CN106527351B - A kind of small line segment Real-time Interpolation that easement curve length is dynamically determined - Google Patents

A kind of small line segment Real-time Interpolation that easement curve length is dynamically determined Download PDF

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CN106527351B
CN106527351B CN201510574854.5A CN201510574854A CN106527351B CN 106527351 B CN106527351 B CN 106527351B CN 201510574854 A CN201510574854 A CN 201510574854A CN 106527351 B CN106527351 B CN 106527351B
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easement curve
line segment
length
curve
turning
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CN106527351A (en
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林浒
郑飂默
孙树杰
李备备
韩旭
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Shenyang Zhongke CNC Technology Co.,Ltd.
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Shenyang Gaojing Numerical Control Intelligent Technology Co Ltd
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
    • G05B19/4103—Digital interpolation
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/42—Servomotor, servo controller kind till VSS
    • G05B2219/42207—Generate points between start and end position, linear interpolation

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  • Computing Systems (AREA)
  • Theoretical Computer Science (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
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  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Numerical Control (AREA)

Abstract

The present invention relates to the small line segment processing technology of fields of numeric control technique, small line segment Real-time Interpolation that specifically a kind of easement curve length is dynamically determined.The present invention is the following steps are included: establish B-spline curves turning transition model；The unit length and thresholding speed of angle calculation easement curve between the largest contours error amount and small line segment that are allowed according to digital control system；Interpolation is carried out to cutter path；Optimize the B-spline easement curve at current turning to reduce process time as target according to the parameter of adjacent corners easement curve.The B-spline corner easement curve at 5 control points of the invention can reduce calculation amount on the basis of guaranteeing continual curvature to the greatest extent；The calculating of unit length can greatly reduce the calculation amount when adjustment of transition curve parameter, and the foundation of easement curve parameter adjustment is constituted together with thresholding speed；The corner optimization method of use can effectively reduce process time on the basis of guaranteeing machining accuracy.

Description

A kind of small line segment Real-time Interpolation that easement curve length is dynamically determined
Technical field
The present invention relates to the small line segment processing technology of fields of numeric control technique, specifically a kind of easement curve length is dynamic The small line segment Real-time Interpolation that state determines.
Background technique
In traditional manufacture field, CAD/CAM generates the G code being made of small line segment, and CNC directly processes small line segment. This method has apparent defect: lower machining accuracy, longer process time, poor surface quality.
Existing research achievement is embodied in industrial circle and research field.Industrial circle, SIMENCE are high-end in 840D etc. The excessive method of corner is used in numerically-controlled machine tool, but the relevant technologies not publicly discuss.Research field uses arc transition, Ferguson curve transition, B-spline transition, cubic spline transition.Its characteristics are as follows: arc transition calculates simply, but circular arc mistake Cross that curvature is discontinuous at easement curve and the tie point of cutter path with Ferguson curve transition, the fluctuation of speed can draw Play cutter vibration.Existing B-spline curves excessively have between control point that position proportional is unknown, control point number is more and Calculate the problems such as complex.Cubic spline curve is as a kind of corner transient mode, with arc transition, Ferguson curve Transition and B-spline transition do not consider optimization problem when adjacent transition curve intersection.
Summary of the invention
For the respective shortcoming of existing common method, the technical problem to be solved in the present invention is to provide a kind of transition The small line segment Real-time Interpolation that length of curve is dynamically determined can optimize and to processing corner easement curve parameter Cutter path afterwards carries out real-time interpolation.
Present invention technical solution used for the above purpose is: a kind of easement curve length is dynamically determined small Line segment Real-time Interpolation, comprising the following steps:
Establish B-spline curves turning transition model；
The unit of angle calculation easement curve between the largest contours error amount and small line segment that are allowed according to digital control system Length and thresholding speed；
Interpolation is carried out to cutter path；
Optimize the B batten at current turning to reduce process time as target according to the parameter of adjacent corners easement curve Easement curve.
B-spline curves turning transition model specifically: according to largest contours error amount, on cutter path three A consecutive points Pi-1、PiAnd Pi+1Point is upper setting control point.
The control point is five, including line segment Pi-1PiOn control point Pt0、Pt1, with point PiThe control point P of coincidencet2, Line segment PiPi+1On control point Pt3、Pt4, wherein Pt2Pt0>Pt2Pt1, Pt2Pt4>Pt2Pt3, largest contours error amount u, which is equal to, to be controlled Point PiControl easement curve Pt1Pt3Distance.
The length of the easement curve are as follows:
Sl=| l | λ
Wherein, l is the line segment P that control point is constitutedt2Pt1Length, λ be turning ∠ Pi-1PiPi+1Locate the unit of easement curve Length, i.e. l1The length of easement curve, l when=11The line segment P constituted for control pointt2Pt1Length.
Speed corresponding to point when the thresholding speed is largest contours error amount u=0.5, it may be assumed that
Wherein,l1The line segment P constituted for control pointt2Pt1Length, α be ∠ Pi-1PiPi+1, T is interpolation Period, e are largest contours error amount.
It is described that interpolation is carried out using 7 sections of velocity planning algorithms and static look-ahead algorithm to cutter path.
The parameter according to adjacent corners easement curve optimizes the B at current turning to reduce process time as target Batten easement curve, comprising the following steps:
Time-optimized function is set:
Wherein, f (t) is process time；
A1=λ1T/2,A2=λ2T/2
V=min (Vthreshold_i,Vthreshold_i+1)
l1=li, l2=L-li
d1=2e/c1, d2=2e/c2
L indicates Pi、Pi+1The distance between, λ1For turning ∠ Pi-1PiPi+1Locate the unit length of easement curve, Vthreshold_i For turning ∠ Pi-1PiPi+1Locate the thresholding speed of easement curve；λ2For turning ∠ PiPi+1Pi+2Locate the unit length of easement curve, Vthreshold_i+1For turning ∠ PiPi+1Pi+2Locate the thresholding speed of easement curve；liFor turning ∠ Pi-1PiPi+1Locate spline curve pair The control point P answeredt2, Pt4Between line segment length, L be point PiWith Pi+1Between line segment length, l1、l2、 d1、d2、c1、c2For meter The intermediate parameters of calculation process, T are interpolation cycle, and e is largest contours error amount, and α is ∠ Pi-1PiPi+1, β is ∠ PiPi+1Pi+2；
L when by f (t) value minimum determines the B-spline easement curve at current turning.
The present invention has the following advantages and beneficial effects:
The B-spline corner easement curve at 1.5 control points can subtract to the greatest extent on the basis of guaranteeing continual curvature Few calculation amount.
2. the calculating of unit length can greatly reduce the calculation amount when adjustment of transition curve parameter, with thresholding speed The foundation of easement curve parameter adjustment is constituted together.
3.7 sections of velocity planning algorithms and static look-ahead algorithm, help to create smooth process velocity.
4. the corner optimization method used can effectively reduce process time on the basis of guaranteeing machining accuracy.
Detailed description of the invention
Fig. 1 is B-spline corner transition model；
Fig. 2 is B-spline corner interim process control point coordinate model；
Fig. 3 is 7 sections of speed planning curve synoptic diagrams；
Fig. 4 is look-ahead window schematic diagram；
Fig. 5 is speed planning cell schematics；
Fig. 6 is adjacent B-spline easement curve schematic diagram；
Fig. 7 is astroid schematic diagram；
Fig. 8 is cutter path comparison diagram；
Fig. 9 is Fig. 8 enlarged diagram；
Figure 10 is processing effect comparison diagram；
Figure 11 is process velocity curve comparison.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawings and embodiments.
1 firstly, establish B-spline curves turning transition model.Pi-1、PiAnd Pi+13 points are three on cutter path Consecutive points, u are the largest contours error amount that system determines, determining turning easement curve is as shown in Figure 1, wherein Pti, i=0, 1,2,3,4 be the control point of batten.
2 optimization easement curves.
(1) thresholding speed is determined.Speed corresponding to point in transition spline curve when parameter u=0.5 is known as the transition Thresholding speed in batten process.Transition spline curve is as shown in Figure 2 at this time.l1For line segment Pt2Pt1Length, control point (Pti, i=0,1,2,3,4) coordinate calculate it is as follows:
It is possible thereby to which spline curve value and derivative value are as a result as follows when calculating u=0.5:
Therefore, when u=0.5, the curvature value of spline curve is as follows:
It can thus be concluded that thresholding speed is as follows:
Wherein,
(2) length of easement curve is calculated.The length of easement curve, following institute are calculated using integration method and Simpson method Show:
The derivative of spline curve is as follows:
Wherein, N'i,3It (u) is the first derivative of basic function, PixFor the x coordinate at control point, PiyFor the y coordinate at control point, PizFor the z coordinate at control point.
By formula (5), (6) it is found that the length and line segment l of transition spline curve1Length is positively correlated, it is assumed that l1It is bent when=1 The length of line is λ, then length of curve SlIt can be expressed as follows:
Sl=| l | λ (7)
3 speed plannings and look-ahead algorithm
(1) as shown in figure 3, using bell-shaped speed planning method, calculation formula is as follows:
Wherein, Amax, JmaxFor the peak acceleration that system allows, acceleration, vsFor starting velocity. v1v2v3v4v5For The intermediate variable of calculating process, t1, t2, t3, t4, t5, t6, t7 is respectively as follows: as shown in Figure 3 plus the accelerator end time, even The accelerator end time, subtract accelerator end time, at the uniform velocity course over time, acceleration and deceleration course over time is even to subtract Fast course over time subtracts the moderating process end time.
(2) as shown in figure 4, carrying out speed planning using static look-ahead approach.
A) in the attainable maximum speed V of path starting point institute when calculating speed planning unit (j) inversely acceleratesend。 P (j).VmaxIndicate the maximum process velocity that speed planning unit (j) allows in path starting point, then vs=min (P (j) .Vmax, Vend) indicate process velocity of next speed planning unit (j-1) at path termination.
B) j value subtracts 1, repeats step a), until j value is 1.
C) speed planning is carried out to present speed planning unit according to vs.
The division of speed planning unit is as shown in figure 5, thresholding speed is arranged to the maximum allowable processing speed when leading portion Degree.
The optimization of 4 easement curves
In order to reduce the process time of turning transition position spline curve, it is as follows that time-optimized function is set:
As shown in fig. 6, relevant parameter is provided that
A1=λ1T/2,A2=λ2T/2
V=min (Vthreshold_i,Vthreshold_i+1)
l1=li, l2=L-li
d1=2e/c1, d2=2e/c2
L indicates Pi、Pi+1The distance between.
Finally, l when by f (t) value minimum determines the easement curve at current turning.
Implementation effect of the invention
Starfish figure as shown in Figure 7 is the processing use-case that experiment uses.As shown in figure 8, for using traditional batten transition side Plan that resulting machining path, Fig. 9 are the enlarged drawing in Fig. 8 inside circle when method is with using context of methods.It can from Fig. 8 Out, the machining path of context of methods planning is smoother when turning is more sharp, more accurate when turning is smoother.
In order to further verify effect of the invention, interpolation command speed is set as 2m/s, peak acceleration 5m/s2, Maximum acceleration is 40m/s3, the interpolation cycle of numerically-controlled machine tool is 0.002s, and largest contours error is 1mm, to such as Fig. 7 institute The figure shown carries out processing verifying.
Processing result when Figure 10 (a) is using traditional corner transition method, Figure 10 (b) are using this paper corner transition Processing result when method, it can be seen that context of methods can obtain more preferably processing quality.
Speed, acceleration and acceleration when Figure 11 (a), (b), (c) are using traditional corner transition method processing Curve graph, Figure 11 (d), (e), (f) are the speed, acceleration and acceleration when being processed using this paper corner transition method Curve graph, it can be seen that context of methods can obtain faster process velocity.

Claims (6)

1. the small line segment Real-time Interpolation that a kind of easement curve length is dynamically determined, which comprises the following steps:
Establish B-spline curves turning transition model；
The unit length of angle calculation easement curve between the largest contours error amount and small line segment that are allowed according to digital control system With thresholding speed；
Interpolation is carried out to cutter path；
According to the parameter of adjacent corners easement curve, to reduce process time as target, the B-spline transition for optimizing current turning is bent Line；
The parameter according to adjacent corners easement curve optimizes the B-spline mistake at current turning to reduce process time as target Cross curve, comprising the following steps:
Time-optimized function is set:
Wherein, f (t) is process time；
A1=λ1T/2,A2=λ2T/2
V=min (Vthreshold_i,Vthreshold_i+1)
l1=li, l2=L-li
d1=2e/c1, d2=2e/c2
L indicates Pi、Pi+1The distance between, λ1For turning ∠ Pi-1PiPi+1Locate the unit length of easement curve, Vthreshold_iTo turn Angle ∠ Pi-1PiPi+1Locate the thresholding speed of easement curve；λ2For turning ∠ PiPi+1Pi+2Locate the unit length of easement curve, Vthreshold_i+1For turning ∠ PiPi+1Pi+2Locate the thresholding speed of easement curve；liFor turning ∠ Pi-1PiPi+1Locate spline curve pair The control point P answeredt2, Pt4Between line segment length, L be point PiWith Pi+1Between line segment length, l1、l2、d1、d2、c1、c2For meter The intermediate parameters of calculation process, T are interpolation cycle, and e is largest contours error amount, and α is ∠ Pi-1PiPi+1, β is ∠ PiPi+1Pi+2；
L when by f (t) value minimum determines the B-spline easement curve at current turning.
2. the small line segment Real-time Interpolation that a kind of easement curve length according to claim 1 is dynamically determined, feature It is, B-spline curves turning transition model specifically: three phases according to largest contours error amount, on cutter path Adjoint point Pi-1、PiAnd Pi+1Control point is set on point.
3. the small line segment Real-time Interpolation that a kind of easement curve length according to claim 2 is dynamically determined, feature It is, the control point is five, including line segment Pi-1PiOn control point Pt0、Pt1, with point PiThe control point P of coincidencet2, line segment PiPi+1On control point Pt3、Pt4, wherein Pt2Pt0>Pt2Pt1, Pt2Pt4>Pt2Pt3, largest contours error amount u is equal to control point Pi Control easement curve Pt1Pt3Distance.
4. the small line segment Real-time Interpolation that a kind of easement curve length according to claim 1 is dynamically determined, feature It is, the length of the easement curve are as follows:
Sl=| l | λ
Wherein, l is the line segment P that control point is constitutedt2Pt1Length, λ be turning ∠ Pi-1PiPi+1Locate the unit length of easement curve, That is l1The length of easement curve, l when=11The line segment P constituted for control pointt2Pt1Length.
5. the small line segment Real-time Interpolation that a kind of easement curve length according to claim 1 is dynamically determined, feature It is, speed corresponding to the point when thresholding speed is largest contours error amount u=0.5, it may be assumed that
Wherein,l1The line segment P constituted for control pointt2Pt1Length, α be ∠ Pi-1PiPi+1, T is interpolation cycle, E is largest contours error amount.
6. the small line segment Real-time Interpolation that a kind of easement curve length according to claim 1 is dynamically determined, feature It is, it is described that interpolation is carried out using 7 sections of velocity planning algorithms and static look-ahead algorithm to cutter path.
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