numerical algorithm or the b iterative algorithm has a deviation of spanning magnitude, the problems of modeling precision and theoretical calculation error exist, and the modeling method needs to be further corrected; otherwise, performing the third step, wherein the numerical solutions obtained by the algorithms of the example a, b and c have no deviation of crossing magnitude, and performing the third step;
thirdly, under the iterative algorithm of b, taking the numerical algorithm of a as a benchmark to obtain 6 error item elements in the feature matrix without truncating high-order infinite small errors6E27(b)(a) Numerical simulation result of numerical deviation magnitude to verify that high-order infinite small parameter-containing representation space geometric error model is not omitted6E27(b) Wherein the b algorithm involved in the form-grinding machine is derived6E27(b) The magnitude of the numerical deviation is guaranteed to be 10-9～10-10The magnitude, even partial numerical deviation is 0, so that the subsequent theoretical error analysis can be ignored, namely the iteration result containing the parameter is proved to be accurate; meanwhile, under the c high-order infinite small-cut algorithm, 6 error item elements in a truncated high-order infinite small error characteristic matrix are obtained by taking the a numerical algorithm as the reference6E27(c)' (a) simulation result of numerical deviation magnitude, and performing analog analysis, wherein the numerical magnitude of the measured value of the instrument, the required working condition value and the actually measured process improvement value is judged, and the c algorithm related to the forming gear grinding machine is obtained6E27(c)The magnitude of the numerical deviation of' (a) is guaranteed to be 10-9～10-10The magnitude, even partial value deviation is 0, although the iteration result of the c algorithm and the a algorithm is based on the small error assumption and neglectsThe high order infinitesimal and inverse matrix solving properties lead to a certain small magnitude of numerical deviation, however, this trace amount6E27(c)' (a) numerical deviation magnitude is lower than that required by actual working conditions, so that the influence can be ignored, and the modeling precision of the selected high-order infinite small round off algorithm meets the working condition requirement;
the second verification method can improve the calculation density and improve the verification reliability, but has a problem of large calculation amount. On the basis of achieving the purpose of mutually verifying the modeling precision in different modes together with the method, theoretical calculation errors caused by the iterative solution precision of high-order infinitesimal to the modeling precision of the space geometric error model of the precise machine tool based on a small error hypothesis theory are separated; the numerical deviation magnitude corresponding to different processing methods in iterative solution of the feature matrix is quantized, the method can be applied to the calibration of the modeling precision of a spatial geometric error model containing parametric representation in precision and ultra-precision machine tool precision modeling technologies, and comprises the following steps:
step one, adopting a multi-dimensional distribution sampling mode, taking 33 geometric errors and 5 geometric displacement quantities which are related to parameter-containing representation of a forming gear grinding machine SKMC-3000/20 as dimensions to improve the calculation density, selecting a group of one-dimensional random arrays, performing unit magnitude conversion on the one-dimensional random arrays, sequentially corresponding to the geometric errors and the geometric displacement quantities which are related to a precision machine tool, and simultaneously storing the one-dimensional random arrays by means of a Zeros function; the unit magnitude conversion is to perform unit magnitude conversion in sequence through a one-dimensional random array matched with the parameter-containing representation geometric error and geometric displacement term number of the precision machine tool, and convert the unit magnitude conversion into a numerical magnitude in accordance with the actual working condition;
second step, at 316In the high-dimensional space grid sampling of the cycle iteration times, firstly, for an a numerical algorithm and a b iterative algorithm, obtaining6E27(a,b)The change rule between the numerical value field and the maximum magnitude thereof; then, for c high-order infinite small round off algorithm, obtaining6E27(c)' rule of variation between numerical field and its most significant magnitude, where the a, b algorithms yield6E27(a,b)And c algorithmTo6E27(c)' although the numerical field, the most significant magnitude and the corresponding iteration number of each error term element have slight deviation, the a and b algorithms are iterated to obtain6E27(a,b)And c algorithm get6E27(c)The numerical magnitude is ensured to be at the same numerical magnitude, the numerical fields are relatively close, and the most-valued magnitude and the corresponding iteration times are relatively consistent; finally, the a numerical algorithm is taken as a reference, and under the b iterative algorithm, the method is obtained6E27(b)(a) The numerical value domain, the most value magnitude and the numerical value deviation existing in the corresponding iteration times are obtained by judging the numerical value deviation magnitude,6E27(b)(a) the maximum deviation magnitude of the 6 error term elements is 10-9～10-13Minimum deviation of the order of 10-9～10-10If so, the model indicates that the high-order infinite small parameter-containing quantity characterization space geometric error model is not truncated6E27(b)Is accurate to perform the third step; the a numerical algorithm is obtained by directly substituting corresponding geometric errors and geometric displacement in a feature matrix through unit magnitude conversion of a random array and then iterating the values of the feature matrix6E27(a)The numerical result of (1), namely the true value obtained by the 4x4 order feature matrix operation containing numerical elements; the b iterative algorithm is to obtain a characteristic matrix containing parameter representation geometric errors and geometric displacement in an iterative mode6E27(b)Containing parameter characterization relations; the c high-order infinite truncation algorithm is obtained by different solving methods based on a small error hypothesis theory and neglecting high-order infinite small6E27(c)' characterization relation containing parameter;
thirdly, under the c high-order infinite small round elimination method, the a numerical algorithm is taken as a reference to obtain6E27(c)' (a) the numerical deviation of the numerical field, the most significant magnitude and the corresponding iteration number is compared and analyzed with the numerical magnitude of the measured value, the required working condition value and the actual process improvement value of the instrument to judge the accuracy of the modeling precision, wherein under the c algorithm,6E27(c)' the maximum deviation obtained by 6 error term elements in the method is 10-8～10-13Minimum deviation of the order of 10-8～10-9(ii) a The c algorithm is based on a small error hypothesis, neglects a removing algorithm of high-order infinitesimal polynomial and containing a denominator, and simultaneously carries out engineering approximate solution on the characteristic matrix through the property of an inverse matrix to obtain a numerical solution of the characteristic matrix, so that the numerical magnitude deviation exists; finally, the algorithm a and the algorithm b are used as the reference in sequence, and under the algorithm b and the algorithm a, the method is obtained6E27(b)(a)、.6E27(a)(b) Mean values of the numerical deviations in the range of the numerical domain and their standard deviations; under the c algorithm, obtain6E27(c)'(a)、6E27(c)' (b) means of numerical deviation and their standard deviation in the numerical range, wherein, in the b, a algorithm,6E27(b)(a)、6E27(a)(b) the average value of the numerical deviation of the iteration result and the standard deviation thereof are both guaranteed to be 10-10～10-11Magnitude of the value; under the c-algorithm, the method comprises the following steps of,6E27(c)'(a)、6E27(c)' (b) the mean value of the numerical deviations of the iteration results and their standard deviation are guaranteed to be at 10-9～10-10The numerical magnitude is used for realizing the quantitative separation and selective use of theoretical calculation errors existing in different processing links and achieving the verification of the submicron and even nanometer magnitude theoretical modeling precision.
In summary, it can be obtained from the statistical and numerical simulation perspectives according to6E27(a,b)And6E27(c)the numerical field, the magnitude deviation of the maximum numerical value, the average value of the numerical deviation in the numerical field range and the standard deviation thereof prove that the second method is more stable and reliable than the first method in verification, and the method for improving the modeling precision of the space geometric error model of the precision machine tool is verified, so that the method is feasible and has higher modeling precision. The second verification method can improve the calculation density and improve the verification reliability, but has the problem of large calculation amount, so that the corresponding verification method can be selected or the complementary verification can be performed through the use condition.
In addition, the method can be expanded and applied to algorithm c for rounding off high-order infinitesimal small by checking different high-order1…cnDisclosure of the inventionThe numerical deviation of the theoretical modeling precision of the spatial geometric error model can be expanded and applied to the precision modeling technology of the ultra-precise multi-axis linkage machine tool, and the precision of the numerical control machine tool can be effectively improved from the aspects of statistics and numerical simulation, so that the checking method has good market application prospect and popularization value.
Claims (2)
1. A method for verifying the modeling precision of a space geometric error model of a precision machine tool is characterized by comprising the following steps:
firstly, selecting at least five groups of one-dimensional random arrays by adopting a one-dimensional distribution sampling mode, and sequentially corresponding to geometric errors and geometric displacement related to a precision machine tool through unit magnitude conversion; the unit magnitude conversion is to carry out unit magnitude conversion in sequence through five groups of one-dimensional random arrays matched with the parameter-containing representation geometric error and geometric displacement term number of the precision machine tool, and convert the unit magnitude conversion into a numerical magnitude conforming to the actual working condition;
secondly, under the condition of the original iteration solving times of the space geometric error model, carrying out numerical simulation analog analysis on the iteration results of the a numerical algorithm, the b iterative algorithm and the c high-order infinitesimal elimination algorithm to respectively obtain numerical real solutions6Eij(a)6 error item elements in the high-order infinitesimal small error characteristic matrix are not omitted6Eij(b)The numerical value of (1) is solved and 6 error item elements in a high-order infinite small error feature matrix are eliminated6Eij(c)The numerical solution of'; the a numerical algorithm is obtained by directly substituting corresponding geometric errors and geometric displacement in a feature matrix through unit magnitude conversion of a random array and then iterating the values of the feature matrix6Eij(a)The numerical result of (1), namely the true value obtained by the 4x4 order characteristic matrix operation containing numerical elements; the b iterative algorithm is to obtain a characteristic matrix containing parameter representation geometric errors and geometric displacement in an iterative mode6Eij(b)Containing parameter characterization relations; the c high-order infinite truncation algorithm is based on a small error hypothesis theory, ignores high-order infinite small and solves the problem through different solving methodsTo obtain6Eij(c)' characterization relation containing parameter, said c higher order infinity truncation algorithm comprises different truncation higher order infinity algorithms c1…cn；
If the numerical magnitude between the c high-order infinite culling algorithm and the numerical solution of the a numerical algorithm or the b iterative algorithm has a deviation of spanning magnitude, the problems of modeling precision and theoretical calculation error exist, and the modeling method needs to be further corrected; otherwise, carrying out the third step;
thirdly, under the iterative algorithm of b, taking the numerical algorithm of a as a benchmark to obtain 6 error item elements in the feature matrix without truncating high-order infinite small errors6Eij(b)(a) Numerical simulation results of numerical deviation magnitude to verify that high-order infinite parametric-containing representation space geometric error model is not truncated6Eij(b)The accuracy of (2); meanwhile, under the c high-order infinite small-cut algorithm, 6 error item elements in a truncated high-order infinite small error characteristic matrix are obtained by taking the a numerical algorithm as the reference6Eij(c)' (a) simulation results of numerical deviation magnitude, and analog analysis is carried out, and if the numerical magnitude is in the same level or lower than the numerical magnitude, the modeling precision of the selected c high-order infinite-small-cut algorithm meets the requirement of the working condition by judging the numerical magnitude of the measured value of the instrument, the required value of the working condition and the actually measured value of the process improvement;
wherein, the geometric error is characterized by reference variable, including relative rotation angle error deltaijRelative displacement error epsilonijWherein i is a linear motion shaft related to the precision machine tool, and j is the linear motion shaft and a rotating shaft related to the machine tool; the parameter-containing quantity represents the geometric displacement, including displacement x, y and z of X, Y, Z linear guide rail shaft and rotation quantity alpha, beta and gamma of A, B, C shaft rotating along X, Y, Z shaft; the characteristic error feature matrix containing parameter quantity, i.e. the transformation matrix of the tool coordinate system and the workpiece coordinate system containing geometric error terms, includes the error feature matrix E without high order infinitesimal truncationijEliminating the error characteristic matrix E with infinitesimal high orderij', setting an error characteristic matrix EijComprises the following steps:
in the formula etax,ηy,ηz,Px,Py,PzThe relative position error and the relative rotation angle error of the tool coordinate system and the workpiece coordinate system along the motion direction of the axis X, Y, Z of the precision machine tool after the characteristic matrix iteration are respectively obtained; the method comprises the steps of characterizing 6 error item elements in an error feature matrix by parameters, and recording 6 error item elements in the error feature matrix without truncation of high-order infinitesimal small errors6Eij(b)And satisfy
The 6 error term elements in the high-order infinite small error characteristic matrix are cut off and recorded as6Eij(c)', and satisfy
Wherein6Eij(a,b)Comprises6Eij(a)、6Eij(b)。
2. A method for verifying the modeling precision of a space geometric error model of a precision machine tool is characterized by comprising the following steps:
step one, adopting a multi-dimensional distribution sampling mode, taking parameter-containing characterization geometric errors and geometric displacement related to a precision machine tool as dimensions, selecting a group of one-dimensional random arrays, and sequentially corresponding to the geometric errors and the geometric displacement related to the precision machine tool through unit magnitude conversion; the unit magnitude conversion is to perform unit magnitude conversion in sequence through a one-dimensional random array matched with the parameter-containing representation geometric error and geometric displacement term number of the precision machine tool, and convert the unit magnitude conversion into a numerical magnitude in accordance with the actual working condition;
secondly, under the condition of the iteration times matched with the memory of the computer, firstly, for the a numerical algorithm and the b iterative algorithm, obtaining6Eij(a,b)The change rule between the numerical value field and the maximum magnitude thereof; then, forc high-order infinite small round off algorithm to obtain6Eij(c)The change rule between the numerical value domain and the maximum magnitude thereof; finally, the a numerical algorithm is taken as a reference, and under the b iterative algorithm, the method is obtained6Eij(b)(a) The numerical value domain, the most value magnitude and the numerical value deviation of the iteration times corresponding to the most value magnitude are judged, if the deviation of the numerical value deviation magnitude is over the magnitude from the iteration result of the a numerical value algorithm, the space geometric error model represented by the parameter-containing quantity has the problems of modeling precision and theoretical calculation error, the modeling method needs to be further corrected, otherwise, the higher-order infinite small space geometric error model represented by the parameter-containing quantity is not omitted6Eij(b)Is accurate to perform the third step; the a numerical algorithm is obtained by directly substituting corresponding geometric errors and geometric displacement in a feature matrix through unit magnitude conversion of a random array and then iterating the values of the feature matrix6Eij(a)The numerical result of (1), namely the true value obtained by the 4x4 order feature matrix operation containing numerical elements; the b iterative algorithm is to obtain a characteristic matrix containing parameter representation geometric errors and geometric displacement in an iterative mode6Eij(b)Containing parameter characterization relations; the c high-order infinite truncation algorithm is obtained by different solving methods based on a small error hypothesis theory and neglecting high-order infinite small6Eij(c)' characterization relation containing parameter;
thirdly, under the c high-order infinite small round elimination method, the a numerical algorithm is taken as a reference to obtain6Eij(c)' (a) numerical value domain, the most value magnitude and the numerical value deviation of the corresponding iteration times are judged, and if the numerical value magnitude is in the same level or lower than the numerical value magnitude, the modeling precision of the selected high-order infinite-small-cut algorithm meets the requirement of the working condition; finally, the algorithm a and the algorithm b are used as the reference in sequence, and under the algorithm b and the algorithm a, the method is obtained6Eij(b)(a)、6Eij(a)(b) The mean value of the numerical deviation in the range of the numerical field and the standard deviation thereof; under the c algorithm, obtain6Eij(c)'(a)、6Eij(c)' (b) numerical value rangeThe mean value of the numerical deviation in the enclosure and the standard deviation thereof are used for quantitatively separating and selectively using theoretical calculation errors existing in different processing links;
wherein, the geometric error is characterized by reference variable, including relative rotation angle error deltaijRelative displacement error epsilonijWherein i is a linear motion shaft related to the precision machine tool, and j is the linear motion shaft and a rotating shaft related to the machine tool; the parameter-containing quantity represents the geometric displacement, including displacement x, y and z of X, Y, Z linear guide rail shaft and rotation quantity alpha, beta and gamma of A, B, C shaft rotating along X, Y, Z shaft; the characteristic error feature matrix containing parameter quantity, i.e. the transformation matrix of the tool coordinate system and the workpiece coordinate system containing geometric error terms, includes the error feature matrix E without high order infinitesimal truncationijEliminating the error characteristic matrix E with infinitesimal high orderij', setting an error characteristic matrix EijComprises the following steps:
in the formula etax,ηy,ηz,Px,Py,PzThe relative position error and the relative rotation angle error of the tool coordinate system and the workpiece coordinate system along the motion direction of the axis X, Y, Z of the precision machine tool after the characteristic matrix iteration are respectively obtained; the method comprises the steps of characterizing 6 error item elements in an error feature matrix by parameters, and recording 6 error item elements in the error feature matrix without truncation of high-order infinitesimal small errors6Eij(b)And satisfy
The 6 error term elements in the high-order infinite small error characteristic matrix are cut off and recorded as6Eij(c)', and satisfy
Wherein6Eij(a,b)Comprises6Eij(a)、6Eij(b)。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910790030.XA CN110489901B (en) | 2019-08-26 | 2019-08-26 | Method for verifying modeling precision of space geometric error model of precision machine tool |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910790030.XA CN110489901B (en) | 2019-08-26 | 2019-08-26 | Method for verifying modeling precision of space geometric error model of precision machine tool |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110489901A CN110489901A (en) | 2019-11-22 |
| CN110489901B true CN110489901B (en) | 2021-02-19 |
Family
ID=68554075
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910790030.XA Active CN110489901B (en) | 2019-08-26 | 2019-08-26 | Method for verifying modeling precision of space geometric error model of precision machine tool |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110489901B (en) |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102699761B (en) * | 2012-06-27 | 2014-09-03 | 电子科技大学 | Error identification method of five-axis numerically controlled machine tool based on S-shaped test specimen |
| US9836563B2 (en) * | 2013-09-26 | 2017-12-05 | Synopsys, Inc. | Iterative simulation with DFT and non-DFT |
| CN104156519A (en) * | 2014-07-30 | 2014-11-19 | 北京工业大学 | Method for designing geometric accuracy of multi-axis numerical control machine tool to improve processing accuracy and reliability |
-
2019
- 2019-08-26 CN CN201910790030.XA patent/CN110489901B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN110489901A (en) | 2019-11-22 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111274671B (en) | Precise repair method for complex product assembly process based on digital twin and operation system thereof | |
| CN104375460B (en) | A kind of Digit Control Machine Tool machining accuracy reliability sensitivity analysis method | |
| CN104007700B (en) | A kind of key geometric error discrimination method of three axis numerically controlled machine based on overall situation sensitivity analysis | |
| Eldred et al. | Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification | |
| Dantan et al. | Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation | |
| CN114237155B (en) | Error prediction and compensation method, system and medium for multi-axis numerical control machining | |
| CN104050316B (en) | Analysis method on basis of distribution characteristics of space machining error of numerical control machine tool | |
| CN103390082B (en) | The sane excellent method of completing the square of a kind of gang tool geometric accuracy | |
| US20020135577A1 (en) | Storage method of substantial data integrating shape and physical properties | |
| CN109241601B (en) | Numerical control machine tool comprehensive performance evaluation method based on improved pulling-out grade method | |
| CN103135446B (en) | Motion trail authentication device of multiaxis numerical control machine tool | |
| CN112733296A (en) | GRNN-based milling error prediction and compensation method for hybrid robot | |
| CN110532667B (en) | Method for improving precision of modeling of space geometric error model of precision machine tool | |
| CN103791878A (en) | Numerically-controlled machine tool geometric accuracy identification method | |
| CN103020399A (en) | Modular machine tool design method | |
| CN112149324A (en) | Rapid modeling method for simulation verification of composite material tool compensation molded surface | |
| CN117556345B (en) | Magnetorheological polishing removal function prediction device and method based on neural network | |
| CN116560301A (en) | Machine tool feeding system mathematical model parameter identification method based on gradient optimization | |
| CN110489901B (en) | Method for verifying modeling precision of space geometric error model of precision machine tool | |
| Naumann et al. | Comparison of basis functions for thermal error compensation based on regression analysis–a simulation based case study | |
| CN114970028A (en) | Digital twin driven research and development method and system for manufacturing equipment | |
| Gorski et al. | Selection of Fused Deposition Modeling Process Parameters using Finite Element Analysis and Genetic Algorithms. | |
| CN116974241B (en) | Geometric optimization method and device for numerical control machine tool for green low-carbon manufacturing | |
| Li et al. | A reconstructed variable regression method for thermal error modeling of machine tools | |
| CN110569539B (en) | Virtual model construction method with geometric error based on actual measurement point cloud fractal fusion |
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 |