CN107479497B - A kind of five-axis robot track profile errors two close cycles compensation method - Google Patents
A kind of five-axis robot track profile errors two close cycles compensation method Download PDFInfo
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- CN107479497B CN107479497B CN201710809040.4A CN201710809040A CN107479497B CN 107479497 B CN107479497 B CN 107479497B CN 201710809040 A CN201710809040 A CN 201710809040A CN 107479497 B CN107479497 B CN 107479497B
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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
- G05B19/404—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 control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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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
- G05B2219/35—Nc in input of data, input till input file format
- G05B2219/35408—Calculate new position data from actual data to compensate for contour error
Abstract
A kind of five-axis robot track profile errors two close cycles compensation method of the present invention belongs to multiaxis NC maching technical field, is related to a kind of profile errors two close cycles compensation method for being used to improve five-shaft numerical control machining accuracy compensated based on profile errors inner ring predictive compensation and outer loop feedback.This method is based on model prediction and feedback compensation, estimate each physical axis movement position of subsequent time, subsequent time and current time point of a knife point and cutter axis orientation profile errors are calculated by tangential backstepping and Newton method, according to reverse Jacobian matrix, predictive compensation is carried out to profile errors in inner ring, feedback compensation is carried out to profile errors in outer ring, improves five-axis robot track contour accuracy.This method synchronizes residual error caused by inhibiting because of external disturbance and model error etc. on the basis of realizing control five-axis robot profile errors in advance, is of great significance to five-shaft numerical control machining accuracy is improved.
Description
Technical field
The invention belongs to precise high-efficiency intelligence multiaxis NC maching technical fields, are related to a kind of for improving five-shaft numerical control
The profile errors two close cycles compensation method of machining accuracy.
Background technique
In multi-shaft interlocked Contour extraction motion process, since single-axis servo controls system following error, multijoint control system
The factors such as the mistake of system dynamic and external disturbance exist, and will lead to and generate deviation between actual motion track and ideal movements track, i.e.,
Profile errors.How profile errors are reduced, is that multi-axis numerical control system development faces to improve multi-shaft interlocked Contour extraction precision
Huge challenge.Three-axis numerical control is processed, since cutter axis orientation is unique, there is only point of a knife point motion profile profile errors.So
And five-shaft numerical control is processed, it is continuously swung, is caused with realizing cutter shaft due to introducing two rotary shafts in addition to three linear axis
In addition to point of a knife point tolerance, also there is cutter axis orientation error, and the two intercouples, is brought greatly for the compensation of five axis profile errors
It is difficult.Therefore, five-axis robot track profile error compensating method is studied, to five-axis robot precision is improved, improves five-axis machine tool
Energy etc. is of great significance.
" the Pre-compensation of contour errors in five-axis CNC of existing technical literature 1
Machine tools ", Zhang etc., International Journal of Machine Tools and
Manufacture, 2013,74:1-11, the document by solve the differential equation, predict five-axis robot point of a knife dot profile error and
Cutter axis orientation profile errors, and then the error amount of prediction is pre-compensated for, but this method is sensitive to system parameter, anti-interference energy
Power is poor.Document 2 " A tool-path control scheme for five-axis machine tools ", Chih-Ching
Lo, International Journal of Machine Tools and Manufacture, 2002,42:79-88, this article
It offers using each shaft position value of feedback, establishes profile errors model, and by converting in real time between each drive shaft and coordinate system, it is real
Existing profile errors feedback compensation, but this method compensates only for the profile errors generated, can not realize and mention before profile errors occur
Preceding control.
Summary of the invention
The present invention is directed to overcome prior art defect, invent a kind of for improving the double spline curve interpolation machining locus of five axis
The two close cycles profile errors compensation method of contour accuracy, this method are based on model prediction and feedback compensation, it is each to estimate subsequent time
Physical axis movement position establishes point of a knife point and cutter axis orientation profile errors computation model, obtains subsequent time profile errors and estimate
Value, while by physical axis physical location value of feedback, current time profile errors value is calculated, realizes profile errors prediction, feedback
Two close cycles compensation, improves five-axis robot track contour accuracy.
The technical scheme is that a kind of five-axis robot track profile errors two close cycles compensation method, characteristic are,
This method is based on model prediction and feedback compensation, estimates each physical axis movement position of subsequent time, passes through tangential backstepping and newton
Method calculates subsequent time and current time point of a knife point and cutter axis orientation profile errors, according to reverse Jacobian matrix, in inner ring pair
Profile errors carry out predictive compensation, carry out feedback compensation to profile errors in outer ring, to improve five-axis robot track profile essence
Degree.Specific step is as follows for method:
The first step is based on model prediction and feedback compensation estimated physical axis movement position
If being C to the point of a knife point path curves equation in the double spline curve of five axis of interpolationP=CP(u), knife is removed on cutter shaft
The outer another point path curves equation of point is CQ=CQ(u), R is enabledp=[Rx,Ry,Rz]TIndicate ideal point of a knife point, Ro=[Ri,
Rj,Rk]TIndicate ideal generating tool axis vector, R=[Rx,Ry,Rz,Ri,Rj,Rk]TIndicate ideal knife bit vector, calculation method are as follows:
Enable Pp=[Px,Py,Pz]TIndicate practical point of a knife point, Po=[Pi,Pj,Pk]TIndicate practical generating tool axis vector, P=[Px,
Py,Pz,Pi,Pj,Pk]TIndicate practical knife bit vector,The practical knife bit vector indicated is estimated
Value；R=[r1,r2,r3,r4,r5]TIndicate physical axis ideal movements position, p=[p1, p2, p3, p4, p5]TIndicate that physical axis is real
Border movement position,Indicate physical axis actual motion position discreet value, the domain numerical control feeding system z
The general expression of transmission function G (z) are as follows:
Wherein, n is system order, a1,a2,…,anAnd b1,b2,…,bnFor system parameter；If λ axis, λ=1,2,3,4,5,
The input ideal movements position and output actual motion position in t-th of sampling period are respectively rλ(t) and pλ(t), then t+1 is a
The λ axis actual motion position model predicted value in sampling periodAre as follows:
To improve actual motion position prediction model to the interference free performance of parameter, corrected by the method for feedback compensation real
Border movement position model predication value obtains the λ axis actual motion position discreet value in final the t+1 sampling period
Accordingly, the physical axis actual motion position discreet value in the t+1 sampling period is
Second step profile errors inner ring predictive compensation
If function ftrIndicate five-axis machine tool direct kinematics transforming function transformation function, it is real according to the physical axis in the t+1 sampling period
Border movement position discreet valueCalculate the practical knife bit vector discreet value in the t+1 sampling period
Define the tangential profile errors function of point of a knife pointBy solving equation
dt(u)=0 intersection point point parameter u is foundf；If the parameter of curve at ideal knife bit vector R is ur, backstepping is calculated by tangential backstepping
Point parameter ub:
By parameter ubAs Newton method initial value, equation d is sought using Newton methodt(u)=0 solution uN:
It enablesIt is to point of a knife locus of points curve intersection point pointCorresponding intersection point point parameter isWhether judge Newton method
Convergence, if | dt(uN) | < | dt(ub) |, illustrate that Newton method restrains, enables intersection point point parameterOtherwise, in ubPlace is again sharp
Intersection point point parameter is calculated with tangential backstepping, accordingly, intersection point point parameter isIt calculates are as follows:
Calculate the point of a knife dot profile error in the t+1 sampling periodAnd cutter axis orientation error
The five axis profile errors vectors for remembering the t+1 sampling period areIf the reverse Jacobean matrix of five-axis machine tool
Battle array beCalculate physical axis profile errors predictive compensation amount
By each physical axis profile errors predictive compensation amountIt is added to corresponding physical axis ideal movements position rλOn obtain
λ axis movement instruction after compensation realizes profile errors inner ring predictive compensation；
The compensation of third step profile errors outer loop feedback
Though the profile errors in that is, t+1 sampling period carry out t-th of sampling period to subsequent time in second step
Predictive compensation, but when actual motion is to the t+1 moment, due to factors such as modeling errors, can still there are remaining profile errors, because
Profile errors are carried out feedback compensation at current time, to further increase contour accuracy by this；Pass through physical axis position feedback
The physical axis actual motion position p (t) in current t-th of sampling period is obtained, according to kinematic transform, calculates t-th of sampling week
Phase, the i.e. practical knife bit vector P at current time:
With parameterPractical point of a knife point P is calculated for initial valuepTo the intersection point point parameter u of ideal point of a knife locus of points curvef:
Calculate the point of a knife dot profile error ε at current timepAnd cutter axis orientation error εo:
Note current time five axis profile errors vectors beCalculate physical axis profile errors feedback compensation amount Δ
R:
While inner ring predictive compensation, in outer ring by each physical axis profile errors predictive compensation amount Δ rλIt is added to corresponding
Physical axis ideal movements position command on compensated after λ axis movement instruction, realize profile errors two close cycles compensation.
The beneficial effects of the present invention are: having invented the profile errors two close cycles compensation method of five-axis robot track, pass through combination
Profile errors inner ring predictive compensation and outer loop feedback compensation, realize on the basis of controlling five-axis robot profile errors in advance, together
Residual error caused by step inhibits because of external disturbance and model error etc., is remarkably improved five-axis robot track contour accuracy；It should
Five axis profile errors calculation methods of the method based on tangential backstepping and Newton method can carry out point of a knife point and cutter axis orientation error same
Step accurately calculates.Residual error caused by inhibiting because of external disturbance and model error etc. is synchronized, five-shaft numerical control processing is smart to improving
Degree is of great significance.
Detailed description of the invention
Fig. 1-method overall flow figure；
The double spline curve knife rail geometrical model figures of five axis in Fig. 2-rectangular coordinate system；Wherein, curve 1 indicates point of a knife point fortune
Dynamic rail trace curve, curve 2 indicate cutter shaft in addition to point of a knife some path curves；
The point of a knife dot profile Error Graph that Fig. 3-utilizes the method for the present invention to obtain using the method for the present invention and not；Wherein, B1 axis
For process time, unit s, B2 axis is point of a knife dot profile error, unit mm；The expression of curve 1 does not utilize the method for the present invention to obtain
The point of a knife dot profile error arrived, curve 2 indicate the point of a knife dot profile error obtained using the method for the present invention；
The cutter axis orientation profile errors figure that Fig. 4-utilizes the method for the present invention to obtain using the method for the present invention and not；Wherein, B1
Axis is process time, and unit s, B2 axis is cutter axis orientation profile errors, unit rad；The expression of curve 1 does not utilize present invention side
The cutter axis orientation profile errors that method obtains, curve 2 indicate the cutter axis orientation profile errors obtained using the method for the present invention.
Specific embodiment
Combination technology scheme and the attached drawing specific embodiment that the present invention will be described in detail.
In the double spline curve interpolation process of five axis, since the factors such as uniaxial following error and multiaxis dynamic mistake are deposited
Practical point of a knife point and cutter shaft motion profile and ideal trajectory is being caused to generate deviation, i.e. profile errors.
Attached drawing 1 is method overall flow figure, and attached drawing 2 is the double spline curve knife rail geometrical models of five axis in rectangular coordinate system
Figure, for the knife rail shown in the attached drawing 2, specific implementation process that the present invention will be described in detail, wherein curve 1, i.e. point of a knife point motion profile
The parameter of curve is；Order: 2；Control point: (0,0,0), (10,2,2), (23,10,10), (- 3,30,30), (10,38,
38),(20,40,40)}；Weight factor: { 1；1；1.5；1.5；1；1}；Knot vector: { 0,0,0,1/4,2/4,3/4,1,1,1 },
Order, weight factor and the knot vector of curve 2 are identical as curve 1, control point are as follows: and (0,0,5), (8,3,7), (18,10,15),
(-8,30,35),(10,39,42),(20,40,45)}。
Method overall flow shown in 1 with reference to the accompanying drawings carries out the double spline curve of five axis and inserts by taking the bis- turntable five-axis machine tools of AC as an example
It adds the compensation of work track profile errors two close cycles to generate, specific steps are as follows:
The first step is based on model prediction and feedback compensation estimated physical axis movement position: utilizing formula (3), according to physical axis
Feed system model prediction subsequent time physical axis actual motion position discreet valueAnd it is moved according to physical axis
Location feedback value, using formula (4), correcting physics axis actual motion position discreet value is obtained
Second step profile errors inner ring predictive compensation: practical knife bit vector discreet value is calculated using formula (5)
Using tangential backstepping and Newton method, is calculated according to formula (8) and estimate point of a knife pointJoin to point of a knife point ideal trajectory intersection point point
NumberAnd then subsequent time point of a knife point and cutter axis orientation profile errors are calculated using formula (9), obtain five axis wheel of subsequent time
Wide error vectorTo calculate physical axis profile errors predictive compensation amount according to formula (10)
The compensation of third step profile errors outer loop feedback: it is calculated and is worked as using formula (11) according to physical axis movement position value of feedback
The practical knife bit vector P at preceding moment, with gained in second stepFor initial value, it is based on tangential backstepping, using formula (12), calculating is worked as
Preceding moment practical point of a knife point is to ideal point of a knife locus of points curve intersection point point parameter uf, current time point of a knife is calculated using formula (13)
Point and cutter axis orientation profile errors, and then physical axis profile errors feedback compensation amount Δ r is calculated using formula (14)；Prediction is mended
The amount of repayingAnd feedback compensation amount Δ r is added in physical axis ideal movements position command simultaneously, realizes that five-axis robot track profile misses
Poor two close cycles compensation.
The point of a knife dot profile Error Graph that attached drawing 3 show using the method for the present invention and the method for the present invention is not utilized to obtain；Its
In, B1 axis is process time, and unit s, B2 axis is point of a knife dot profile error, unit mm；The expression of curve 1 does not utilize the present invention
The point of a knife dot profile error that method obtains, curve 2 indicate the point of a knife dot profile error obtained using the method for the present invention；As it can be seen that not
The point of a knife dot profile max value of error obtained using the method for the present invention is about 0.26mm, the point of a knife point obtained using the method for the present invention
Profile errors maximum value is reduced to 0.09mm；
The cutter axis orientation profile errors figure that attached drawing 4 show using the method for the present invention and the method for the present invention is not utilized to obtain；
Wherein, B1 axis is process time, and unit s, B2 axis is cutter axis orientation profile errors, unit rad；The expression of curve 1 does not utilize
The cutter axis orientation profile errors that the method for the present invention obtains, curve 2 indicate that the cutter axis orientation profile obtained using the method for the present invention is missed
Difference；As it can be seen that the cutter axis orientation profile errors maximum value for not utilizing the method for the present invention to obtain is about 0.005rad, present invention side is utilized
The cutter axis orientation profile errors maximum value that method obtains is reduced to 0.0019rad；
Comprehensive attached drawing 3 and attached drawing 4 are as it can be seen that this method can effectively reduce point of a knife point and cutter axis orientation wheel during five-axis robot
Wide error improves five axis Contour extraction precision.It is synchronous to inhibit on the basis of realizing control five-axis robot profile errors in advance
Because of residual error caused by external disturbance and model error etc..
Claims (1)
1. a kind of five-axis robot track profile errors two close cycles compensation method, characteristic are, this method be based on model prediction and
Feedback compensation estimates each physical axis movement position of subsequent time, by tangential backstepping and Newton method calculating subsequent time and currently
Moment point of a knife point and cutter axis orientation profile errors carry out predictive compensation to profile errors in inner ring according to reverse Jacobian matrix,
Feedback compensation is carried out to profile errors in outer ring, to improve five-axis robot track contour accuracy, specific step is as follows for method:
The first step is based on model prediction and feedback compensation estimated physical axis movement position
If being C to the point of a knife point path curves equation in the double spline curve of five axis of interpolationP=CP(u), on cutter shaft in addition to point of a knife
Another point path curves equation is CQ=CQ(u), R is enabledp=[Rx,Ry,Rz]TIndicate ideal point of a knife point, Ro=[Ri,Rj,Rk]T
Indicate ideal generating tool axis vector, R=[Rx,Ry,Rz,Ri,Rj,Rk]TIndicate ideal knife bit vector, calculation method are as follows:
Enable Pp=[Px,Py,Pz]TIndicate practical point of a knife point, Po=[Pi,Pj,Pk]TIndicate practical generating tool axis vector, P=[Px,Py,Pz,
Pi,Pj,Pk]TIndicate practical knife bit vector,The practical knife bit vector discreet value indicated；R=
[r1,r2,r3,r4,r5]TIndicate physical axis ideal movements position, p=[p1,p2,p3,p4,p5]TIndicate physical axis actual motion position
It sets,Indicate physical axis actual motion position discreet value, numerical control feeding system z domain transmission function G
(z) general expression are as follows:
Wherein, n is system order, a1,a2,…,anAnd b1,b2,…,bnFor system parameter；If λ axis, λ=1,2,3,4,5, t
The input ideal movements position and output actual motion position in a sampling period are respectively rλ(t) and pλ(t), then the t+1 sampling
The λ axis actual motion position model predicted value in periodAre as follows:
To improve actual motion position prediction model to the interference free performance of parameter, pass through the practical fortune of method amendment of feedback compensation
Dynamic position model predicted value, obtains the λ axis actual motion position discreet value in final the t+1 sampling period
Accordingly, the physical axis actual motion position discreet value in the t+1 sampling period is
Second step profile errors inner ring predictive compensation
If function ftrFive-axis machine tool direct kinematics transforming function transformation function is indicated, according to the practical fortune of the physical axis in the t+1 sampling period
Dynamic position discreet valueCalculate the practical knife bit vector discreet value in the t+1 sampling period
Define the tangential profile errors function of point of a knife pointBy solving equation dt(u)
=0 finds intersection point point parameter uf；If the parameter of curve at ideal knife bit vector R is ur, backstepping point parameter is calculated by tangential backstepping
ub:
By parameter ubAs Newton method initial value, equation d is sought using Newton methodt(u)=0 solution uN:
It enablesIt is to point of a knife locus of points curve intersection point pointCorresponding intersection point point parameter isJudge whether Newton method is received
It holds back, if | dt(uN) | < | dt(ub) |, illustrate that Newton method restrains, enables intersection point point parameterOtherwise, in ubPlace re-uses
Tangential backstepping calculates intersection point point parameter, and accordingly, intersection point point parameter isIt calculates are as follows:
Calculate the point of a knife dot profile error in the t+1 sampling periodAnd cutter axis orientation error
The five axis profile errors vectors for remembering the t+1 sampling period areIf the reverse Jacobian matrix of five-axis machine tool isCalculate physical axis profile errors predictive compensation amount
By each physical axis profile errors predictive compensation amountIt is added to corresponding physical axis ideal movements position rλOn compensated
λ axis movement instruction afterwards realizes profile errors inner ring predictive compensation；
The compensation of third step profile errors outer loop feedback
Though the profile errors in that is, t+1 sampling period are predicted t-th of sampling period to subsequent time in second step
Compensation, but when actual motion arrive the t+1 moment when, due to factors such as modeling errors, still can exist remnants profile errors, therefore,
Current time carries out feedback compensation to profile errors, to further increase contour accuracy；It is obtained by physical axis position feedback
The physical axis actual motion position p (t) in current t-th of sampling period calculates t-th of sampling period, i.e., according to kinematic transform
The practical knife bit vector P at current time:
With parameterPractical point of a knife point P is calculated for initial valuepTo the intersection point point parameter u of ideal point of a knife locus of points curvef:
Calculate the point of a knife dot profile error ε at current timepAnd cutter axis orientation error εo:
Note current time five axis profile errors vectors beCalculate physical axis profile errors feedback compensation amount Δ r:
While inner ring predictive compensation, in outer ring by each physical axis profile errors predictive compensation amount Δ rλIt is added to corresponding object
λ axis movement instruction after being compensated in reason axis ideal movements position command realizes the compensation of profile errors two close cycles.
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| CN109116808B (en) * | 2018-08-23 | 2020-04-10 | 西安交通大学 | Linkage track profile precision prediction method based on numerical control machine tool big data |
| CN109240214B (en) * | 2018-11-12 | 2020-04-21 | 电子科技大学 | Contour error estimation and visualization method for multi-axis numerical control machining |
| CN109960215B (en) * | 2019-04-10 | 2020-05-19 | 大连理工大学 | Off-line compensation method for contour error of machining track of four-axis lathe |
| CN110244658B (en) * | 2019-06-04 | 2020-11-24 | 浙江工业大学 | Method for improving interpolation position precision of cutting bed based on improved BP neural network |
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| CN110647105B (en) * | 2019-09-20 | 2022-03-29 | 天津职业技术师范大学(中国职业培训指导教师进修中心) | Limited control set model prediction contour control method suitable for double-shaft or three-shaft feed driving system |
| CN112787551A (en) * | 2019-11-02 | 2021-05-11 | 天津职业技术师范大学(中国职业培训指导教师进修中心) | Method for improving robustness and contour performance of double-shaft or three-shaft feed driving system |
| CN111650881B (en) * | 2020-05-12 | 2021-09-10 | 武汉理工大学 | Method, system and storage medium for predicting and compensating positioning error of numerical control machine |
| CN111913438B (en) * | 2020-08-04 | 2022-03-04 | 天津大学 | Control method for nonlinear error of tool nose point and tool shaft direction in five-axis machining |
| CN112327752A (en) * | 2020-11-16 | 2021-02-05 | 大连理工大学 | Double-ring compensation method for contour error of four-axis turning track |
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