CN107272598A - Nurbs curve interpolating method known to a kind of machining path length - Google Patents
Nurbs curve interpolating method known to a kind of machining path length Download PDFInfo
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Abstract
The present invention provides nurbs curve interpolating method known to a kind of machining path length, calculates accelerator displacement and moderating process displacement in the flexible acceleration and deceleration method of five-part form；Speed planning species is classified according to machining path length；Calculate nurbs curve total interpolation points of the machining path length for L；Calculate current interpolated point feed speed；Obtain each interpolation cycle interpolated points'parameter and coordinate value, handled by acceleration and deceleration before interpolation, meeting on lathe acceleration and deceleration capability foundation discussion, processing feed speed is improved to greatest extent, due to being that acceleration and deceleration are handled before interpolation, without adjusting interpolated points'parameter again, machining accuracy can not only be so improved, High-speed machining is also achieved.
Description
Technical field
The present invention relates to nurbs curve interpolating method known to a kind of machining path length.
Background technology
High speed and high precision processing does not require nothing more than digital control system and possesses real-time interpolation algorithm, and control accuracy must reach Asia
Micron order, the real-time of interpolation algorithm even decides the possibility that High-speed machining is realized.Non-uniform rational B-spline (Non-
Uniform Rationa1 B-spline, NURBS) curve has good shape ability to express, in automobile, aircraft, shipbuilding etc.
Application is more and more wider in terms of the shape-designing of type surface parts and processing and manufacturing, it has also become freedom of expression curve and surface in STEP-NC
Unique forms.It is terse with the processed file code that NURBS forms are represented, and without loss of significance, its size of code only has tradition
The 1/10~1/100 of NC codes, with the advantage that small section of straight line is incomparable.But, digital control system will can support NURBS bent
Line five-part form flexibility acceleration and deceleration interpolation, it is necessary to first construct the flexible acceleration and deceleration interpolator of nurbs curve five-part form, interpolation rate and essence
Degree is directly influenceed by interpolator.
Digit Control Machine Tool in process, when running into startup, stopping or intersegmental switching, if velocity variations are too big, has
Greater impact may be produced in itself to lathe, cause motor concussion and step-out etc., machining accuracy will be impacted, or even harm
The lathe life-span.Usual way is that speed is controlled in lathe startup, stopping and intersegmental switching, that is, is carried out at acceleration and deceleration
Reason.Startup stage is lathe is accelerated feeding by increasing feeding pulse frequency, and lathe stop phase is by reducing feeding arteries and veins
Frequency is rushed, makes lathe slow down until speed is zero.Speed planning quality plays crucial work for the flatness of machine tool motion
With for realizing that high speed and high precision processing is significant.
Common Acceleration-deceleration Control Method has：Linear acceleration and deceleration method, Exponential acceleration and deceleration method etc..Linear acceleration and deceleration method is calculated
Complexity is not high, easily realizes, its rate control process is that speed is adjusted in proportion according to the time, but this method is smooth
Property is poor.The realization of Exponential acceleration and deceleration method is also simple, and it is to adjust feed speed according to exponential law, and its flatness is preferable.
But both approaches can all have velocity jump in acceleration incipient stage and deceleration ending phase, cause acceleration discontinuous,
So as to produce the service life of greater impact, the crudy of influence part, and lathe to lathe.
Using traditional line and Exponential acceleration and deceleration method, can not meet processing part it is increasingly sophisticated, processing element precision
The requirement of continuous improvement, in order to adapt to the property complicated and changeable of modern digital control processing workpiece, it is ensured that the machining accuracy and lathe of workpiece
Service life, flexibility plus-minus the short-cut counting method also increasingly favored.On the one hand, flexible acceleration and deceleration can be according to working motion
Maximal rate, output pulse frequency etc., construct suitable acceleration and deceleration characteristic curve；On the other hand, flexible acceleration and deceleration are in control system
Changeable acceleration and deceleration curves are realized in system using specific process, traditional its speed of acceleration and deceleration method are compared to excessively more flat
It is suitable.
It is inevitable due to the presence of curvature when acceleration and deceleration curved surface flexible using high-speed cutting processing nurbs curve five-part form
Larger velocity perturbation can be caused., will more than the design ability to bear of Machine Tool Feeding System dynamic rate if acceleration is excessive
Crudy to whole system of processing, process and part causes to have a strong impact on.Add therefore, it is necessary to design good flexibility
Method for slowing-down control, control acceleration, acceleration changing pattern, realizes the smoothing processing of speed.
Nurbs curve direct interpolation technology has the advantages that high speed, high accuracy and great surface quality, compared to traditional short straight line
Interpolation, with inborn advantage, still, because nurbs curve uses special analytic expression structural form, direct interpolation is also present
Some technical barriers：
First, nurbs curve direct interpolation pursues high speed and high-precision Problems.Nurbs curve direct interpolation is in rule
The interpolated point for meeting machine tooling characteristic is calculated in fixed interpolation cycle, it is necessary first to obtain the parameter of these points, then by NURBS
Curve definitions formula obtains interpolation point coordinates.During nurbs curve interpolation, to realize High-speed machining, it is desirable to which The faster the better for speed, still
It is at a high speed and high in some radius of curvature smaller parts, it is necessary to reduce speed to improve machining accuracy in order to meet high finishing requirements
Finishing can not get both sometimes.Accordingly, it would be desirable to which on the basis of machining accuracy is met, process velocity is improved as far as possible；
Second, nurbs curve direct interpolation need to carry out feed speed control.Traditional acceleration and deceleration method typically takes speed controlling after interpolating
Control method, its way is the parameter for first calculating interpolated point, then carries out rate smoothing processing to the interpolated point again, due to
The special structural form of nurbs curve definition, this method needs to calculate interpolated points'parameter twice, there is certain error.
The content of the invention
The technical problem to be solved in the present invention, is to provide nurbs curve interpolation side known to a kind of machining path length
Method, directly judges acceleration and deceleration classification by nurbs curve segment length, is handled by acceleration and deceleration before interpolation, is meeting lathe acceleration and deceleration
On capability foundation discussion, processing feed speed is improved to greatest extent, because acceleration and deceleration are handled before formula interpolation, without adjusting interpolated point again
Parameter, can not only so improve machining accuracy, also achieve High-speed machining.
What the present invention was realized in：Nurbs curve interpolating method known to a kind of machining path length, including following step
Suddenly：
Accelerator displacement and moderating process displacement in step 1, the flexible acceleration and deceleration method of calculating five-part form；
Step 2, according to machining path length speed planning species is classified；
Step 3, calculating machining path length are counted for the L total interpolation of nurbs curve；
Step 4, the current interpolated point feed speed of calculating；
Step 5, each interpolation cycle interpolated points'parameter of acquisition and coordinate value.
Further, the step 1 further comprises：
Using the flexible acceleration and deceleration method of five-part form, t is made1For acceleration duration, t2To subtract acceleration duration, t3For constant velocity stage
Duration, t4For acceleration and deceleration duration, t5To subtract decelerating phase duration, amaxFor system maximum permissible acceleration；Five-part form flexibility is made to add
Deceleration commencing speed is vsWith end speed ve；Then each phases-time is：
Wherein v is interpolation command speed；
Make s1To add boost phase displacement, s2To subtract boost phase displacement, s3For constant velocity stage's displacement, s4For acceleration and deceleration rank
Section is moved, s5To subtract decelerating phase displacement；Then each phase displacement equation is：
Wherein v0To add boost phase commencing speed, v1To subtract boost phase commencing speed, v2For constant velocity stage's speed, v3
For acceleration and deceleration stage commencing speed, v4To subtract decelerating phase commencing speed；
Wherein k is customized constant value, by the t in (3-1) formula1、t2、t3、t4、t5Substitute into (3-2), calculating obtains s1、
s2、s3、s4、s5；
The flexible acceleration and deceleration of nurbs curve five-part form to be processed are carried out at speed planning using the flexible acceleration and deceleration of five-part form
Reason, including accelerate, subtract accelerations, at the uniform velocity, acceleration and deceleration, slow down five stages, wherein accelerate, subtract acceleration for accelerator,
Acceleration and deceleration, deceleration are moderating process, make s1To add boost phase displacement, s2To subtract boost phase displacement, s3For constant velocity stage position
Move, s4For acceleration and deceleration phase displacement, s5To subtract decelerating phase displacement, then
Accelerator displacement SaccFor：
Sacc=s1+s2
At the uniform velocity process displacement is Scon：
Scon=s3
Moderating process displacement SdecFor：
Sdec=s4+s5。
Further, the step 2 further comprises：
It is L to make the flexible acceleration and deceleration path length of nurbs curve five-part form to be processed, right according to machining path length L values
Nurbs curve five-part form flexibility acceleration and deceleration speed planning is classified：
(2) the complete acceleration and deceleration of constant velocity stage are included
If L ＞ Sacc+Sdec, then there is accelerator, at the uniform velocity process and moderating process, it is each comprising the flexible acceleration and deceleration of five-part form
Individual stage, speed reaches system maximum permission speed；
(2) the complete acceleration and deceleration of constant velocity stage are not included
If L=Sacc+Sdec, then there is accelerator and moderating process, not comprising at the uniform velocity process, speed reaches that system is maximum
Permissible velocity；
(5) not exclusively acceleration and deceleration
If L ＜ Sacc+Sdec, due to being influenceed by distance factor, treat that interpolation path length is less than actual accelerator with subtracting
Fast process path sum, then accelerator and moderating process can not be fully completed, the maximum feed speed that can actually reach is less than
Command speed.
Further, the step 3 further comprises：
After being divided into three classes according to machining path length to speed planning, each speed planning interpolation points are calculated respectively
Amount；
(1) the complete acceleration and deceleration of constant velocity stage are included
Now, the flexible acceleration and deceleration speed planning of five-part form includes whole 5 ranks of accelerator, at the uniform velocity process and moderating process
Section, speed reaches command speed F, and acceleration and acceleration reach peak acceleration and acceleration, according to step 1 Chinese style
(3-1) obtains accelerator plus boost phase, subtracts boost phase duration t1、t2, and acceleration and deceleration and subtract the time in decelerating phase
t4And t5, and actual acceleration distance S'accWith deceleration distance S'dec,
Then have：
Wherein vsFor commencing speed, veTo terminate speed,
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
(2) the complete acceleration and deceleration of constant velocity stage are not included
Now, 4 stages of the flexible acceleration and deceleration speed planning of five-part form comprising accelerator and moderating process, speed reaches
Command speed F, acceleration and acceleration reach peak acceleration and acceleration, not comprising at the uniform velocity process, according to formula (3-1)
Obtain the accelerator acceleration stage, subtract boost phase duration t1、t2、t4And t5,
Wherein vsFor commencing speed, veTo terminate speed,
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
(6) not exclusively acceleration and deceleration
Now, 4 stages of the flexible acceleration and deceleration speed planning of five-part form comprising accelerator and moderating process, maximal rate
Command speed F can not be reached, not comprising at the uniform velocity process, t3=0,
Accelerating region and deceleration section length are respectively the half for treating interpolation path length in the speed planning species, i.e.,：Sacc=
Sdec=L/2；
Consider accelerator, obtaining accelerator displacement according to formula (3-2) is：
Obtained by two formulas above：
The formula is unary biquadratic equation, is calculated by Descartes's method or Ferrari method and obtains real root ta, then have：
t1=t2=ta
Similarly moderating process subtracts acceleration and subtracts deceleration time and is：
t4=t5=tb
The maximum feed speed that can be reached is：
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
Further, the step 4 further comprises：
Five-part form flexibility acceleration and deceleration method, rate equation is：
Wherein, T0=0, T1=t1, T2=T1+t2, T3=T2+t3, T4=T3+t4, T5=T4+t5；
t1For acceleration duration, t2To subtract acceleration duration, t3For constant velocity stage's duration, t4For acceleration and deceleration duration, t5To subtract
Fast stage duration；After the nurbs curve that machining path length is L is inputted, by the processing of step 1, step 2 and step 3, obtain
To the nurbs curve speed planning type that current length is L, and interpolated point number is N,
Further, if current interpolated point is n, n=1,2 ..., N,
Then current interpolation moment t=nT, wherein T are interpolation cycle
Current interpolated point C (u are then calculated according to formula (5-1)i) feed speed be v (ui)。
Further, the step 5 further comprises：
In each interpolation cycle, it is known that current interpolated points'parameter vector ui, using Taylor series expansion method, by parameter uiIt is right
Time t carries out Taylor expansion, calculates the locus point C (u that next cycle should reachi+1) parameter vector ui+1, formula is：
Wherein T represents interpolation cycle, and H.O.T is Taylor expansion higher order term, makes current interpolated point C (ui), its feed rate
Obtained by step 4, be v (ui)；
Parameter u is to time t first approximation expression formula：
Parameter u is to time t Two-order approximation expression formula：
Nurbs curve expression formula C (u) is：
Wherein PiFor your control point information, wiFor weight factor information, p is nurbs curve number of times,
N in formulai,p(u) it is p specification B-spline basic function, by following formula recurrence calculation：
Wherein, U={ u0,u1,...,un+p+1It is referred to as knot vector, u is the independent variable of nurbs curve；
Therefore, according to current interpolated point feed speed v (ui) and nurbs curve definition, pass through formula (6-2) and (6-3)
The single order for calculating nurbs curve is led and led with second order, then substitutes into formula (6-1), calculates next interpolated points'parameter ui+1, i.e., under
One interpolated point C (ui+1)。
The invention has the advantages that：Nurbs curve interpolating method known to a kind of machining path length of the present invention, can be with
Directly according to length of curve to be processed, the species of speed planning is judged, and to each speed planning species, can directly obtain
Interpolation is counted, and each interpolation cycle interpolated point feed speed, then according to these information, obtains the position of next interpolated point
Put, the present invention not only realizes rate smoothing interpolation, and the invention is simple and practical, be easy to design to realize.
Brief description of the drawings
The present invention is further illustrated in conjunction with the embodiments with reference to the accompanying drawings.
Fig. 1 is a kind of flow chart one of nurbs curve interpolating method known to machining path length.
Fig. 2 is nurbs curve interpolating method flowchart 2 known to a kind of machining path length.
Embodiment
The present invention is nurbs curve interpolating method known to a kind of machining path length.In the method, user inputs
The machining code stated with nurbs curve is parsed by CNC interpreters, explains nurbs curve information, and by offline pre-
Curve is segmented by processing according to curve geometrical property, is obtained comprising nurbs curve segment length, head and the tail end points parameter vector etc.
Data.Then, speed planning processing is carried out to nurbs curve using five-part form flexible acceleration and deceleration, according to five-part form acceleration and deceleration mould
Type calculates accelerator and moderating process displacement respectively, and then according to nurbs curve length to be processed, speed planning is divided into 3
Class, is inputted after nurbs curve segment length to be processed, is entered in corresponding classification processing, obtains correspondence interpolated point sum, then
Further according to the flexible acceleration and deceleration speed planning method of five-part form, the feed speed of each interpolated point is calculated, afterwards, then by current point
Parameter vector, feed speed obtain next interpolated points'parameter vector.Obtain next interpolated points'parameter vector, you can according to two
The distance between point, decomposites each axle feeding component, then drives each axle to complete to feed by drive system, realizes that nurbs curve is straight
Patch benefit.
As shown in figure 1, illustrate in detail included by nurbs curve interpolating method known to a kind of machining path length
Five parts, wherein the object that the result that each part is produced is handled as next partial data.
First part CNC explains the part machining code stated with nurbs curve of user's input, obtains NURBS bent
Line information；Part II CNC is pre-processed offline to nurbs curve, and nurbs curve is carried out with radius of curvature minimum point
Segmentation, and curve segment length and head and the tail parameter value are obtained, constitute the nurbs curve section of known paths；Part III, admission velocity
Speed planning, using the flexible acceleration and deceleration method of five-part form, is divided into three classes by planning by nurbs curve segment length to be processed；4th
Partial velocity planning is handled, and according to nurbs curve segment length to be processed, which class speed planning judgement is appropriate for, obtains the section
The total interpolation points in path；Part V, in each interpolation cycle, calculates next with information such as current interpolated point and feed speeds
Individual interpolated points'parameter, and each interpolated point coordinate value is obtained by NURBS definitions, complete Interpolation Process.
As shown in Fig. 2 illustrating nurbs curve section interpolation in detail implements step.
Step includes：
Step 1：Nurbs curve segment information to be processed, including curved section path length L, head and the tail endpoint parameter etc. are read, is held
Row step 2.
Step 2：According to nurbs curve to be processed section path length, judge that current curves section adapts to which type of speed
Plan species,
Perform step 3.
Step 3：The a length of L corresponding speed planning species of nurbs curve section, calculates its interpolated point total respectively by path
Number, performs step 4.
Step 4：Counter O reset is set, and counter prepares the record several numbers of interpolation, performs step 5.
Step 5：According to current interpolated points'parameter, current interpolated point feed speed calculates next interpolated points'parameter.Perform
Step 6
Step 6：According to nurbs curve definition, its coordinate value is calculated according to next interpolated points'parameter, step 7 is performed.
Step 7：Adjacent 2 points of distances and each axial coordinate component are calculated, it is dynamic to complete feeding by servo-drive system driving lathe
Make, realize that interpolated point is exported, perform step 8
Step 8：Counter adds up, if counter values are more than interpolated point sum, perform step 9, otherwise continues to hold
Row step 5.
Step 9：This section of nurbs curve interpolation is completed.
Nurbs curve interpolating method known to a kind of machining path length, comprises the following steps：
Step 1, using the flexible acceleration and deceleration method of five-part form, make t1For acceleration duration, t2To subtract acceleration duration, t3To be even
Fast stage duration, t4For acceleration and deceleration duration, t5To subtract decelerating phase duration, amaxFor system maximum permissible acceleration.
It is v to make the flexible acceleration and deceleration commencing speed of five-part form five-part formsWith end speed veMeet.
(3-1) then each phases-time is：
Wherein v is interpolation command speed.
Make s1To add boost phase displacement, s2To subtract boost phase displacement, s3For constant velocity stage's displacement, s4For acceleration and deceleration rank
Section is moved, s5To subtract decelerating phase displacement.
(3-2) each phase displacement equation is：
Wherein v0 is adds boost phase commencing speed, and v1 is subtracts boost phase commencing speed, and v2 is constant velocity stage's speed, v3
For acceleration and deceleration stage commencing speed, v0 is to subtract decelerating phase commencing speed.
Wherein k is constant value (value is typically set by experience, and the value size will influence acceleration change speed), will
T in (3-1) formula1、t2、t3、t4、t5Substitute into (3-2), it is possible to which calculating obtains s1、s2、s3、s4、s5。
The flexible acceleration and deceleration of nurbs curve five-part form to be processed are carried out at speed planning using the flexible acceleration and deceleration of five-part form
Reason, including accelerate, subtract accelerations, at the uniform velocity, acceleration and deceleration, slow down five stages, wherein accelerate, subtract acceleration for accelerator,
Acceleration and deceleration, deceleration are moderating process.Make s1To add boost phase displacement, s2To subtract boost phase displacement, s3For constant velocity stage position
Move, s4For acceleration and deceleration phase displacement, s5To subtract decelerating phase displacement.
Accelerator displacement SaccFor：
Sacc=s1+s2
At the uniform velocity process displacement is Scon：
Scon=s3
Moderating process displacement SdecFor：
Sdec=s4+s5
Step 2, the flexible acceleration and deceleration path length of nurbs curve five-part form to be processed is made to be L, according to machining path length L
Value, can classify to the flexible acceleration and deceleration speed planning of nurbs curve five-part form：
(3) the complete acceleration and deceleration of constant velocity stage are included
If L ＞ Sacc+Sdec, then there is accelerator, at the uniform velocity process and moderating process, it is each comprising the flexible acceleration and deceleration of five-part form
Individual stage, speed can reach system maximum permission speed.
(2) the complete acceleration and deceleration of constant velocity stage are not included
If L=Sacc+Sdec, then there is accelerator and moderating process, not comprising at the uniform velocity process, speed can reach system
Maximum permission speed.
(7) not exclusively acceleration and deceleration
If L ＜ Sacc+Sdec, due to being influenceed by distance factor, treat that interpolation path length is less than actual accelerator with subtracting
Fast process path sum, accelerator and moderating process can not be fully completed, and the maximum feed speed that can actually reach is less than finger
Make speed.
Step 3, speed planning is divided into three classes according to machining path length after, each speed planning interpolation is calculated respectively
Point quantity.
(1) the complete acceleration and deceleration of constant velocity stage are included
Now, the flexible acceleration and deceleration speed planning of five-part form includes whole 5 ranks of accelerator, at the uniform velocity process and moderating process
Section, speed can reach command speed F, and acceleration and acceleration can reach peak acceleration and acceleration.Can be according to step
Rapid 1 formula (3-1) obtains accelerator plus boost phase, subtracts boost phase duration t1、t2, and acceleration and deceleration and deceleration rank
Section time t4And t5, and actual acceleration distance S'accWith deceleration distance S'dec。
Then have：
Wherein vsFor commencing speed, veTo terminate speed
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
(2) the complete acceleration and deceleration of constant velocity stage are not included
Now, 4 stages of the flexible acceleration and deceleration speed planning of five-part form comprising accelerator and moderating process, speed is reachable
To command speed F, acceleration and acceleration can reach peak acceleration and acceleration, not comprising at the uniform velocity process.Can root
The accelerator acceleration stage is obtained according to formula (3-1), subtracted
Boost phase duration t1、t2、t4And t5。
Wherein vsFor commencing speed, veTo terminate speed
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
(8) not exclusively acceleration and deceleration
Now, 4 stages of the flexible acceleration and deceleration speed planning of five-part form comprising accelerator and moderating process, maximal rate
Command speed F can not be reached, not comprising at the uniform velocity process, t3=0.
Accelerating region and deceleration section length are respectively the half for treating interpolation path length in the speed planning species, i.e.,：Sacc=
Sdec=L/2；
Consider accelerator (moderating process can regard accelerator inverse process as, and method is identical), understood according to formula (3-2)
Accelerator displacement is：
It can be obtained by two formulas above：
The formula is unary biquadratic equation, can be calculated by Descartes's method or Ferrari method and obtain real root ta, then have：
t1=t2=ta
Moderating process can similarly be obtained subtract acceleration and subtract deceleration time and be：
t4=t5=tb
The maximum feed speed that can be reached is：
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
The flexible acceleration and deceleration method of step 4, (5-1) five-part form, rate equation is：
Wherein,
t1For acceleration duration, t2To subtract acceleration duration, t3For constant velocity stage's duration, t4For acceleration and deceleration duration, t5To subtract
Fast stage duration；When input machining path length be L nurbs curve after, by step 1), step 2) and step 3) place
Reason, it is known which kind of speed planning process is current length should enter for L nurbs curve, and interpolated point number is N.
Further, if current interpolated point is n, n=1,2 ..., N.
Then current interpolation moment t=nT, wherein T are interpolation cycle
Then current interpolated point C (u can be calculated according to formula (5-1)i) feed speed be v (ui)。
Step 5, in each interpolation cycle, it is known that current interpolated points'parameter vector ui, Taylor series expansion method can be used,
By parameter uiTaylor expansion is carried out to time t, the locus point C (u that next cycle should reach are calculatedi+1) parameter vector
ui+1, formula is：
Wherein T represents interpolation cycle, and H.O.T is Taylor expansion higher order term (can typically ignore).
Make current interpolated point C (ui), its feed rate can be by step 4) obtain, it is v (ui)。
Parameter u is to time t first approximation expression formula：
Parameter u is to time t Two-order approximation expression formula：
Nurbs curve expression formula C (u) is：
Wherein Pi- control point information, wi- weight factor information, p-NURBS degree of curve.
N in formulai,p(u) it is p specification B-spline basic function, can be by following formula recurrence calculation：
Wherein, U={ u0,u1,...,un+p+1It is referred to as knot vector, u is the independent variable of nurbs curve.
Therefore, according to current interpolated point feed speed v (ui) and nurbs curve definition, formula (6-2) and (6- can be passed through
3) single order for calculating nurbs curve is led and led with second order, then substitutes into formula (6-1), can calculate next interpolated points'parameter
ui+1, i.e., next interpolated point C (ui+1)。
Although the foregoing describing the embodiment of the present invention, those familiar with the art should manage
Solution, the specific embodiment described by us is merely exemplary, rather than for the restriction to the scope of the present invention, is familiar with this
The equivalent modification and change that the technical staff in field is made in the spirit according to the present invention, should all cover the present invention's
In scope of the claimed protection.
Claims (6)
1. nurbs curve interpolating method known to a kind of machining path length, it is characterised in that：Comprise the following steps：
Accelerator displacement and moderating process displacement in step 1, the flexible acceleration and deceleration method of calculating five-part form；
Step 2, according to machining path length speed planning species is classified；
Step 3, calculating machining path length are counted for the L total interpolation of nurbs curve；
Step 4, the current interpolated point feed speed of calculating；
Step 5, each interpolation cycle interpolated points'parameter of acquisition and coordinate value.
2. nurbs curve interpolating method known to a kind of machining path length as claimed in claim 1, it is characterised in that：It is described
Step 1 further comprises：
Using the flexible acceleration and deceleration method of five-part form, t is made1For acceleration duration, t2To subtract acceleration duration, t3For constant velocity stage's duration,
t4For acceleration and deceleration duration, t5To subtract decelerating phase duration, amaxFor system maximum permissible acceleration；The flexible acceleration and deceleration of five-part form are made to open
Beginning speed is vsWith end speed ve；Then each phases-time is：
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</msub>
<mo>-</mo>
<msub>
<mi>s</mi>
<mrow>
<mi>d</mi>
<mi>e</mi>
<mi>c</mi>
</mrow>
</msub>
</mrow>
<mi>v</mi>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>t</mi>
<mn>4</mn>
</msub>
<mo>=</mo>
<msub>
<mi>t</mi>
<mn>5</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>e</mi>
</msub>
</mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
Wherein v is interpolation command speed；
Make s1To add boost phase displacement, s2To subtract boost phase displacement, s3For constant velocity stage's displacement, s4For acceleration and deceleration stage position
Move, s5To subtract decelerating phase displacement；Then each phase displacement equation is：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>v</mi>
<mn>0</mn>
</msub>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>24</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>1</mn>
<mn>4</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>v</mi>
<mn>1</mn>
</msub>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>a</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<msubsup>
<mi>t</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>24</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>2</mn>
<mn>4</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>3</mn>
</msub>
<mo>=</mo>
<msub>
<mi>s</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>v</mi>
<mn>2</mn>
</msub>
<msub>
<mi>t</mi>
<mn>3</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>4</mn>
</msub>
<mo>=</mo>
<msub>
<mi>s</mi>
<mn>3</mn>
</msub>
<mo>+</mo>
<msub>
<mi>v</mi>
<mn>3</mn>
</msub>
<msub>
<mi>t</mi>
<mn>4</mn>
</msub>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>24</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>4</mn>
<mn>4</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>5</mn>
</msub>
<mo>=</mo>
<msub>
<mi>s</mi>
<mn>4</mn>
</msub>
<mo>+</mo>
<msub>
<mi>v</mi>
<mn>4</mn>
</msub>
<msub>
<mi>t</mi>
<mn>5</mn>
</msub>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>a</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<msubsup>
<mi>t</mi>
<mn>5</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>24</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>5</mn>
<mn>4</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
Wherein v0To add boost phase commencing speed, v1To subtract boost phase commencing speed, v2For constant velocity stage's speed, v3For plus-minus
Fast stage commencing speed, v4To subtract decelerating phase commencing speed；
Wherein k is customized constant value, by the t in (3-1) formula1、t2、t3、t4、t5Substitute into (3-2), calculating obtains s1、s2、s3、
s4、s5；
Speed planning processing, bag are carried out to the flexible acceleration and deceleration of nurbs curve five-part form to be processed using five-part form flexible acceleration and deceleration
Include plus accelerate, subtract accelerations, at the uniform velocity, acceleration and deceleration, slow down five stages, wherein add accelerate, subtract acceleration be accelerator, add and subtract
Speed, deceleration are moderating process, make s1To add boost phase displacement, s2To subtract boost phase displacement, s3For constant velocity stage's displacement,
s4For acceleration and deceleration phase displacement, s5To subtract decelerating phase displacement, then
Accelerator displacement SaccFor：
Sacc=s1+s2
At the uniform velocity process displacement is Scon：
Scon=s3
Moderating process displacement SdecFor：
Sdec=s4+s5。
3. nurbs curve interpolating method known to a kind of machining path length as claimed in claim 2, it is characterised in that：Institute
Step 2 is stated to further comprise：
It is L to make the flexible acceleration and deceleration path length of nurbs curve five-part form to be processed, according to machining path length L values, to NURBS
Curve five-part form flexibility acceleration and deceleration speed planning is classified：
(1) the complete acceleration and deceleration of constant velocity stage are included
If L ＞ Sacc+Sdec, then there is accelerator, at the uniform velocity process and moderating process, include each rank of the flexible acceleration and deceleration of five-part form
Section, speed reaches system maximum permission speed；
(2) the complete acceleration and deceleration of constant velocity stage are not included
If L=Sacc+Sdec, then there is accelerator and moderating process, not comprising at the uniform velocity process, speed reaches that system is maximum allowable
Speed；
(3) not exclusively acceleration and deceleration
If L ＜ Sacc+Sdec, due to being influenceed by distance factor, treat that interpolation path length is less than actual accelerator and slowed down
Journey path sum, then accelerator and moderating process can not be fully completed, the maximum feed speed that can actually reach less than instruction
Speed.
4. nurbs curve interpolating method known to a kind of machining path length as claimed in claim 2, it is characterised in that：Institute
Step 3 is stated to further comprise：
After being divided into three classes according to machining path length to speed planning, each speed planning interpolated point quantity is calculated respectively；
(1) the complete acceleration and deceleration of constant velocity stage are included
Now, the flexible acceleration and deceleration speed planning of five-part form includes accelerator, at the uniform velocity process and moderating process whole 5 stages,
Speed reaches command speed F, and acceleration and acceleration reach peak acceleration and acceleration, according to step 1 Chinese style (3-1)
Obtain accelerator plus boost phase, subtract boost phase duration t1、t2, and acceleration and deceleration and subtract time in decelerating phase t4With
t5, and actual acceleration distance S'accWith deceleration distance S'dec,
Then have：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>s</mi>
</msub>
</mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>t</mi>
<mn>3</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>L</mi>
<mo>-</mo>
<msub>
<msup>
<mi>s</mi>
<mo>&prime;</mo>
</msup>
<mrow>
<mi>a</mi>
<mi>c</mi>
<mi>c</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<msup>
<mi>s</mi>
<mo>&prime;</mo>
</msup>
<mrow>
<mi>d</mi>
<mi>e</mi>
<mi>c</mi>
</mrow>
</msub>
</mrow>
<mi>v</mi>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>t</mi>
<mn>4</mn>
</msub>
<mo>=</mo>
<msub>
<mi>t</mi>
<mn>5</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>e</mi>
</msub>
</mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein vsFor commencing speed, veTo terminate speed,
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
<mrow>
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>3</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>4</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>5</mn>
</msub>
</mrow>
<mi>T</mi>
</mfrac>
<mo>;</mo>
</mrow>
(2) the complete acceleration and deceleration of constant velocity stage are not included
Now, 4 stages of the flexible acceleration and deceleration speed planning of five-part form comprising accelerator and moderating process, speed reaches instruction
Speed F, acceleration and acceleration reach peak acceleration and acceleration, not comprising at the uniform velocity process, are obtained according to formula (3-1)
The accelerator acceleration stage, subtract boost phase duration t1、t2、t4And t5,
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>s</mi>
</msub>
</mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>t</mi>
<mn>3</mn>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>t</mi>
<mn>4</mn>
</msub>
<mo>=</mo>
<msub>
<mi>t</mi>
<mn>5</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>e</mi>
</msub>
</mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein vsFor commencing speed, veTo terminate speed,
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
<mrow>
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>4</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>5</mn>
</msub>
</mrow>
<mi>T</mi>
</mfrac>
<mo>;</mo>
</mrow>
(4) not exclusively acceleration and deceleration
Now, in 4 stages of the flexible acceleration and deceleration speed planning of five-part form comprising accelerator and moderating process, maximal rate can not
Command speed F is reached, not comprising at the uniform velocity process, t3=0,
Accelerating region and deceleration section length are respectively the half for treating interpolation path length in the speed planning species, i.e.,：Sacc=Sdec=
L/2；
Consider accelerator, obtaining accelerator displacement according to formula (3-2) is：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
<mi>c</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>S</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>S</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<msub>
<mi>v</mi>
<mn>0</mn>
</msub>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>24</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>1</mn>
<mn>4</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>v</mi>
<mn>1</mn>
</msub>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>a</mi>
<mi>max</mi>
</msub>
<msubsup>
<mi>t</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>24</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>2</mn>
<mn>4</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mn>2</mn>
<msub>
<mi>v</mi>
<mn>0</mn>
</msub>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>a</mi>
<mi>max</mi>
</msub>
<msubsup>
<mi>t</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>1</mn>
<mn>4</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Obtained by two formulas above：
<mrow>
<msubsup>
<mi>kt</mi>
<mn>1</mn>
<mn>4</mn>
</msubsup>
<mo>+</mo>
<mn>3</mn>
<msub>
<mi>a</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<msubsup>
<mi>t</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mn>12</mn>
<msub>
<mi>v</mi>
<mn>0</mn>
</msub>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<mn>3</mn>
<mi>L</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
The formula is unary biquadratic equation, is calculated by Descartes's method or Ferrari method and obtains real root ta, then have：
t1=t2=ta
Similarly moderating process subtracts acceleration and subtracts deceleration time and is：
t4=t5=tb
The maximum feed speed that can be reached is：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>v</mi>
<mi>max</mi>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>v</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>max</mi>
</msub>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>2</mn>
<mn>3</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>v</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>1</mn>
<mn>3</mn>
</msubsup>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>max</mi>
</msub>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<msubsup>
<mi>kt</mi>
<mn>2</mn>
<mn>3</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<msub>
<mi>v</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>max</mi>
</msub>
<msub>
<mi>t</mi>
<mi>a</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
It is T to make interpolation cycle, then machining path length is L nurbs curve, and interpolation points are altogether：
<mrow>
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>t</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>4</mn>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mn>5</mn>
</msub>
</mrow>
<mi>T</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msub>
<mi>t</mi>
<mi>a</mi>
</msub>
<mo>+</mo>
<mn>2</mn>
<msub>
<mi>t</mi>
<mi>b</mi>
</msub>
</mrow>
<mi>T</mi>
</mfrac>
<mo>.</mo>
</mrow>
5. nurbs curve interpolating method known to a kind of machining path length as claimed in claim 1, it is characterised in that：Institute
Step 4 is stated to further comprise：
Five-part form flexibility acceleration and deceleration method, rate equation is：
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>v</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<msup>
<mi>k&tau;</mi>
<mn>3</mn>
</msup>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>0</mn>
<mo>&le;</mo>
<mi>t</mi>
<mo>&le;</mo>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>&tau;</mi>
<mo>=</mo>
<mi>t</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>v</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>max</mi>
</msub>
<mi>&tau;</mi>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<msup>
<mi>k&tau;</mi>
<mn>3</mn>
</msup>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
<mo>&le;</mo>
<mi>t</mi>
<mo>&le;</mo>
<msub>
<mi>T</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>&tau;</mi>
<mo>=</mo>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>v</mi>
<mn>2</mn>
</msub>
</mtd>
<mtd>
<mrow>
<msub>
<mi>T</mi>
<mn>2</mn>
</msub>
<mo>&le;</mo>
<mi>t</mi>
<mo>&le;</mo>
<msub>
<mi>T</mi>
<mn>3</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>v</mi>
<mn>3</mn>
</msub>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<msup>
<mi>k&tau;</mi>
<mn>3</mn>
</msup>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>T</mi>
<mn>3</mn>
</msub>
<mo>&le;</mo>
<mi>t</mi>
<mo>&le;</mo>
<msub>
<mi>T</mi>
<mn>4</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>&tau;</mi>
<mo>=</mo>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>T</mi>
<mn>3</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>v</mi>
<mn>4</mn>
</msub>
<mo>-</mo>
<msub>
<mi>a</mi>
<mi>max</mi>
</msub>
<mi>&tau;</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<msup>
<mi>k&tau;</mi>
<mn>3</mn>
</msup>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>T</mi>
<mn>4</mn>
</msub>
<mo>&le;</mo>
<mi>t</mi>
<mo>&le;</mo>
<msub>
<mi>T</mi>
<mn>5</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>&tau;</mi>
<mo>=</mo>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>T</mi>
<mn>4</mn>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>5</mn>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
Wherein, T0=0, T1=t1, T2=T1+t2, T3=T2+t3, T4=T3+t4, T5=T4+t5；
t1For acceleration duration, t2To subtract acceleration duration, t3For constant velocity stage's duration, t4For acceleration and deceleration duration, t5For deceleration rank
Duan Shichang；After the nurbs curve that machining path length is L is inputted, by the processing of step 1, step 2 and step 3, worked as
Preceding length is L nurbs curve speed planning type, and interpolated point number is N,
Further, if current interpolated point is n, n=1,2 ..., N,
Then current interpolation moment t=nT, wherein T are interpolation cycle
Current interpolated point C (u are then calculated according to formula (5-1)i) feed speed be v (ui)。
6. nurbs curve interpolating method known to a kind of machining path length as claimed in claim 1, it is characterised in that：Institute
Step 5 is stated to further comprise：
In each interpolation cycle, it is known that current interpolated points'parameter vector ui, using Taylor series expansion method, by parameter uiTo time t
Taylor expansion is carried out, the locus point C (u that next cycle should reach are calculatedi+1) parameter vector ui+1, formula is：
(6-1)
Wherein T represents interpolation cycle, and H.O.T is Taylor expansion higher order term, makes current interpolated point C (ui), its feed rate is by step
4 obtain, and are v (ui)；
Parameter u is to time t first approximation expression formula：
(6-2)
Parameter u is to time t Two-order approximation expression formula：
(6-3)
Nurbs curve expression formula C (u) is：
<mrow>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>N</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>p</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>w</mi>
<mi>i</mi>
</msub>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
</mrow>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>N</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>p</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>w</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
</mrow>
Wherein PiFor your control point information, wiFor weight factor information, p is nurbs curve number of times,
N in formulai,p(u) it is p specification B-spline basic function, by following formula recurrence calculation：
<mrow>
<msub>
<mi>N</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>p</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
<msub>
<mi>N</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>p</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mi>p</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mi>p</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>u</mi>
<mo>)</mo>
<msub>
<mi>N</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>p</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mi>p</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
Wherein, U={ u0,u1,...,un+p+1It is referred to as knot vector, u is the independent variable of nurbs curve；
Therefore, according to current interpolated point feed speed v (ui) and nurbs curve definition, calculated by formula (6-2) and (6-3)
The single order of nurbs curve is led leads with second order, then substitutes into formula (6-1), calculates next interpolated points'parameter ui+1, i.e., it is next to insert
Mend point C (ui+1)。
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| CN109656200A (en) * | 2018-12-10 | 2019-04-19 | 大族激光科技产业集团股份有限公司 | The flexible Acceleration-deceleration Control Method and system of board |
| CN111496798A (en) * | 2020-05-18 | 2020-08-07 | 北京配天技术有限公司 | Robot conveyor belt tracking method, equipment and storage device |
| CN111562766A (en) * | 2020-05-08 | 2020-08-21 | 重庆科技学院 | Cross sliding table performance simulation control method and system, storage medium and computer |
| CN111857059A (en) * | 2020-07-21 | 2020-10-30 | 天津大学 | Improved S-shaped acceleration and deceleration model calculation method |
| CN112015142A (en) * | 2020-08-26 | 2020-12-01 | 无锡信捷电气股份有限公司 | NURBS-based small segment processing method |
| CN113156893A (en) * | 2021-03-26 | 2021-07-23 | 西安交通大学 | Five-axis machine tool speed planning method based on S-shaped acceleration and deceleration |
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| CN108189038A (en) * | 2018-01-18 | 2018-06-22 | 广东工业大学 | A kind of industry six shaft mechanical arm straight-line trajectory method and system for planning of practicality |
| CN109656200A (en) * | 2018-12-10 | 2019-04-19 | 大族激光科技产业集团股份有限公司 | The flexible Acceleration-deceleration Control Method and system of board |
| CN109656200B (en) * | 2018-12-10 | 2020-09-25 | 大族激光科技产业集团股份有限公司 | Flexible acceleration and deceleration control method and system for machine table |
| CN111562766B (en) * | 2020-05-08 | 2023-06-02 | 重庆科技学院 | Cross sliding table performance simulation control method, system, storage medium and computer |
| CN111562766A (en) * | 2020-05-08 | 2020-08-21 | 重庆科技学院 | Cross sliding table performance simulation control method and system, storage medium and computer |
| CN111496798A (en) * | 2020-05-18 | 2020-08-07 | 北京配天技术有限公司 | Robot conveyor belt tracking method, equipment and storage device |
| CN111857059A (en) * | 2020-07-21 | 2020-10-30 | 天津大学 | Improved S-shaped acceleration and deceleration model calculation method |
| CN111857059B (en) * | 2020-07-21 | 2024-03-22 | 天津大学 | Improved S-shaped acceleration and deceleration model calculation method |
| CN112015142A (en) * | 2020-08-26 | 2020-12-01 | 无锡信捷电气股份有限公司 | NURBS-based small segment processing method |
| CN113156893B (en) * | 2021-03-26 | 2023-08-01 | 西安交通大学 | Five-axis machine tool speed planning method based on S-shaped acceleration and deceleration |
| CN113156893A (en) * | 2021-03-26 | 2021-07-23 | 西安交通大学 | Five-axis machine tool speed planning method based on S-shaped acceleration and deceleration |
| CN113635301B (en) * | 2021-07-29 | 2023-02-28 | 中国地质大学（武汉） | Six-axis mechanical arm movement speed control improvement method |
| CN113635301A (en) * | 2021-07-29 | 2021-11-12 | 中国地质大学（武汉） | Six-axis mechanical arm movement speed control improvement method |
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Application publication date: 20171020 |