CN107368637A - Precise horizontal machining center geometric accuracy optimizing distribution method based on interval theory - Google Patents
Precise horizontal machining center geometric accuracy optimizing distribution method based on interval theory Download PDFInfo
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Abstract
The invention discloses a kind of precise horizontal machining center geometric accuracy optimizing distribution method based on interval theory, it comprises the following steps：(1) it is theoretical based on Multibody Kinematics, the mapping model established between each geometric error of lathe and lathe space error；(2) interval theory is based on, carries out carrying out sensitivity analysis to each error source；(3) interval theory is based on, establishes range optimization distribution model；(4) genetic algorithm is based on, is solved with MATLAB softwares so as to realize geometric accuracy optimization distribution.The error source that the present invention makes to be difficult to realize is relaxed to the feasible section of maximum, greatly reduces production cost, improves lathe production efficiency of assembling.
Description
Technical field
The present invention relates to Digit Control Machine Tool geometric accuracy optimization distribution field, especially a kind of precision based on interval theory crouches
Formula machining center geometric accuracy optimizing distribution method.
Background technology
Precise numerical control machine is the machine-tool of basic manufacturing equipment, and its design directly affects manufacturing with working ability
Development.The quality of high-grade, digitally controlled machine tools quality, the accuracy of manufacture and assembly precision of lathe are directly shown, and machine tool accuracy designs
With the quality of precision distribution, there is significant impact to its quality.
For machine tool accuracy assignment problem, domestic and foreign scholars carried out it is relatively broad and deep probe into, achieve certain
Progress.Mainly have component tolerances weight European norm maximum method, Monte Carlo Method, dimension chain method, based on tolerance-cost
The methods of precision distribution method of model, these methods are directed to parallel institution mostly, and can not directly instruct high-grade numerical control machine
The manufacture assembling process of bed.At present, domestic Machine Tool Enterprises lead to when carrying out precise numerical control machine accuracy Design and precision distribution
Frequently with the method for traditional analogy, the inquiry of lathe handbook and designer's estimation, do not tackle the problem at its root, design
Lathe can too rely on the experience of designer unavoidably, can not be formed it is scientific, theorize, the design method of systematization.
The space error of precise numerical control machine point to be cut to point of a knife point directly reflects the machining accuracy of lathe, and space
Error is by caused by each kinematic pair geometric error coupling.Therefore, how on the premise of complete machine space error is met,
Rationally, it is economical and the problem of rapidly optimization distribution geometric error is current precise numerical control machine assembling manufacturing urgent need to resolve.
The content of the invention
A kind of precision horizontal processing based on interval theory is provided it is an object of the invention to solve above-mentioned technical problem
Center geometric accuracy optimizing distribution method, its error source that can make to be difficult to realize are relaxed to the feasible section of maximum.
In order to solve the above-mentioned technical problem, the present invention adopts the following technical scheme that：
A kind of precise horizontal machining center geometric accuracy optimizing distribution method based on interval theory, comprises the following steps：
Step (1)：Digit Control Machine Tool is regarded as to the multi-body system being in series by multiple rigid bodies first；Secondly many body system is used
System kinematical theory describes the topological relation on Digit Control Machine Tool between each moving component；Reuse homogeneous coordinate transformation matrix phase
Multiply the pose transformational relation between adjacent component disjunctor coordinate system on expression Digit Control Machine Tool；Finally set up each geometry of Digit Control Machine Tool
Mapping model between error and lathe space error；
Step (2)：Based on interval theory, sensitivity is defined according to the interval extension factor, line sensitivity of going forward side by side is analyzed with anti-
Reflect influence degree of each error source to complete machine space error；
Step (3)：Using each error source interval width as design variable, complete machine space body diagonal error be constraints,
Each error source sensitivity coefficient and the algebraical sum of interval width inverse square product are object function, establish range optimization distribution mould
Type；
Step (4)：Based on genetic algorithm, solved with MATLAB softwares so as to realize geometric accuracy optimization distribution.
The beneficial effects of the invention are as follows：The present invention proposes the geometry based on interval theory for precise horizontal machining center
Precision optimizing distribution method, the complete machine space error that lathe geometric error is established based on Multibody Kinematics theory map mould
Type, sensitivity analysis is carried out based on interval theory and establishes range optimization distribution model, be finally based on genetic algorithm utilization
MATLAB softwares distribute to solve so as to realize that geometric accuracy optimizes, and the error source for making to be difficult to realize is relaxed to the feasible region of maximum
Between, production cost is greatly reduced, improves lathe production efficiency of assembling.
Brief description of the drawings
Fig. 1 is the flow of the precise horizontal machining center geometric accuracy optimizing distribution method of the invention based on interval theory
Figure；
Fig. 2 is u2000/800H precise horizontal machining center three-dimensional model diagrams；
Fig. 3 is principle of genetic algorithm figure；
Fig. 4 is each geometric error source precision optimizing allocation result.
Wherein, 1- lathe beds 2-X is to slide unit 3-B to turntable 4- workpiece 5- column 6- main spindle box 7- main shaft 8- cutters.
Embodiment
The present invention is further detailed explanation with reference to the accompanying drawings and examples：
As shown in figure 1, the precise horizontal machining center geometric accuracy optimization distribution provided by the invention based on interval theory
Method, comprise the following steps：
(1) mapping model established between each geometric error of lathe and lathe space error；
The geometric error of Digit Control Machine Tool, according to whether it is related to machine tool motion position, position correlation geometric error can be divided into
And position independence geometric error (PIGEs) (PDGEs).The present invention is by taking u2000/800H precise horizontal machining centers as an example, model
As shown in Fig. 2 being illustrated to the method for the present invention, above-mentioned machining center is common in the case where only considering translation shaft geometric error
There are 21 geometric errors：9 site errors related to three axis coordinate positions and 9 angular errors, and position are independent
Three axis between 3 error of perpendicularitys, 18 position correlation geometric errors, 3 position independence geometric errors altogether, such as
Shown in table 1.
21 geometric errors of the Digit Control Machine Tool of table 1
| Reference axis | PDGEs | PIGEs |
| X-axis | δx(x),δy(x),δz(x),εx(x),εy(x),εz(x) | -- |
| Y-axis | δx(y),δy(y),δz(y),εx(y),εy(y),εz(y) | εxy |
| Z axis | δx(z),δy(z),δz(z),εx(z),εy(z),εz(z) | εxz,εyz |
δ in tablex、δy、δzSite error is represented, subscript represents the direction of error；εx、εy、εzRepresent angular errors, inferior horn
Mark represents the direction of angular errors rotation axis；X, y, z in bracket represents the direction of motion of X, Y, Z axis.εxy、εyz、εzxRespectively
The error of perpendicularity between denotation coordination axle X and Y, Y and Z, X and Z." -- " represents no error.
Digit Control Machine Tool is a kind of multi-body system being in series by multiple rigid bodies, and theory of multi body system can be used to describe number
The topological relation between each moving component on lathe is controlled, adjacent component on Digit Control Machine Tool is represented with homogeneous coordinate transformation matrix multiple
Pose transformational relation between disjunctor coordinate system, so as to set up 21 geometric errors of Digit Control Machine Tool and lathe end position and attitude error
Between mapping model (hereinafter referred to as machine tool error model).
Preferable static, the motion spy of adjacent body is obtained according to the topological structure of Fig. 2 u2000/800H horizontal Machining centers
Matrix and preferable static, kinematic error eigenmatrix are levied, as shown in table 2.
The preferable static, kinematic matrix of the adjacent body of table 2 and preferable static, kinematic error matrix
T in tableijp、ΔTijp、Tijs、ΔTijsPreferable static feature matrix, the ideal movements feature of adjacent body are represented respectively
Matrix, preferable Quiet Error eigenmatrix, ideal movements error character matrix；X, y, z represents machine tool motion coordinate respectively；xijp、
yijp、zijpMachine tool structure parameter is represented respectively；I4×4Represent quadravalence unit matrix；I, j=1,2,3 ..., 8；1 represents lathe bed, 2 tables
Show X to slide unit, 3 represent B to turntable, and 4 represent workpiece, and 5 represent column, and 6 represent main spindle box, and 7 represent main shaft, and 8 represent cutter.
If homogeneous coordinates value P of the point of a knife point under main shaft coordinate systemtFor：
Pt=[0 0 t 1]T
T represents tool length in formula.
If homogeneous coordinates value P of the point to be processed under workpiece coordinate system on workpiecewFor：
Pw=[xw yw zw 1]T
xw,yw,zwRepresent coordinate value of the point to be processed under workpiece coordinate system on workpiece.
Homogeneous coordinates value P of the point of a knife point under preferable lathe bed coordinate systemt-idealFor：
Pt-ideal=T04pT04sT45pT45sT56pT67pPt
Homogeneous coordinates value P of the point to be processed under preferable lathe bed coordinate system on workpiecew-idealFor：
Pw-ideal=T01pT01sT12pT12sT23pPw
Under ideal conditions, point to be processed is to overlap on point of a knife point and workpiece, then has：
Pt-ideal=Pw-ideal
Homogeneous coordinates value P of the point of a knife point under actual lathe bed coordinate systemt-actualFor：
Pt-actual=T04pΔT04pT04sΔT04sT45pΔT45pT45sΔT45sT56pΔT56pT67pΔT67pPt
Homogeneous coordinates value P of the point to be processed under preferable lathe bed coordinate system on workpiecew-actualFor：
Pw-actual=T01pΔT01pT01sΔT01sT12pΔT12pT12sΔT12sT23pΔT23pPw
Space error is：
In formula：A、Respectively geometric error mapping matrix and geometric error vector.
By the geometric error of the related geometric error of above-mentioned lathe geometric error model opsition dependent and position independence write as
Lower form：
In formulaRepresentation space error；AD、AIThe respectively related geometric error mapping matrix in position and position independence
Geometric error mapping matrix；εD、εIThe respectively geometric error vector of the related geometric error vector sum position independence in position.
(2) interval theory is based on, carries out carrying out sensitivity analysis to each error source；
Interval number is defined as：
Superscript I expressions interval number, the superscript I implications occurred below are identical in formula；The upper and lower of section is represented respectively
Limit.
By geometric error spatial model section：
Superscript T represents transposition in formula.
Interval extension factor ηi,jIt is defined as：
λ is used to describe the positive and negative of the interval extension factor in formula；The section of i-th of space error component is represented respectively
Bound；Represent the section bound of j-th of geometric error component of a vector；Ai,jRepresent the of geometric error mapping matrix
I rows, the element of jth row.
Sensitivity definition is：
For site error source, sensitivity definition：
For angular error source, due to the influence of Abbe error, sensitivity definition：
In formulaRepresent sensitivity when lathe is located at coordinate and tool length is；Represent lathe positioned at seat
The interval extension factor of mark and tool length when being；Represent that lathe is located at the area when origin of coordinates and tool length are zero
Between broadening factor.
(3) interval theory is based on, establishes range optimization distribution model：
It is about by design variable, complete machine space body diagonal error and each error source border of each error source interval width
Beam condition, each error source sensitivity coefficient and the algebraical sum of interval width inverse square product are object function, and it is excellent to establish section
Change distribution model.
Min represents to minimize in formula；F represents object function；XIRepresent the set of interval variable；N represents interval variable
Sum；μiRepresent the sensitivity of i-th of interval variable；W represents interval width；Represent i-th of interval variable；
Δ x, Δ y, Δ z represent X, Y, the space error of Z-direction respectively；[xI] represent interval variable constraint section.
(4) genetic algorithm (GA) is based on, is solved with the GAs Toolbox of MATLAB softwares so as to realize geometry
Precision optimizing distributes；
Based on genetic algorithm, schematic diagram is as shown in figure 3, the genetic algorithm instrument of the MATLAB softwares with R2014a versions
Case, genetic parameter use default value, carry out emulation solution, and operation result is as shown in figure 4, the optimization distribution of each error source geometric accuracy
As a result it is as shown in table 3.
Each error source geometric accuracy optimization allocation result of table 3
| Error source | δx(x) | δx(x) | δx(x) | δx(x) | δx(x) | δx(x) | δx(x) | δx(x) | δx(x) |
| Empirical value/um | 6 | 5 | 5 | 6 | 5 | 5 | 6 | 5 | 5 |
| Optimal value/urad | 8.9 | 7.4 | 7.4 | 8.9 | 7.4 | 7.4 | 8.9 | 7.4 | 7.4 |
| Relax/% | 48.3 | 48 | 48 | 48.3 | 48 | 48 | 48.3 | 48 | 48 |
| Error source | εx(x) | εx(x) | εx(x) | εx(x) | εx(x) | εx(x) | εx(x) | εx(x) | εx(x) |
| Empirical value/um | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |
| Optimal value/urad | 11.5 | 12 | 11.7 | 11.9 | 10.7 | 9.5 | 11.2 | 11 | 11.9 |
| Relax/% | 43.8 | 50 | 46.3 | 48.8 | 33.8 | 18.8 | 40 | 37.5 | 48.8 |
| Error source | εxy | εxy | εxy | ||||||
| Empirical value/um | 10 | 10 | 10 | ||||||
| Optimal value/urad | 14.9 | 11.1 | 12.8 | ||||||
| Relax/% | 49 | 11 | 28 | ||||||
Although the preferred embodiments of the present invention are described above in conjunction with accompanying drawing, the invention is not limited in upper
The embodiment stated, above-mentioned embodiment is only schematical, be not it is restricted, this area it is common
Technical staff in the case of present inventive concept and scope of the claimed protection is not departed from, may be used also under the enlightenment of the present invention
By make it is many in the form of, these are belonged within protection scope of the present invention.
Claims (1)
- A kind of 1. precise horizontal machining center geometric accuracy optimizing distribution method based on interval theory, it is characterised in that including Following steps：Step (1)：Digit Control Machine Tool is regarded as to the multi-body system being in series by multiple rigid bodies first；Secondly transported using multi-body system Dynamic theory describes the topological relation between each moving component on Digit Control Machine Tool；Reuse homogeneous coordinate transformation matrix multiple table Show the pose transformational relation between adjacent component disjunctor coordinate system on Digit Control Machine Tool；Finally set up each geometric error of Digit Control Machine Tool With the mapping model between lathe space error；Step (2)：Based on interval theory, sensitivity is defined according to the interval extension factor, line sensitivity of going forward side by side analysis is each to reflect Influence degree of the error source to complete machine space error；Step (3)：It is constraints, respectively misses by design variable, complete machine space body diagonal error of each error source interval width Poor source sensitivity coefficient and the algebraical sum of interval width inverse square product are object function, establish range optimization distribution model；Step (4)：Based on genetic algorithm, solved with MATLAB softwares so as to realize geometric accuracy optimization distribution.
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Cited By (7)
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| CN108052747A (en) * | 2017-12-17 | 2018-05-18 | 北京工业大学 | A kind of geometric precision of machine tool optimization method based on Method of valuo analysis |
| CN108873810A (en) * | 2018-07-12 | 2018-11-23 | 沈阳机床股份有限公司 | A kind of critical error source discrimination influencing the decay of three axis machining center precision |
| CN108920773A (en) * | 2018-06-08 | 2018-11-30 | 华中科技大学 | A kind of the ultraprecise kinematic system detailed protocol design method and system of kinetics-driven |
| CN110666590A (en) * | 2019-09-12 | 2020-01-10 | 天津大学 | Machine tool body diagonal error measuring method based on multi-beam laser interferometer |
| CN112558547A (en) * | 2021-02-19 | 2021-03-26 | 成都飞机工业（集团）有限责任公司 | Quick optimization method for geometric error compensation data of translational shaft of five-axis numerical control machine tool |
| CN115638754A (en) * | 2022-10-03 | 2023-01-24 | 北京工业大学 | Three-coordinate measuring machine precision distribution method based on inter-zone analytic method |
| CN117032072A (en) * | 2023-08-28 | 2023-11-10 | 哈尔滨工业大学 | Geometric error distribution method for five-axis ultra-precision machine tool |
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| CN108052747A (en) * | 2017-12-17 | 2018-05-18 | 北京工业大学 | A kind of geometric precision of machine tool optimization method based on Method of valuo analysis |
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| CN108873810A (en) * | 2018-07-12 | 2018-11-23 | 沈阳机床股份有限公司 | A kind of critical error source discrimination influencing the decay of three axis machining center precision |
| CN108873810B (en) * | 2018-07-12 | 2021-03-12 | 沈阳机床股份有限公司 | Key error source identification method influencing precision decay of triaxial machining center |
| CN110666590A (en) * | 2019-09-12 | 2020-01-10 | 天津大学 | Machine tool body diagonal error measuring method based on multi-beam laser interferometer |
| CN112558547A (en) * | 2021-02-19 | 2021-03-26 | 成都飞机工业（集团）有限责任公司 | Quick optimization method for geometric error compensation data of translational shaft of five-axis numerical control machine tool |
| CN112558547B (en) * | 2021-02-19 | 2021-06-08 | 成都飞机工业（集团）有限责任公司 | Quick optimization method for geometric error compensation data of translational shaft of five-axis numerical control machine tool |
| CN115638754A (en) * | 2022-10-03 | 2023-01-24 | 北京工业大学 | Three-coordinate measuring machine precision distribution method based on inter-zone analytic method |
| CN115638754B (en) * | 2022-10-03 | 2024-03-15 | 北京工业大学 | Three-coordinate measuring machine precision distribution method based on interval analytic hierarchy process |
| CN117032072A (en) * | 2023-08-28 | 2023-11-10 | 哈尔滨工业大学 | Geometric error distribution method for five-axis ultra-precision machine tool |
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