CN106125673B - Based on the approximate profile errors real-time estimation method of space circular arc - Google Patents
Based on the approximate profile errors real-time estimation method of space circular arc Download PDFInfo
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- CN106125673B CN106125673B CN201610625829.XA CN201610625829A CN106125673B CN 106125673 B CN106125673 B CN 106125673B CN 201610625829 A CN201610625829 A CN 201610625829A CN 106125673 B CN106125673 B CN 106125673B
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
- G05B19/4103—Digital interpolation
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/34—Director, elements to supervisory
- G05B2219/34096—Approximate, replace curve, surface with circle, linear segments, least error
Abstract
The present invention is based on the approximate profile errors real-time estimation methods of space circular arc to belong to precise high-efficiency Computerized Numerical Control processing technology field, is related to being based on the approximate profile errors real-time estimation method of space circular arc in a kind of spline curve Interpolation Process.This method, based on the initial parameter values that Newton iteration is used on first order Taylor Series Expansion Method calculating parameter curve, recycles Newton iteration method before every step Newton iterative calculation intersection point point, and single step iteration parameter final value is calculated according to initial parameter values.To avoid that the algorithm calculating time is significantly increased, according to iteration ends precision conditions and maximum iteration condition double constraints end loop, intersection point point estimates of parameters is obtained, calculates profile errors vector estimated value.This method still can effectively ensure that the estimated accuracy of profile errors when following error is larger, have great Practical significance to improving high-grade, digitally controlled machine tools spline curve interpolation machining profile precision.
Description
Technical field
The invention belongs to precise high-efficiency Computerized Numerical Control processing technology fields, are related to being based in a kind of spline curve interpolation process
The approximate profile errors real-time estimation method of space circular arc.
Background technology
With the fast development of high-end equipment field, the Technology of High-speed Numerical-control Manufacturing application of complex curved surface parts is increasingly
Extensively.In view of complex curved surface parts processing knife rail is mostly the curve with complex geometry feature, using traditional straight line, circular interpolation
During digital control processing, due to the presence of single order discontinuity point when straight line, arc section approach ideal curve, NC Machining Process can be caused
The frequent acceleration and deceleration of middle feed shaft, influence processing quality and processing efficiency.Parametric spline curve direct interpolation technology can overcome biography
The defects of system straight line, circular interpolation processing, therefore obtained extensive research.However, during parameter curve direct interpolation, by
In reasons such as hysteresis characteristic and the dynamic property mismatches of each feed shaft servo-control system, larger machining locus wheel can be caused
Wide error, and the error increases with the increase of feed speed, so as to reduce the machining accuracy of complex curved surface parts.For solution
Certainly this problem, domestic and foreign scholars propose a series of advanced control algolithms, and cross-coupling control is Typical Representative therein.
Cross-coupling controller is mainly made of profile errors algorithm for estimating and control law, and therefore, high-precision profile errors estimation is
It ensures cross-coupling controller performance and then improves the premise of digital control system Contour extraction precision.To sum up, research Parameter Spline is bent
High-efficiency and precision numerical control of the real-time high-precision method of estimation of profile errors to realization complex curved surface parts in line interpolation process
Processing is of great significance.
Document " A Novel Contour Error Estimation for Position Loop-Based Cross-
Coupled Control ", Yang etc., IEEE/ASME Transactions on Mechatronics, 2011,16 (4)：
643-655, the document proposes one kind based on the approximate profile errors method of estimation of close circular arc, however, this method is only applicable to
Two dimensional surface profile, and estimated accuracy is relatively low when following error is larger；Document " A Real-time contouring error
estimation for multi-axis motion systems using the second-order
Approximation ", Zhu etc., International Journal of Machine Tools and Manufacture,
2013,68：75-80, the document propose that a kind of Two-order approximation space profiles error based on point to curve distance formula is estimated in real time
Meter method, however this method estimated accuracy when following error is larger is equally relatively low, and algorithm for estimating acquisition is that actual point arrives
The distance value of ideal curve rather than profile errors vector value.
Invention content
The present invention is directed to overcome prior art defect, a kind of space profiles suitable for parametric spline curve interpolator are invented
Error real-time estimation method, this method based on first order Taylor Series Expansion Method calculating parameter curve for being fitted space circular arc
Characteristic point, and space circular arc approximate substitution desired profile is constructed, so as to calculate profile errors vector value, realize space profiles error
High-precision estimation.
The technical scheme is that a kind of based on the approximate profile errors real-time estimation method of space circular arc, characteristic exists
In, this method based on the characteristic point that profile errors estimation is used in first order Taylor Series Expansion Method calculating parameter spline curve, then
Space circular arc is fitted, and obtain its central coordinate of circle according to characteristic point；Finally, according to actual processing point with being fitted space circular arc
Position relationship calculates profile errors vector estimated value；Method is as follows：
The first step calculates characteristic point
The equation of setting parameter spline curve is C=C (u), and wherein u is parameter of curve, and current ideal cutter location is R, corresponding
Parameter of curve value be ur, practical cutter location is P, then following error vector EtFor：
Et=R-P (1)
To reflect ideal curve pattern near practical cutter location P comprehensively, with following error vector in the current preferable knife of curve
On the basis of the projected length in tangential direction at site, according to first order Taylor Series Expansion Method, determine to be used on parameter curve
First characteristic point R of space circular arc fittinga, on the basis of 1.5 times of projected length, determine second characteristic point Rb, with projection
On the basis of 0.5 times of length, third characteristic point R is determinedc；RaParameter of curve u at pointaComputational methods be：
Wherein, s is curve arc long, TrMistake is cut for unit of the preferable knife rail at R points, parameter u is to the derivative of s：
Wherein, C ' (ur) leading for parameter u is sweared in u for parametric equation C (u)rThe value at place；TrFor：
Formula (1), (3), (4) are brought into formula (2) to obtain：
Therefore RbParameter of curve u at pointbFor：
RcParameter of curve u at pointcFor：
Therefore Ra、Rb、RcPoint is calculated as R respectivelya=C (ua), Rb=C (ub) and Rc=C (uc)；According to characteristic point Ra、RbAnd
RcRealize the fitting of space circular arc；
Second step is fitted space circular arc
Pass through Ra、RbAnd Rc3 points determining space circle the center of circle be line segment RaRbMiddle vertical plane qa, line segment RaRcMiddle vertical plane
qbAnd Ra、Rb、RcPlane q determined by 3 pointscThe intersection point of three planes, wherein, plane qaExpression formula be：
In formula, (x, y, z) is the coordinate value of any point in plane；Plane qbExpression formula be：
Plane qcExpression formula be：
If the center of circle for being fitted space circle is Or=[Oxr Oyr Ozr]T, then its must meet formula (8), (9) and (10), therefore
Central coordinate of circle is calculated as：
The space circular arc constructed is with OrFor the center of circle, with | | Ra-Or| | it is radius in plane qcOn circle；
Third step calculates profile errors vector estimated value
Enable profile errors estimated value by practical cutter location P to second step construction space circular arc distance；Because of space circle
Place plane is qcIf qcThe per unit system arrow in face is nc, then：
P points are in qcSubpoint P in planepFor：
Pp=P- (nc·(P-Ra))nc (13)
Formula (12) is substituted into (13) and obtains PpIt puts and is：
The estimated value table of profile errors vector is shown asThen according to practical cutter location P and fitting space circle OrGeometry close
System determines that its calculation formula is：
The parameter curve geological information provided in each interpolation cycle of digital control system according to interpolator and practical cutter spacing
Point coordinates performs the real-time estimation that above-mentioned steps realize profile errors vector value at every bit.
The beneficial effects of the invention are as follows：It establishes based on the approximate profile errors estimation model of space circular arc, is that parameter is bent
The real-time high-precision estimation of line Interpolation Spaces track machining profile error provides effective way；It is abundant when estimating profile errors
The preferable knife rail pattern near practical cutter location is considered, can also ensure the estimation essence of profile errors when following error is larger
Degree.
Description of the drawings
Fig. 1-space knife rail profile geometrical model figure.
Fig. 2-profile errors method of estimation schematic diagram, wherein, R is preferable cutter location, and P is practical cutter location, TrFor ideal
Unit of the knife rail at R points cuts mistake, setIt is following error in TrProjected length on direction, RaFor first characteristic point, RbIt is
Two characteristic points, RcFor third characteristic point, qaFor line segment RaRbMiddle vertical plane, qbFor line segment RaRbMiddle vertical plane, qcFor Ra、Rb、
Rc3 points of planes determined, OrTo be fitted the center of circle of space circle, PpIt is P points in qcSubpoint in plane,It is sweared for profile errors
The estimated value of amount.
Fig. 3-this method estimation profile errors and the deviation map of actual profile error, wherein, X-axis represents interpolation cycle sequence
Number, Y-axis represents deviation, unit mm.
Fig. 4-Zhu et al. methods estimate profile errors and the deviation map of actual profile error；Wherein, X-axis represents interpolation week
Phase serial number, Y-axis represent deviation, unit mm.
Specific embodiment
Combination technology scheme and the attached drawing specific embodiment that the present invention will be described in detail.
During parametric spline curve direct interpolation, due to the hysteresis characteristic and dynamic of each feed shaft servo-control system
The reasons such as performance mismatch, can cause larger machining locus profile errors, need to be in real-time estimation to improve machining profile precision
On the basis of profile errors, profile control is carried out.Accordingly, invention is a kind of real based on the approximate high-accurate outline error of space circular arc
When method of estimation.
Attached drawing 1 is space knife rail profile geometrical model figure, with attached knife rail wheel in non-uniform rational B-spline space shown in FIG. 1
For exterior feature, specific implementation process that the present invention will be described in detail, the non-uniform rational B-spline parameter of the space knife rail profile is：Exponent number：
2；Control point：{(0,0,0)；(-8,-20,0)；(30,-5,-5)；(60,-20,0)；(47,0,0)；(60,20,0)；(30,5,-
5)；(-8,20,0)；(0,0,0)}；Weight factor：{1,0.9,0.75,1.5,6,3.5,1.8,1.5,1}；Knot vector：{0,0,
0,0.15,0.3,0.45,0.6,0.75,0.85,1,1,1}.By MATLAB/SIMULINK Numerical Simulating Platforms, three axis are established
NC Machine Tools Feeding Serve control system model, the transmission function G of X-axis feed control systemx(s) it is：
The transmission function G of Y-axis feed control systemy(s) it is：
The transmission function G of Z axis feed control systemz(s) it is：
Curve interpolating is carried out, and at each to space knife rail profile shown in attached drawing 1 according to second order Taylor series expansion method
According to preferable cutter location R, practical cutter location P and contour curve parameter information in interpolation cycle, this method real-time estimation is utilized
Profile errors；Attached drawing 2 is profile errors method of estimation schematic diagram, and the detailed process of implementation is as follows：
The first step calculates characteristic point：Characteristic point parameter u is calculated according to formula (5), (6), (7)a、ub、uc, and then obtain three
A characteristic point Ra、RbAnd Rc；
Second step is fitted space circular arc：According to the characteristic point R obtained in the first stepa、RbAnd Rc, using formula (8), (9),
(10) line segment R is obtainedaRbMiddle vertical plane qa, line segment RaRcMiddle vertical plane qbAnd Ra、Rb、Rc3 points of determining plane q of institutec, Jin Erli
The space circular arc center of circle O by three characteristic points is calculated with formula (11)rCoordinate；
Third walks, and calculates profile errors vector estimated value：It is put down according to where formula (14) calculates practical cutter location P in circular arc
Face qcOn projection Pp, and then utilize the estimated value of formula (15) acquisition profile errors vector
It repeats the above steps in each interpolation cycle, you can obtain the profile errors estimated value at each interpolated point, separately
Outside, actual profile error true value is calculated using offline non real-time method, the profile errors value and actual error that this method is estimated
Value comparison obtains the two deviation as shown in Figure 3；Advantage in terms of profile errors estimated accuracy to illustrate the invention, equally
Using Zhu et al. in document " A Real-time contouring error estimation for multi-axis
Motion systems using the second-order approximation ", Zhu etc., International
Journal of Machine Tools and Manufacture, 2013,68：75-80, middle proposition based on point to curve away from
Second order spatial profile errors method of estimation from formula carries out profile errors estimation, and by the estimated value and actual error of this method
Value comparison, obtains deviation as shown in Figure 4；Attached drawing 3 and attached drawing 4 are compared as it can be seen that the estimated bias maximum value of this method is
The estimated bias maximum value of 0.0093mm, Zhu et al. method is 0.0899mm, illustrates that using this method profile can be effectively improved
Error estimation accuracy has good profile errors estimation effect.
The present invention is towards when compensating the profile errors of generation in parametric spline curve interpolation actual processing with control
High-precision estimates the great demand of profile errors, has invented based on the approximate profile errors real-time estimation method of space circular arc, right
The raising of NC Machine Tools Feeding Serve System Contour extraction precision is of great significance.
Claims (1)
1. one kind is that this method is in every step newton based on the approximate profile errors real-time estimation method of space circular arc, characteristic
Iterate to calculate intersection point point before, based on first order Taylor Series Expansion Method calculating parameter curve be used for Newton iteration initial parameter values,
Newton iteration method is recycled, single step iteration parameter final value is calculated according to initial parameter values；Finally, to avoid that algorithm calculating is significantly increased
Time according to iteration ends precision conditions and maximum iteration condition double constraints end loop, obtains intersection point point parameter and estimates
Evaluation calculates profile errors vector estimated value；Method is as follows：
The first step calculates characteristic point
The equation of setting parameter spline curve is C=C (u), and wherein u is parameter of curve, and current ideal cutter location is R, corresponding song
Line parameter value is ur, practical cutter location is P, then following error vector EtFor：
Et=R-P (1)
To reflect ideal curve pattern near practical cutter location P comprehensively, with following error vector in the current preferable cutter location of curve
On the basis of projected length in the tangential direction at place, according to first order Taylor Series Expansion Method, determine to be used for space on parameter curve
First characteristic point R of circular fittinga, on the basis of 1.5 times of projected length, determine second characteristic point Rb, with projected length
0.5 times on the basis of, determine third characteristic point Rc；RaParameter of curve u at pointaComputational methods be：
Wherein, s is curve arc long, TrMistake is cut for unit of the preferable knife rail at R points, parameter u is to the derivative of s：
Wherein, C ' (ur) leading for parameter u is sweared in u for parametric equation C (u)rThe value at place；TrFor：
Formula (1), (3), (4) are brought into formula (2) to obtain：
RbParameter of curve u at pointbFor：
RcParameter of curve u at pointcFor：
Therefore Ra、Rb、RcPoint is calculated as R respectivelya=C (ua), Rb=C (ub) and Rc=C (uc)；According to characteristic point Ra、RbAnd RcIt is real
The fitting of existing space circular arc；
Second step is fitted space circular arc
Pass through Ra、RbAnd Rc3 points determining space circle the center of circle be line segment RaRbMiddle vertical plane qa, line segment RaRcMiddle vertical plane qbWith
And Ra、Rb、RcPlane q determined by 3 pointscThe intersection point of three planes, wherein, plane qaExpression formula be：
In formula, (x, y, z) is the coordinate value of any point in plane；Plane qbExpression formula be：
Plane qcExpression formula be：
If the center of circle for being fitted space circle is Or=[Oxr Oyr Ozr]T, then its must meet formula (8), (9) and (10), therefore the center of circle
Coordinate is calculated as：
The space circular arc constructed is with OrFor the center of circle, with | | Ra-Or| | it is radius in plane qcOn circle；
Third step calculates profile errors vector estimated value
Enable profile errors estimated value by practical cutter location P to second step construction space circular arc distance；Because where space circle
Plane is qcIf qcThe per unit system arrow in face is nc, then：
P points are in qcSubpoint P in planepFor：
Pp=P- (nc·(P-Ra))nc (13)
Formula (12) is substituted into (13) and obtains PpIt puts and is：
The estimated value table of profile errors vector is shown asThen according to practical cutter location P and fitting space circle OrGeometrical relationship it is true
Determining its calculation formula is：
In each interpolation cycle of digital control system, the parameter curve geological information and practical cutter location that are provided according to interpolator are sat
Mark performs the real-time estimation that above-mentioned steps realize profile errors vector value at every bit.
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| CN108646669B (en) * | 2018-04-09 | 2020-05-19 | 华中科技大学 | Approximate evaluation method for surface contour error of curved surface machining part |
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| TWI680360B (en) * | 2018-10-09 | 2019-12-21 | 財團法人工業技術研究院 | Arc processing device and method using the same |
| CN109491321B (en) * | 2018-12-05 | 2021-05-14 | 沈阳工业大学 | Contour error estimation method based on H-shaped precision motion platform |
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