CN108227630A - A kind of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator - Google Patents
A kind of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator Download PDFInfo
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- 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
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Abstract
The present invention relates to a kind of NC Machining of Free-form Surfaces methods using time parameter polynomial interpolator.Specifically include three big steps：Predict look-ahead velocity planning, the time parameter multinomial machining locus generation based on B spline and time parameter multinomial real-time interpolation；(1) speed planning is carried out by reading parameter curve type Free-Form Surface Machining track, generates the Free-Form Surface Machining process discrete data of high speed and super precision；2) the high speed and high precision processing process discrete data after speed planning is characterized using the B spline fitting techniques of given accuracy, is then converted into succinct increment type time parameter polynomial surface machining locus；(3) it works out corresponding real-time interpolation program according to the time parameter polynomial surface machining locus of generation to control numerically-controlled machine tool in real time, completes Free-Form Surface Machining.Present invention improves the contour accuracies and surface quality of the free form surface processed, significantly improve Free-Form Surface Machining efficiency, reduce data volume needed for Free-Form Surface Machining.
Description
Technical field
The invention belongs to Computerized Numerical Control processing technology fields, and in particular to a kind of NC Machining of Free-form Surfaces method especially may be used
It is offline to carry out speed planning and generate succinct comprising Machining of Curved Surface geometry and velocity information with according to parameter curve machining locus
Machining of Curved Surface data develop corresponding real-time online time parameter polynomial interpolator algorithm.
Background technology
With the development of aerospace and optical field, Free-form Surface Parts such as blade of aviation engine, optical lens
Deng processing request it is higher and higher.It is freely bent but compared with ruled surface can be represented such as spherical surface, quadratic surface with equation
Face is generally characterized using a large amount of point cloud or a large amount of segmentation equations.This considerably increases the complexity of NC Machining of Free-form Surfaces
Property.In current production practices, Free-Form Surface Machining is still using a large amount of small line segment discrete locis, then by line smoothing
Free-Form Surface Machining is realized with speed planning.But since the stringent control of online calculation amount in real time is so that in line smoothing and speed
Planning all can not achieve good high speed and super precision Free-Form Surface Machining.A kind of small line of published high-speed, high precision digital control processing
Section real-time smooth transition interpolation method carries out carrying out small line segment track transition, and use S acceleration and deceleration using B-spline three times
Method plans speed, but transition precision is difficult to be controlled, and S deceleration planning methods are difficult to reach speed planning
Optimality.
Therefore it in Free-Form Surface Machining, is obtained widely with the numerical-control processing method of the parameter curve track of continual curvature
Using.But since parameter of curve and curve arc long do not have explicit function relationship generally, limit what is processed using parameter curve
Speed planning and real-time interpolation process so that the NC Machining of Free-form Surfaces of parameter curve machining locus is difficult in production practices
It promotes and applies.
The technology of being disclosed solves the problems, such as that parameter curve is applied to encounter in Free-Form Surface Machining, to using parameter curve
Offline speed planning (Beudaert X, Lavernhe S, Tournier C (2012) Feedrate of machining locus
interpolation with axis jerk constraints on 5-axis NURBS and G1tool path.Int
J Mach Tools Manuf 57:73-82.) with parameter interpolation (Erkorkmaz K, Altintas Y (2005) Quintic
Spline Interpolation With Minimal Feed Fluctuation.J Manuf Sci Eng 127:339.)
It is studied respectively.But all consider speed planning and interpolating method without collaboration so that be difficult to during parameter interpolation
Ensure the high speed and high precision processing process completed by speed planning.And ensure parameter interpolation according to offline speed planning process controller
Bed motion then needs mass of redundancy data.
The smooth prediction interpolation system of published small line segment path compression is mainly characterized by first using B-spline to small
Line segment track is fitted, using S type look-ahead velocity planing methods and a variety of interpolating methods.But how will be fast without introducing
In the succinct high-precision a variety of interpolating methods applied to its proposition of result after metric stroke.
Invention content
The present invention is for the NC Machining of Free-form Surfaces the complex nature of the problem and the prior art for using parameter curve track
It is insufficient, it is proposed that a kind of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator.This method collaboration considers
The characteristics of online calculating in real time and off-line calculation, realizes that speed planning is generated with process data using off-line calculation, improves speed
The terseness of the optimality that metric is drawn and generation data.Online real-time interpolation is only with the polynomial interpolator of time parameter, drop
The low computational complexity of real-time interpolation, improves the robustness calculated in real time.Promote parametric type Free-Form Surface Machining track
Application in production practices.
The present invention is to be achieved through the following technical solutions：
A kind of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator is suitable for numerically-controlled machine tool processing certainly
By curved surface, the numerically-controlled machine tool includes real-time machine tool controller and machine body, and the machine body includes workbench and each
Kinematic axis.The method of the present invention includes three operating procedures：
(1) prediction look-ahead velocity planning
By reading parameter curve type Free-Form Surface Machining track and carrying out speed planning, the freely bent of high speed and super precision is generated
Face process discrete data；
(2) the time parameter multinomial machining locus generation based on B-spline
The Free-Form Surface Machining process discrete data generated using the B-spline fitting techniques of given accuracy to step (1)
It is characterized, is then converted into succinct increment type time parameter polynomial surface machining locus；
(3) time parameter multinomial real-time interpolation
According to increment type time parameter polynomial surface machining locus, write in real-time machine tool controller corresponding slotting in real time
Algorithm is mended, free form surface high speed and high precision processing is completed in control numerically-controlled machine tool movement；
By the NC Machining of Free-form Surfaces method, the contour accuracy of processed free form surface and surface matter are improved
Amount, significantly improves Free-Form Surface Machining efficiency, reduces data volume needed for Free-Form Surface Machining.
The technical solution further limited is as follows：
A kind of concrete operation step of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator is as follows：
(1) prediction look-ahead velocity planning
(1.1) it is moved according to requirement on machining accuracy and process unit service ability extraction most high-order for speed planning three times
Learn constraint, and using triangle inequality with introduce proportionality coefficient method to kinematical constraint carry out dimensionality reduction simplification, by it is all about
Beam is converted into the one-dimensional constraint related with parameter of curve；
The speed planning kinematical constraint includes each kinematic axis constraint of lathe and is constrained with processing technology；
(1.2) along machining locus, pre-decelerating is carried out to the tracing point for violating one-dimensional constraint using prediction look-ahead approach,
Accelerate a time step if without the tracing point for violating one-dimensional constraint during prediction；According to based on minimal principle from
Computational methods are dissipated, acceleration is calculated with most Higher-order Constraint, satisfaction constraint is then calculated by numerical integration and processing is imitated
The optimal Machining of Curved Surface process discrete data of rate；
(2) the time parameter multinomial machining locus generation based on B-spline
(2.1) according to speed planning complete Machining of Curved Surface process discrete data, using time parameter B-spline into
Row fitting asks for B-spline knot vectors, and using minimum in fit procedure using the node Forecasting Methodology of given accuracy
Square law solves control point；Finally Machining of Curved Surface process is characterized with the B-spline of time parameter, obtains B-
Spline machining locus；
(2.2) using B-spline- multinomials transfer algorithm (being converted into multinomial by B-spline), by B-spline plus
Work track is converted into increment type time parameter polynomial surface machining locus；
(3) time parameter multinomial Real-time interpolation algorithm
Time parameter multinomial real-time interpolation program is write in real-time machine tool controller, is obtained according to by step (2.2)
Increment type time parameter polynomial surface machining locus pass through real-time interpolation program numerically-controlled machine tool controlled to move, realize freely bent
Face high speed and high precision processing.
The technical solution further limited is as follows：
In the step (1.1), by introduce proportionality coefficient with using triangle inequality method to lathe each kinematic axis
Constraint is simplified：
The constraint of machine tool motion axis is summarized as follows
In formula,Represent speed, acceleration and the acceleration of the i-th axis；Represent the speed of the i-th axis
The constraint of degree, acceleration and acceleration；
By introducing proportionality coefficient with axle acceleration and acceleration Multi-dimensional constraint will be moved using triangle inequality method
Be converted to the one-dimensional constraint related with parameter of curve；Wherein acceleration constraint processing formula be：
Wherein acceleration constraint processing formula be：
δ in formula1With δ2For acceleration proportionality coefficient, μ1,μ2With μ3For acceleration proportionality coefficient, proportionality coefficient is according to lathe
It is selected with track characteristic；In formulaWithIt is speed, acceleration and the acceleration of trajectory range respectively；Q in formulas,qss,qsss
Respectively parameter of curve is to the first derivative of curve arc long, second dervative and three order derivatives.
In the step (1.2), pre-decelerating, tool are carried out to the following tracing point for violating constraint using prediction look-ahead approach
Gymnastics is made as follows：
Prediction prediction moderating process will accelerate to be slowed down first since current point with the minimum acceleration of permission
Degree reduce to zero, then proceed to successively decrease to acceleration with minimum acceleration, a step of often successively decreasing again by acceleration with most greatly plus
Speed increase is to zero until decrease of speed is until zero；Speed, acceleration and acceleration are constrained respectively in this process into
Performing check；
It is decremented in zeroth order section in initial acceleration if there is tracing point violates velocity and acceleration constraint, then the point can be with
It is set as violating the crucial tracing point of constraint；Machining locus need to decelerate to the crucial tracing point of violation constraint from initial track point, slow down
Mode is slowed down according to prediction prediction searching method；
Continue depletion stage in acceleration, if there is tracing point violates acceleration constraint, then violate adding at tracing point
Acceleration is recalculated according to acceleration constraint；After obtaining acceleration, then predict that deceleration algorithm continues；If there is tracing point
Constraint of velocity is violated, then the point could be provided as violating constraint of velocity key tracing point；Machining locus need to subtract from initial track point
Speed is slowed down to constraint of velocity key tracing point, ways of deceleration is violated according to prediction prediction searching method；
Zero process is incremented in acceleration, violates acceleration constraint if there is tracing point, then acceleration increasing process needs
Stop；Deceleration prediction process decelerates to the point, and prediction prediction process is continued to execute since the point up to acceleration and speed
Zero is all kept to, and constantly continues to detect each constraint；
Zero process is incremented in acceleration, violates constraint of velocity if there is tracing point, then the acceleration increasing process stops
Only, acceleration decrementing procedure is then carried out again；If reached at violation speed trajectory point, speed still violates constraint of velocity,
Then above process cycle carries out；If speed meets constraint requirements when reaching this, which is track key point machining locus
The crucial tracing point of violation constraint need to be decelerated to from initial track point, ways of deceleration slows down according to prediction prediction searching method.
In the step (2.1), fitting B-spline knot vectors, tool are asked for using the node Forecasting Methodology of given accuracy
Body determination process is as follows：
The position data { t, p } of each kinematic axis at any time is fitted for n times B-spline, error of fitting may be used down
Formula is estimated：
ε is the n times B-spline errors of fitting of estimation in formula,It is each axis maximum displacement to time n times derivative value
The vector of composition,For the vector that each axis least displacement forms time n times derivative value, Δ t is time parameter n times B-
The node interval of spline；
According to the error of fitting ε of estimation, under assigned error δ, the determining algorithm of knot vector is as follows：
Step a：Given first nodal value of knot vector is the time T for being fitted former first position of data1=t1, i=
1, j=1；
Step b：I=i+1, and judge whether i is equal to former discrete data quantity, if equal go to step d；It is unequal
When, sequence performs step c；
Step c：Computation interval [Tj,ti] n times B-spline error of fitting ε, and judge whether ε is more than or equal to given fitting
Error delta, if meeting ε >=δ, it is determined that next node vector is Tj+1=tiAnd j=j+1；Go to step b；
Step d：Enable knot vector Tj+1Equal to the former data endpoint time, end node vector calculates.
In the step (2.2), time parameter B-spline machining locus is converted into increment type time parameter multinomial
The algorithm of Machining of Curved Surface track is：
It is for p time parameter B-spline：
It is for increment type p order polynomials：
P(p)(t)=a0+a1·t+a2·t2+a3·t3…+an·tp,0≤t≤T
A=[a0,a1,…an]
P(p)(t)=A λTλ=[1, t, t2,…tp]
For odd times time parameter B-spline, in node interval [ti,ti+1] be converted to increment type time parameter multinomial
Algorithm is：
By time parameter B-spline in node interval [ti,ti+1] functional value at corresponding endpoint is calculated with accordingly leading
Numerical valueFor p B-spline,
Hermite interpolation may be used by L vectors and directly obtain the coefficient vector A of p order polynomials and time variable section T.
For even time parameter B-spline, in node interval [ti,ti+1], i=1,3,5 ... .. are converted to increment type
Time parameter multinomial algorithm is：
By time parameter B-spline in node interval [ti,ti+1] functional value at corresponding endpoint is calculated with accordingly leading
Numerical valueFor p B-spline, by L
Vector may be used Hermite interpolation and directly obtain the coefficient vector A of p order polynomials and time variable section T；
For even time parameter B-spline, in node interval [ti+1,ti+2] i=1,3,5 ... .. be converted to increment type
Time parameter multinomial algorithm is：
By time parameter B-spline in node interval [ti+1,ti+2] functional value at corresponding endpoint is calculated with accordingly leading
Numerical valueFor p B-
Spline may be used Hermite interpolation by L vectors and directly obtain the coefficient vector A of p order polynomials and time variable area
Between T.
In the step (3), time parameter multinomial Real-time interpolation algorithm is：
According to the increment type split time Parametric polynomial surface machining locus that step (2) generates, i-th section of multinomial coefficient
Vector is AiIf total elapsed time is T this moment, t is divided between each section of time parameter polynomial timej；
Then time variableFor：
Variable vector λiFor：
It is in each axis of motion position calculation formula that the moment interpolation obtains：
P(p)=Ai·λi T
It is T according to interpolation algorithm and total elapsed time, you can acquire each movement shaft position of the moment lathe, successively
Machine Free-Form Surface Machining.
The advantageous effects of the present invention embody in the following areas：
(1) the NC Machining of Free-form Surfaces method cooperateed with using off-line calculation with real-time online, improves computational accuracy, drop
Low on-line calculation.Off-line calculation and real-time operation respectively advantage are given full play to.
(2) it using offline prediction look-ahead velocity planing method, can obtain than the processing efficiency using S type acceleration and deceleration methods
More preferably Machining of Curved Surface process, and constrain can strict guarantee, according to embodiment, using under identical constraint, speed of the present invention
Loss late is about 70% or so, and uses commercialization S type acceleration and deceleration methods, and speed loss rate is all more than 85%；
(3) using based on given accuracy B-spline fitting algorithms generation increment type time parameter polynomial surface processing rail
Mark, can realize the characterization to speed planning data under given accuracy, and the characterization time parameter multinomial of generation reduces speed
Data volume after metric stroke, amount of data compression are more than 80%, and generation uses increment type time parameter multinomial can be effective
Reduce cumulative errors；
(4) using time parameter polynomial interpolator method, the parameter curve geometry for avoiding large amount of complex is calculated, is counted in real time
It calculates simply, real-time computational accuracy is higher, and it is good to calculate robustness in real time.
Description of the drawings
Fig. 1 is flow chart of the present invention.
1 artificial tooth corona parametric type track machining path schematic diagram of Fig. 2 embodiments.
Fig. 3 a are acceleration plots.
Fig. 3 b are speed curve diagram.
Fig. 4 acceleration increasing process encounters schematic diagram when acceleration violates constraint.
The 1 artificial tooth corona speed schematic diagram of embodiment that Fig. 5 is planned using the present invention.
1 artificial tooth corona X-axis speed planning of Fig. 6 embodiments is as a result, fitting of a polynomial result and error of fitting schematic diagram.
1 artificial tooth corona Y-axis speed planning of Fig. 7 embodiments is as a result, fitting of a polynomial result and error of fitting schematic diagram.
1 artificial tooth corona Z axis speed planning of Fig. 8 embodiments is as a result, fitting of a polynomial result and error of fitting schematic diagram.
Fig. 9 uses 1 artificial tooth corona Free-form Surface Parts result figure of process embodiment of the present invention.
2 artificial tooth root parameters type track machining path schematic diagram of Figure 10 embodiments.
The 2 artificial tooth root of the tooth speed schematic diagram of embodiment that Figure 11 is planned using the present invention.
2 artificial tooth root of the tooth X-axis speed planning of Figure 12 embodiments is as a result, fitting of a polynomial result and error of fitting schematic diagram.
2 artificial tooth root of the tooth Y-axis speed planning of Figure 13 embodiments is as a result, fitting of a polynomial result and error of fitting schematic diagram.
2 artificial tooth root of the tooth Z axis speed planning of Figure 14 embodiments is as a result, fitting of a polynomial result and error of fitting schematic diagram.
Figure 15 uses 2 artificial tooth root of the tooth Free-form Surface Parts result figure of process embodiment of the present invention.
Specific embodiment
Below in conjunction with the accompanying drawings, the present invention is further described by embodiment.Following embodiment will be helpful to ability
The technical staff in domain further understands the present invention, but the invention is not limited in any way.It should be pointed out that this field
For those of ordinary skill, without departing from the inventive concept of the premise, various modifications and improvements can be made.These all belong to
In protection scope of the present invention.The implementation of the present invention is described in detail, but protection scope of the present invention is unlimited below in conjunction with attached drawing
In following embodiments.
As shown in Figure 1, included using the idiographic flow of the NC Machining of Free-form Surfaces method of time parameter polynomial interpolator：
The parametric type Machining of Curved Surface track designed first according to processing curve and the shape of tool, such as NURBS, carry out speed planning.Speed
Metric draw optimal objective for so that process time it is most short, be constrained to according to machining accuracy and process unit ability propose it is various about
Beam.After constructing speed planning mathematical model, constraint is simplified with introducing the method for proportionality coefficient using triangle inequality,
So that then constraint carries out speed rule only with machining locus relating to parameters using the prediction look-ahead algorithm based on principle of minimum
It draws.A large amount of discrete datas are obtained after the completion of speed planning, are not easy to real-time interpolation application.The present invention proposes in order to solve this problem
Time parameter multinomial teeth processing route generating method based on B-spline.This method uses the B- of given accuracy first
Spline approximating methods characterize speed planning as a result, B-spline then is converted to increment type time parameter multinomial.Finally
Reality will be inputed to using the Free-Form Surface Machining data comprising geometry and velocity information of increment type time parameter multinomial characterization
When time parametric polynomial interpolation algorithm, by real-time interpolation control lathe according to locus with planning speed run.It is real
The Free-Form Surface Machining of existing high speed and super precision.
Embodiment 1：
The present embodiment uses numerically-controlled machine tool to include real-time machine tool controller and machine body, and machine body includes workbench
With three kinematic axis.
1st, it is tested using one section of parametric type artificial tooth corona Machining of Curved Surface track as shown in Figure 2.This hair is used first
It is bright that speed planning is carried out to this section of track：
(1) speed planning model
In formulaWithIt is speed, acceleration and the acceleration of trajectory range；Flim,Alim,JlimFor trajectory range
Speed, acceleration and acceleration constraint,Represent speed, acceleration and the acceleration of the i-th axis；
Represent the constraint of the speed of the i-th axis, acceleration and acceleration.
In the present embodiment, according to machining accuracy with equipment characteristic, select constraints for：
Each axis kinematical constraint of 1 lathe of table
Table 2 is along track kinematical constraint
(2) constraint simplifies
Wherein kinematic axis constraint of velocity processing formula is：
Wherein moving axle acceleration constraint processing formula is：
Wherein kinematic axis acceleration constraint processing formula be：
δ in formula1With δ2For acceleration proportionality coefficient, μ1,μ2With μ3For acceleration proportionality coefficient, proportionality coefficient is according to lathe
It is selected with track characteristic.Q in formulas,qss,qsssIt is parameter of curve to the single order of curve arc long, second order and three order derivatives.
The 3 constraints conversion factor of table
(3) prediction look-ahead velocity planning
Constraint simplify after, there is only with the relevant constraint of trajectory parameters.Using the method for prediction prediction to Machining of Curved Surface mistake
Cheng Jinhang speed plannings.It predicts prediction process as shown in Figure 3a and Figure 3b shows, is added first since current point with the minimum of permission
Speed is slowed down, and acceleration is reduced to zero, then proceedes to successively decrease to acceleration with minimum acceleration, often successively decreases a step again
Acceleration is incremented to zero until decrease of speed is until zero with maximum acceleration.In this process respectively to speed, acceleration
Degree and acceleration constraint are tested.
Continue depletion stage in acceleration, if there is tracing point violates acceleration constraint, then violate adding at tracing point
Acceleration is recalculated according to acceleration constraint.After obtaining acceleration, then predict that deceleration algorithm continues.If there is tracing point
Constraint of velocity is violated, then the point could be provided as violating the crucial tracing point of constraint.Machining locus need to be decelerated to from initial track point
The crucial tracing point of constraint is violated, ways of deceleration slows down according to prediction prediction searching method.
Zero process is incremented in acceleration, violates acceleration constraint if there is tracing point, then as shown in figure 4, acceleration
Increasing process needs to stop.Deceleration prediction process decelerates to the point, and prediction prediction process is continued to execute since the point up to adding
Speed and speed are all kept to zero, and constantly detect each constraint.
Zero process is incremented in acceleration, violates constraint of velocity if there is tracing point, then the acceleration increasing process stops
Only, acceleration decrementing procedure is then carried out again.If reached at violation speed trajectory point, speed still violates constraint of velocity,
Then above process cycle carries out.If speed meets constraint requirements when reaching this, which is track key point machining locus
The crucial tracing point of violation constraint need to be decelerated to from initial track point, ways of deceleration slows down according to prediction prediction searching method.
The results are shown in Figure 5 for speed planning, average speed 10.99mm/s, and speed loss rate is 70%.According to part
Enlarged drawing can be seen that the continuity of rate curve.But speed planning result is a large amount of discrete data, data volume is 100,000
A data point, each data point dimension are four, time interval 1ms.In order to reduce data volume, the practicality of speed planning is improved
Property.The present invention is characterized using the relationship that the time parameter multinomial based on B-spline changes over time each shaft position.
Data volume after being characterized using cubic polynomial is about 10,000, and each data point dimension is seven.Amount of data compression is 80%.
2nd, the time parameter multinomial machining locus generation based on B-spline：
In B-spline fit procedures, it is preferred that ask for fitting B- using the node Forecasting Methodology of given accuracy
Spline knot vectors, specific determination process are as follows：
The position data { t, p } of each kinematic axis at any time is fitted for n times B-spline, error of fitting may be used down
Formula is estimated：
ε is the n times B-spline errors of fitting of estimation in formula,It is each axis maximum displacement to time n times derivative value
The vector of composition,For the vector that each axis least displacement forms time n times derivative value, Δ t is the n times B- of time parameter
Spline node intervals.
According to assigned error in the error of fitting of estimation and the present embodiment be δ=0.001mm, the determining algorithm of knot vector
It is as follows：
Step a：Given first nodal value of knot vector is the time T for being fitted former first position of data1=t1, i=
1, j=1；
Step b：I=i+1, and judge whether i is equal to former discrete data quantity, if equal go to step d；It is unequal
When, sequence performs step c；
Step c：Computation interval [Tj,ti] n times B-spline error of fitting ε, and judge whether ε is more than or equal to given fitting
Error delta, if meeting ε >=δ, it is determined that next node vector is Tj+1=tiAnd j=j+1；Go to step b；
Step d：Enable knot vector Tj+1Equal to the former data endpoint time, end node vector calculates；
In order to reduce cumulative errors, it is multinomial that time parameter B-spline tracks are converted into increment type time parameter by the present invention
Formula.Time parameter B-spline machining locus is converted into the polynomial surface machining locus algorithm using split time as parameter
For：
It is for p time parameter B-spline：
It is for increment type p order polynomials：
P(p)(t)=a0+a1·t+a2·t2+a3·t3…+an·tp,0≤t≤T
A=[a0,a1,…ap]
P(p)(t)=A λTλ=[1, t, t2,…tp]
For odd times time parameter B-spline, in node interval [ti,ti+1] be converted to increment type time parameter multinomial
Algorithm is：
By time parameter B-spline in node interval [ti,ti+1] functional value at corresponding endpoint is calculated with accordingly leading
Numerical valueFor p B-spline,
Hermite interpolation may be used by L vectors and directly obtain the coefficient vector A of p order polynomials and time variable section T.
For even time parameter B-spline, in node interval [ti,ti+1], i=1,3,5 ... .. are converted to increment type
Time parameter multinomial algorithm is：
By time parameter B-spline in node interval [ti,ti+1] functional value at corresponding endpoint is calculated with accordingly leading
Numerical valueFor p B-spline, by L
Vector may be used Hermite interpolation and directly obtain the coefficient vector A of p order polynomials and time variable section T.
For even time parameter B-spline, in node interval [ti+1,ti+2], i=1,3,5 ... .. are converted to increment
Formula time parameter multinomial algorithm is：
By time parameter B-spline in node interval [ti+1,ti+2] functional value at corresponding endpoint is calculated with accordingly leading
Numerical valueFor p B-
Spline may be used Hermite interpolation by L vectors and directly obtain the coefficient vector A of p order polynomials and time variable area
Between T.
Fig. 6, Fig. 7, Fig. 8 are that each shaft position generated using the present invention changes over time function curve, and according in figure
Each axis characterization error can illustrate that the precision of polynomial fitting method proposed by the present invention meets the requirement of 0.001mm.
3rd, time parameter multinomial real-time online interpolation algorithm, it is specific as follows：
According to the split time parametric polynomial track that p B-spline machining locus of time parameter is converted into, more than i-th section
Binomial coefficient vector is AiIf total elapsed time is T this moment, t is divided between each section of time parameter polynomial timej。
Then time variableFor：
Variable vector λiFor：
It is in each axis of motion position calculation formula that the moment interpolation obtains：
P(p)=Ai·λi T
The algorithm is write on real-time controller, and control lathe moves, the present invention is multinomial using time parameter
Formula interpolation algorithm reduces real-time calculation amount, improves and calculates robustness in real time.Fig. 9 is digital control processing side using the present invention
The artificial tooth corona mercolized wax mould of method processing illustrates the practicability of the present invention.
Embodiment 2：
The present embodiment uses numerically-controlled machine tool with embodiment 1.
Versatility in order to further illustrate the present invention selects one section of parametric type artificial tooth root of the tooth curved surface as shown in Figure 10 to add
It is tested work track.The constraint of selection and conversion factor are same as Example 1.Using the present invention to this section of track into scanning frequency
Metric is drawn, and the result of speed planning is as shown in figure 11, average speed 9.78mm/s, and speed loss rate is 73%.According to part
Enlarged drawing can be seen that the continuity of rate curve.Similarly in order to reduce data volume, the practicability of speed planning result is improved.
The relationship changed over time using the present invention to each shaft position of speed planning result is characterized, amount of data compression 83%.Root
According to Figure 12, the characterization error of each axis of Figure 13, Figure 14 can illustrate that the precision of polynomial fitting method proposed by the present invention meets and want
It asks.Figure 15 is the artificial tooth diseased Root Surfaces wax-pattern of numerical-control processing method using the present invention processing, illustrates the versatility of the present invention.
Specific embodiments of the present invention are described above.It is to be appreciated that the invention is not limited in above-mentioned
Particular implementation, those skilled in the art can make various deformations or amendments within the scope of the claims, this not shadow
Ring the substantive content of the present invention.
Claims (7)
1. a kind of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator is processed freely suitable for numerically-controlled machine tool
Curved surface, the numerically-controlled machine tool include real-time machine tool controller and machine body, it is characterised in that including three operating procedures：
(1) prediction look-ahead velocity planning
By reading parameter curve type Free-Form Surface Machining track and carrying out speed planning, the free form surface for generating high speed and super precision adds
Work process discrete data；
(2) the time parameter multinomial machining locus generation based on B-spline
The Free-Form Surface Machining process discrete data that step (1) generates is carried out using the B-spline fitting techniques of given accuracy
Characterization, is then converted into succinct increment type time parameter polynomial surface machining locus；
(3) time parameter multinomial real-time interpolation
According to increment type time parameter polynomial surface machining locus, corresponding real-time interpolation is write in real-time machine tool controller and is calculated
Free form surface high speed and high precision processing is completed in method, control numerically-controlled machine tool movement；
By the NC Machining of Free-form Surfaces method, the contour accuracy and surface quality of processed free form surface are improved,
Free-Form Surface Machining efficiency is significantly improved, reduces data volume needed for Free-Form Surface Machining.
2. a kind of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator according to claim 1,
It is characterized in that concrete operation step is as follows：
(1) prediction look-ahead velocity planning
(1.1) according to requirement on machining accuracy and process unit service ability extraction most high-order for three times speed planning kinematics about
Beam, and dimensionality reduction simplification is carried out to kinematical constraint with introducing the method for proportionality coefficient using triangle inequality, institute's Constrained is turned
Turn to the one-dimensional constraint related with parameter of curve；
The speed planning kinematical constraint includes each kinematic axis constraint of lathe and is constrained with processing technology；
(1.2) along machining locus, pre-decelerating is carried out to the tracing point for violating one-dimensional constraint using prediction look-ahead approach, is being looked forward to the prospect
Accelerate a time step if without the tracing point for violating one-dimensional constraint in the process；According to the discrete meter based on minimal principle
Calculation method, with most Higher-order Constraint calculate acceleration, then by numerical integration be calculated satisfaction constraint and processing efficiency most
Excellent Machining of Curved Surface process discrete data；
(2) the time parameter multinomial machining locus generation based on B-spline
(2.1) the Machining of Curved Surface process discrete data completed according to speed planning, is intended using the B-spline of time parameter
It closes, B-spline knot vectors is asked for using the node Forecasting Methodology of given accuracy in fit procedure, and using least square
Method solves control point；Finally Machining of Curved Surface process is characterized with the B-spline of time parameter, obtains B-
Spline machining locus；
(2.2) using B-spline- multinomials transfer algorithm (being converted into multinomial by B-spline), B-spline is processed into rail
Mark is converted into increment type time parameter polynomial surface machining locus；
(3) time parameter multinomial Real-time interpolation algorithm
Time parameter multinomial real-time interpolation program is write in real-time machine tool controller, according to the increasing obtained by step (2.2)
Amount formula time parameter polynomial surface machining locus controls numerically-controlled machine tool to move by real-time interpolation program, realizes that free form surface is high
Fast high finishing.
3. the NC Machining of Free-form Surfaces method according to claim 2 using time parameter polynomial interpolator, feature
It is：In step (1.1), by introducing proportionality coefficient, to lathe, each kinematic axis constraint carries out with using triangle inequality method
Simplify：
The constraint of machine tool motion axis is summarized as follows
In formula,Represent speed, acceleration and the acceleration of the i-th axis；It represents the speed of the i-th axis, add
The constraint of speed and acceleration；
It is converted by introducing proportionality coefficient with axle acceleration will be moved using triangle inequality method with acceleration Multi-dimensional constraint
For the one-dimensional constraint related with parameter of curve；Wherein acceleration constraint processing formula be：
Wherein acceleration constraint processing formula be：
δ in formula1With δ2For acceleration proportionality coefficient, μ1,μ2With μ3For acceleration proportionality coefficient, proportionality coefficient is according to lathe and rail
Mark feature selecting；In formulaWithIt is speed, acceleration and the acceleration of trajectory range respectively；Q in formulas,qss,qsssRespectively
It is parameter of curve to the first derivative of curve arc long, second dervative and three order derivatives.
4. the NC Machining of Free-form Surfaces method according to claim 2 using time parameter polynomial interpolator, feature
It is：In step (1.2), pre-decelerating, concrete operations are carried out to the following tracing point for violating constraint using prediction look-ahead approach
It is as follows：
Prediction prediction moderating process subtracts acceleration to be slowed down first since current point with the minimum acceleration of permission
To zero, then proceed to successively decrease to acceleration with minimum acceleration, a step of often successively decreasing is again by acceleration with maximum acceleration
Zero is incremented to until decrease of speed is until zero；The constraint of speed, acceleration and acceleration is examined respectively in this process
It tests；
It is decremented in zeroth order section in initial acceleration if there is tracing point violates velocity and acceleration constraint, then the point can be set
Crucial tracing point is constrained to violate；Machining locus need to decelerate to the crucial tracing point of violation constraint, ways of deceleration from initial track point
Slow down according to prediction prediction searching method；
Continue depletion stage in acceleration, if there is tracing point violates acceleration constraint, then violating at tracing point plus accelerating
Degree is recalculated according to acceleration constraint；After obtaining acceleration, then predict that deceleration algorithm continues；If there is tracing point violates
Constraint of velocity, then the point could be provided as violate constraint of velocity key tracing point；Machining locus need to be decelerated to from initial track point
Constraint of velocity key tracing point is violated, ways of deceleration slows down according to prediction prediction searching method；
Zero process is incremented in acceleration, violates acceleration constraint if there is tracing point, then acceleration increasing process needs stop
Only；Deceleration prediction process decelerates to the point, and prediction prediction process is continued to execute since the point up to acceleration and speed all subtract
It is zero, and constantly continues to detect each constraint；
Zero process is incremented in acceleration, violates constraint of velocity if there is tracing point, then the acceleration increasing process stops, so
Carry out acceleration decrementing procedure again afterwards；If reached at violation speed trajectory point, speed still violates constraint of velocity, then above-mentioned
Process cycle carries out；If speed meets constraint requirements when reaching this, which need to be from first for track key point machining locus
Beginning tracing point decelerates to the crucial tracing point of violation constraint, and ways of deceleration slows down according to prediction prediction searching method.
5. the NC Machining of Free-form Surfaces method according to claim 2 using time parameter polynomial interpolator, feature
It is：In step (2.1), fitting B-spline knot vectors are asked for using the node Forecasting Methodology of given accuracy, it is specific to determine
Process is as follows：
The position data { t, p } of each kinematic axis at any time is fitted for n times B-spline, error of fitting may be used following formula into
Row estimation：
ε is the n times B-spline errors of fitting of estimation in formula,Time n times derivative value is formed for each axis maximum displacement
Vector,For the vector that each axis least displacement forms time n times derivative value, Δ t is time parameter n times B-spline's
Node interval；
According to the error of fitting ε of estimation, under assigned error δ, the determining algorithm of knot vector is as follows：
Step a：Given first nodal value of knot vector is the time T for being fitted former first position of data1=t1, i=1, j
=1；
Step b：I=i+1, and judge whether i is equal to former discrete data quantity, if equal go to step d；It is suitable when unequal
Sequence performs step c；
Step c：Computation interval [Tj,ti] n times B-spline error of fitting ε, and judge whether ε is more than or equal to given error of fitting
δ, if meeting ε >=δ, it is determined that next node vector is Tj+1=tiAnd j=j+1；Go to step b；
Step d：Enable knot vector Tj+1Equal to the former data endpoint time, end node vector calculates.
6. the NC Machining of Free-form Surfaces method according to claim 2 using time parameter polynomial interpolator, feature
It is：In step (2.2), time parameter B-spline machining locus is converted into the processing of increment type time parameter polynomial surface
The algorithm of track is：
It is for p time parameter B-spline：
It is for increment type p order polynomials：
P(p)(t)=a0+a1·t+a2·t2+a3·t3…+an·tp,0≤t≤T
A=[a0,a1,…an]
P(p)(t)=A λTλ=[1, t, t2,…tp]
For odd times time parameter B-spline, in node interval [ti,ti+1] be converted to increment type time parameter multinomial algorithm
For：
By time parameter B-spline in node interval [ti,ti+1] calculate functional value at corresponding endpoint and respective derivative valueFor p B-spline, by L
Vector may be used Hermite interpolation and directly obtain the coefficient vector A of p order polynomials and time variable section T.
For even time parameter B-spline, in node interval [ti,ti+1], i=1,3,5 ... .. are converted to the increment type time
Parametric polynomial algorithm is：
By time parameter B-spline in node interval [ti,ti+1] calculate functional value at corresponding endpoint and respective derivative valueFor p B-spline, by L vectors
Hermite interpolation may be used and directly obtain the coefficient vector A of p order polynomials and time variable section T；
For even time parameter B-spline, in node interval [ti+1,ti+2] i=1,3,5 ... .. be converted to the increment type time
Parametric polynomial algorithm is：
By time parameter B-spline in node interval [ti+1,ti+2] calculate functional value at corresponding endpoint and respective derivative valueFor p B-spline,
Hermite interpolation may be used by L vectors and directly obtain the coefficient vector A of p order polynomials and time variable section T.
7. the NC Machining of Free-form Surfaces method according to claim 2 using time parameter polynomial interpolator, feature
It is, in step (3), time parameter multinomial Real-time interpolation algorithm is：
According to the increment type split time Parametric polynomial surface machining locus that step (2) generates, i-th section of system of polynomials number vector
For AiIf total elapsed time is T this moment, t is divided between each section of time parameter polynomial timej；
Then time variableFor：
Variable vector λiFor：
It is in each axis of motion position calculation formula that the moment interpolation obtains：
It is T according to interpolation algorithm and total elapsed time, you can acquire each movement shaft position of the moment lathe, process successively
Complete Free-Form Surface Machining.
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