CN112486101B - NURBS curve self-adaptive look-ahead interpolation method - Google Patents

NURBS curve self-adaptive look-ahead interpolation method Download PDF

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CN112486101B
CN112486101B CN202011466074.6A CN202011466074A CN112486101B CN 112486101 B CN112486101 B CN 112486101B CN 202011466074 A CN202011466074 A CN 202011466074A CN 112486101 B CN112486101 B CN 112486101B
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interpolation
deceleration
acceleration
speed
point
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CN112486101A (en
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盖荣丽
马淑雅
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Dalian University
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Dalian University
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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
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/34—Director, elements to supervisory
    • G05B2219/34083—Interpolation general

Abstract

The invention discloses a NURBS curve self-adaptive look-ahead interpolation method, which comprises the following steps: obtaining interpolation parameters of each interpolation point by adopting a second-order Taylor expansion type; finding out an extremely low speed point according to the curvature change condition, and segmenting a curve; using the constraint conditions of curve bow height error, normal maximum acceleration, jerk, machine tool self-characteristics and machine tool dynamics characteristics to adaptively adjust the feeding speed; path planning is carried out through a trigonometric function acceleration and deceleration control algorithm to obtain acceleration and deceleration start and end parameters, and the parameters are recorded into an acceleration and deceleration array; according to the obtained deceleration section information, performing look-ahead interpolation to obtain acceleration section information and acceleration and deceleration distances; and calculating the feeding speed in real time for interpolation through the obtained interpolation parameters, the feeding speed and the trigonometric function acceleration and deceleration equation. The invention realizes flexible acceleration and deceleration control, ensures stable change of processing speed, improves the smoothness of the surface of the workpiece, and ensures high-speed and high-precision processing of the workpiece by adaptively adjusting the feeding speed.

Description

NURBS curve self-adaptive look-ahead interpolation method
Technical Field
The invention relates to the technical field of numerical control machining, in particular to a NURBS curve self-adaptive look-ahead interpolation method.
Background
Along with the continuous development of the numerical control machine tool, the traditional interpolation mode can not meet the current high-speed high-precision machining requirement, and the feeding speed is easy to fluctuate, so that the flatness of the surface of a workpiece is influenced. Because NURBS curve has good intuitiveness, locality, convergence and approximation, the data transmission quantity is small, the transmission speed is high, and the curve can be directly interpolated. The NURBS curve is applied to process complex curve surfaces, so that the processing precision and efficiency of a workpiece can be greatly improved, and the NURBS interpolation technology has become a main index for measuring the processing capacity of a numerical control machine tool.
When a workpiece with a complex profile is processed at a high speed, if a large number of points with high curvature exist in a processing path, once the cutter is interpolated to the points, the cutter needs to be decelerated in time. In order to ensure the machining accuracy, the feed speed must be reduced to a predetermined range. If the direction of the interpolation point is suddenly changed, the feeding speed is not correspondingly reduced, and finally, the over-cutting phenomenon is generated. Therefore, the numerical control system is required to find the high curvature point in advance and decelerate in the machining process, and the feeding speed can be adjusted in time before the cutter is machined to the designated position, so that over-cutting is avoided. In order to solve the above problems, scholars at home and abroad begin to study interpolation methods based on prospective technology. The look-ahead is a key technology for analyzing a subsequent path in advance, acquiring information such as path length, speed constraint conditions and the like, and optimizing the feeding speed by an interpolator in a self-adaptive manner according to the characteristics and processing parameters of a machine tool through information such as optimal feeding speed, acceleration control and the like of interpolation points, so that the maximum processing efficiency is acquired and severe change of the feeding speed is avoided. The prior interpolation method based on the prospective technology has the following problems: the precision is poor, machining efficiency is low, real-time interpolation can not be performed, and the speed is unstable.
Disclosure of Invention
Aiming at the problems in the prior art, the application provides a NURBS curve self-adaptive look-ahead interpolation method, which can obtain continuous acceleration and jerk curves, reduce feed speed fluctuation and improve the efficiency and precision of processing workpieces.
In order to achieve the above purpose, the technical scheme of the application is as follows: the NURBS curve self-adaptive look-ahead interpolation method comprises the following steps:
obtaining interpolation parameters of each interpolation point by adopting a second-order Taylor expansion type;
finding out an extremely low speed point according to the curvature change condition, and segmenting a curve;
using the constraint conditions of curve bow height error, normal maximum acceleration, jerk, machine tool self-characteristics and machine tool dynamics characteristics to adaptively adjust the feeding speed;
path planning is carried out through a trigonometric function acceleration and deceleration control algorithm to obtain acceleration and deceleration start and end parameters, and the parameters are recorded into an acceleration and deceleration array;
according to the obtained deceleration section information, performing look-ahead interpolation to obtain acceleration section information and acceleration and deceleration distances;
and calculating the feeding speed in real time for interpolation through the obtained interpolation parameters, the feeding speed and the trigonometric function acceleration and deceleration equation.
Further, the interpolation parameters of each interpolation point are obtained by adopting a second-order Taylor expansion type, and the method specifically comprises the following steps:
wherein x is i As the current interpolation point, the interpolation parameter corresponding to P (x), T is the interpolation period, and v (T) is the feed synthesis speed; a k-order NURBS curve consists of control vertex d i Weight factor omega i Sum node vector u= (x) i ,x i+1 ...x i+k ) The definition is that the formula is as follows:
wherein: x is an independent variable, d i (i=0, 1..n) is the control vertex, ω 0 ,ω n ＞0，ω i ≥0，N i,k (x) Is a B spline basis function;
the B spline basis function formula is as follows:
in three dimensions, NURBS curve expression is:
P(x)＝x(x)m+y(x)n+z(x)p (0≤x≤1)
wherein m, n, p are unit vectors of x, y, z axes respectively, the feed combining speed v (t) is:
further, finding out a very low speed point according to the curvature change condition, and segmenting a curve, specifically: if v (i-1) > v (i), v (i+1) > v (i), v (i) is a very low speed point, and a curve between two adjacent very low speed points is an interpolation section.
Furthermore, the feeding speed is adaptively adjusted by using constraint conditions of curve bow height error, normal maximum acceleration, jerk, self-characteristics of a machine tool and dynamics characteristics of the machine tool, and specifically:
the feeding speed under the arch height error constraint is as follows:
wherein ER is the maximum bow height error, ρ i The curvature radius is T, and the interpolation period is T;
the feeding speed under the normal maximum acceleration and the jerk is as follows:
wherein A is nmax For maximum normal acceleration, J nmax Is the maximum normal jerk.
The feed speed based on the characteristics of the machine tool itself is:
wherein: v (V) i 、A i 、J i Feed speed, acceleration and jerk for the ith interpolation period, V max 、A max 、J max For maximum speed, acceleration and jerk, V i+1 、A i+1 、J i+1 Interpolation cycle speed, acceleration, and jerk for the i+1th;
the feed speed based on the machine dynamics is:
wherein F is lim For maximum cutting force, K c For the cutting force correction factor, a o For the cutting depth, f is the feeding amount of each tooth, and alpha, beta and gamma are parameters related to the workpiece material, the cutter and the cutting condition of the cutter;
the self-adaptive feeding speed adjusting mode comprises the following steps:
wherein F is the maximum speed during processing.
Further, path planning is performed through a trigonometric function acceleration and deceleration control algorithm to obtain acceleration and deceleration start and end parameters, and the parameters are recorded into an acceleration and deceleration array, specifically:
the speed equation for the acceleration and deceleration phase is:
the speed equation for the uniform deceleration phase is:
V 2 (t)＝v 1 -a max (t-t 1 ) t 1 ＜t≤t 2
the speed equation for the deceleration phase:
wherein t is time and the starting time is 0; v (V) 1 (t)、V 2 (t) and V 3 (t) is a speed formula of an acceleration and deceleration stage, a uniform acceleration stage and an acceleration and deceleration stage respectively; v s For initial speed v e To end the speed v 1 At t 1 A feed speed at a moment; the duration of the acceleration and deceleration stage is 0-t 1 The duration of the uniform deceleration phase is t 1 ～t 2 The duration of the deceleration phase is t 2 ～t 3 。
Furthermore, according to the obtained deceleration section information, the acceleration section information and the acceleration/deceleration distance are obtained through prospective interpolation, specifically: let the current working position of the tool be p i The interpolation section is P i P i+1 To ensure the next interpolation point p of the tool i+1 When moving, the feeding speed can be reduced to a specified speed on the premise of ensuring the processing precision, and the judgment is carried out by adopting the prospective distance:
judging the reference speed v k And the magnitude of maximum speed allowed by curve segment V, if V k < V, described in p i The speed is not over-run, and the speed is not required to be reduced at the current point;
obtaining the next interpolation point p i+1 Interpolation parameter x at i+1 The interpolation parameter x i+1 The method comprises the steps of obtaining by adopting second-order Taylor expansion calculation;
comparison p i And p i+1 Is of a size of (2); if p is i ＜p i+1 Description p i A starting position at a deceleration stage; otherwise, p is i+1 As a starting point for the deceleration phase.
Further, the reference speed v is determined k The specific formula of the maximum speed V allowed by the curve segment is as follows:
v k ＝min(F,v k-1 +A max T)
wherein v is k-1 Is p i-1 Reference speed at.
Furthermore, the theoretical deceleration distance required by the tool from the deceleration starting point to the speed minimum point is from the interpolation point p to meet the machining precision requirement i Velocity v at i Decelerating to the interpolation point p j Velocity v at j The required theoretical path is S d Obtaining a theoretical deceleration distance S d Back toSequentially searching interpolation parameters until the interpolation parameter x is found k The method comprises the following steps: l (L) j -l k ≥S d Wherein l is j Interpolation of tool to point p j The length of the path travelled by the tool, l k Point p for tool interpolation i+1 The length of the path travelled; comparison p i And p i+1 If p is of the size of i ＜p i+1 Description p i At the start position of the deceleration stage, otherwise, p i+1 As a starting point for the deceleration phase; the path length travelled is determined by equation S (t).
Further, p is calculated when the tool interpolation point is obtained i+1 Path length of walk l k Before, whether the deceleration stage contains a uniform deceleration stage is judged, and the judgment method is as follows:
if it isMaximum acceleration a max The method can achieve that the deceleration stage is divided into an acceleration and deceleration stage, a uniform deceleration stage and a deceleration and deceleration stage;
if it isThere is no uniform deceleration phase but its maximum acceleration a max The method can achieve that the deceleration stage is divided into an acceleration and deceleration stage, a uniform deceleration stage and a deceleration and deceleration stage;
if it isMaximum acceleration a max Cannot be achieved, and there is no uniform deceleration section, the maximum acceleration a that can be achieved at this time l And (3) recalculating: />
As a further step, the feeding speed is calculated in real time for interpolation by the obtained interpolation parameters, feeding speed and trigonometric function acceleration and deceleration equation, specifically: let the current interpolation parameter be x i The current acceleration/deceleration section is ADL [ i ]]Then:
when x is i ＜ADL[i]Xs, the cutter continues to move at a uniform speed;
when ADL [ i ]].xs＜x i ＜ADL[i]Xe, calculating the real-time feeding speed according to a speed equation V (t);
when x is i-1 ＜ADL[i].xe，x i ＞ADL[i]Xe, adding 1 to x, and keeping the cutter to do uniform motion;
if x occurs during deceleration i ＜ADL[i]Xe and V (x) i )≤ADL[i]When xe, continuously keeping the cutter to do uniform motion;
wherein ADL [ i ]]ADL [ i ] for the ith section of the acceleration/deceleration array obtained before real-time interpolation].xs、ADL[i]Xe is the initial and final interpolation parameters of the acceleration and deceleration section, V (x) i ) For interpolation parameter x i At a speed.
The invention has advantages over existing methods in terms of:
1. the processing flexibility is good. Compared with a polynomial speed control algorithm, the trigonometric function has the property of infinitely conducting, can ensure the continuity of acceleration, jerk and even higher-order curves, realizes flexible acceleration and deceleration control, ensures stable change of processing speed and improves the smoothness of the surface of a workpiece.
2. The processing efficiency is high. The trigonometric function acceleration and deceleration formula is simple and easy to calculate, the calculated amount is small, the interpolation parameter calculation mode adopts a second-order Taylor expansion mode, the feeding speed fluctuation in real-time interpolation is effectively reduced, and the machine tool oscillation is reduced.
3. The processing precision is high. The feeding speed self-adaptive look-ahead interpolation algorithm is adopted, speed constraint is carried out according to characteristics of curve bow height error, normal maximum acceleration, jerk, machine tool dynamics and the like, stable operation of the cutter at sharp corners or inflection points is guaranteed, and numerical control requirements of high speed and high precision can be met on the premise of not exceeding maximum speed, acceleration and jerk.
Drawings
FIG. 1 is a flow chart of a NURBS curve adaptive look-ahead interpolation method;
FIG. 2 is a graph of velocity, acceleration and jerk for a deceleration section including a uniform deceleration section;
FIG. 3 is a graph of velocity, acceleration and jerk for a deceleration section without a uniform deceleration section;
FIG. 4 is a schematic diagram of calculating bow height error using a circular arc approximation;
FIG. 5 is a graph of a "five-pointed star" NURBS to be processed;
FIG. 6 is a graph of velocity profile obtained by the method of the present invention;
FIG. 7 is a graph of acceleration obtained by the method of the present invention;
FIG. 8 is a graph of jerk obtained by the method of the present invention;
FIG. 9 is a graph of the error obtained by the method of the present invention;
FIG. 10 is a graph of velocity versus a fourth order polynomial control algorithm of the method of the present invention; wherein the solid line is a fourth order polynomial and the dashed line is the method of the present invention;
FIG. 11 is a graph of acceleration versus a fourth order polynomial control algorithm of the method of the present invention;
FIG. 12 is a graph comparing jerk of the method of the present invention with that of a fourth order polynomial control algorithm;
FIG. 13 is a graph of error versus the fourth order polynomial control algorithm of the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and to specific embodiments: this is taken as an example to describe the present application further.
The method is simulated and verified on a PC, the programming software is Microsoft Visual C ++6.0, a C language programming program is used, the simulation and verification is performed on a MATLAB platform, and the selected spline curve is NURBS curve.
The main technical interpolation parameters of the test environment are as follows:
operating system: microsoft Windows 7
CPU：Intel(R)Core(TM)i7-7700
The main frequency: 3.60GHz
Memory: 8G (8G)
Interpolation parameters of the numerical control system are as follows:
maximum speed f=0.05 m/s
Maximum acceleration A max ＝0.002m/s 2
Maximum jerk J max ＝0.0002m/s 3
Maximum chord height error E max ＝0.002mm
Interpolation period t=0.002 s
This embodiment is exemplified by the processing of a "five-star" shaped curve, as shown in fig. 5.
The embodiment provides a NURBS curve adaptive look-ahead interpolation method, and the entire interpolation flow chart is shown in fig. 1. The system comprises a preprocessing module and a real-time interpolation module.
The preprocessing module comprises: obtaining interpolation parameters of each interpolation point by adopting a second-order Taylor expansion type; searching for the extremely low speed point of the NURBS curve, segmenting the NURBS curve according to the extremely low speed point, dividing an acceleration and deceleration area, and obtaining the distance travelled, namely the length of each curve segment according to a trigonometric function acceleration and deceleration position equation; speed constraint is carried out according to factors such as curve bow height error, maximum normal acceleration, jerk and machine tool dynamics; based on the deceleration section information obtained in the first section, the acceleration section information and the acceleration/deceleration distance are obtained by look-ahead interpolation.
The real-time interpolation module calculates the feeding speed in real time by taking the period as a unit according to the obtained information such as the path length, the path start and end points, the speed and the like of the acceleration and deceleration section, and makes corresponding speed constraint.
1. The interpolation parameters of each interpolation point are obtained by adopting a second-order Taylor expansion type, and the method specifically comprises the following steps:
wherein x is i As the current interpolation point, the interpolation parameter corresponding to P (x), T is the interpolation period, and v (T) is the feed synthesis speed; a k-order NURBS curve consists of control vertex d i Weight factor omega i Sum node vector u= (x) i ,x i+1 ...x i+k ) Definition of the definitionThe formula is as follows:
wherein: x is an independent variable, d i (i=0, 1..n) is the control vertex, ω 0 ,ω n ＞0，ω i ≥0，N i,k (x) Is a B spline basis function;
the B spline basis function formula is as follows:
in three dimensions, NURBS curve expression is:
P(x)＝x(x)m+y(x)n+z(x)p (0≤x≤1)
wherein m, n, p are unit vectors of x, y, z axes respectively, the feed combining speed v (t) is:
2. finding out a very low speed point according to curvature change conditions, segmenting a curve, and finding out the very low speed point according to the following strategy:
if v (i-1) > v (i), v (i+1) > v (i), then v (i) is the very low velocity point.
The curve between two adjacent speed extreme points is an interpolation interval.
3. The feeding speed is adaptively adjusted by using constraint conditions of curve bow height error, normal maximum acceleration, jerk, self-characteristics of a machine tool and dynamics characteristics of the machine tool, and the method specifically comprises the following steps:
the feeding speed under the arch height error constraint is as follows:
wherein ER is the mostLarge bow height error ρ i The curvature radius is T, and the interpolation period is T;
the feeding speed under the normal maximum acceleration and the jerk is as follows:
wherein A is nmax For maximum normal acceleration, J nmax Maximum normal jerk;
the feed speed based on the characteristics of the machine tool itself is:
wherein: v (V) i 、A i 、J i Feed speed, acceleration and jerk for the ith interpolation period, V max 、A max 、J max For maximum speed, acceleration and jerk, V i+1 、A i+1 、J i+1 Interpolation cycle speed, acceleration, and jerk for the i+1th;
the feed speed based on the machine dynamics is:
wherein F is lim For maximum cutting force, K c For the cutting force correction factor, a o For the cutting depth, f is the feeding amount of each tooth, and alpha, beta and gamma are parameters related to the workpiece material, the cutter and the cutting condition of the cutter;
correspondingly, the self-adaptive feeding speed adjustment mode is as follows:
wherein F is the maximum speed during processing.
4. Path planning is carried out through a trigonometric function acceleration and deceleration control algorithm to obtain acceleration and deceleration start and end parameters, and the parameters are recorded into an acceleration and deceleration array, wherein the specific formula is as follows:
the speed equation for the acceleration and deceleration phase is:
the speed equation of the uniform deceleration stage is:
V 2 (t)＝v 1 -a max (t-t 1 )t 1 ＜t≤t 2
the speed equation of the deceleration stage is:
t 2 ＜t≤t 3
wherein t is time and the starting time is 0; v (V) 1 (t)、V 2 (t) and V 3 (t) is a speed formula of an acceleration and deceleration stage, a uniform acceleration stage and an acceleration and deceleration stage respectively; v s For initial speed v e To end the speed v 1 At t 1 A feed speed at a moment; the duration of the acceleration and deceleration stage is 0-t 1 The duration of the uniform deceleration phase is t 1 ～t 2 The duration of the deceleration phase is t 2 ～t 3 。
5. According to the obtained deceleration section information, the acceleration section information and the acceleration and deceleration distance are obtained through prospective interpolation, and the specific flow is as follows:
assuming that the current machining position of the tool is p i The interpolation section is P i P i+1 To ensure the next interpolation point p of the tool i+1 During movement, the feeding speed can be ensuredThe machining accuracy is reduced to a specified speed on the premise that the machining accuracy is reduced, and the judgment is performed by using the look-ahead distance.
(1) Judging the reference speed v k Maximum speed V allowed by curve segment, if V k < V, described in p i The speed is not over-run, and the speed is not required to be reduced at the current point;
(2) Calculating the next interpolation point p i+1 Interpolation parameter x at k+1 ；
(3) Comparison p i And p i+1 Is of a size of (a) and (b). If p is i ＜p i+1 Description p i At the start position of the deceleration stage, otherwise, p i+1 As a starting point for the deceleration phase.
Judging the reference speed v k The maximum speed V allowed by the curve segment is calculated by the following specific formula:
v k ＝min(F,v k-1 +A max T)
wherein v is k-1 Is p i-1 Reference speed at.
Calculating the next interpolation point p by adopting second-order Taylor expansion i+1 Interpolation parameter x at k+1 The specific formula is as follows:
wherein x is i The interpolation parameter corresponding to the current interpolation point P (x), T is the interpolation period, and v (T) is the feed synthesis speed.
The theoretical deceleration distance required for decelerating the cutter from the deceleration starting point to the speed minimum point is from the interpolation point p to meet the requirement of machining precision i Velocity v at i Decelerating to the interpolation point p j Velocity v at j The required theoretical path is the deceleration distance S d ；
Obtaining a theoretical deceleration distance S d Then, the interpolation parameters are sequentially searched forward until the interpolation parameter x is found k The method comprises the following steps: l (L) j -l k ≥S d
Wherein l j To interpolate to point p j The length of the path travelled by the tool, l k Point p for tool interpolation i+1 Path length traversed, comparison p i And p i+1 Is of a size of (a) and (b). If p is i ＜p i+1 Description p i At the start position of the deceleration stage, otherwise, p i+1 As a starting point for the deceleration phase.
In calculating l k Before, whether the deceleration stage contains a uniform deceleration stage is judged, and the judgment method is as follows: comparison ofAndis of a size of (a) and (b).
If it isMaximum acceleration a max The deceleration stage can be divided into an acceleration and deceleration stage, a uniform deceleration stage and a deceleration and deceleration stage;
if it isThere is no uniform deceleration phase but its maximum acceleration a max The method can achieve that the deceleration stage is divided into an acceleration and deceleration stage, a uniform deceleration stage and a deceleration and deceleration stage;
if it isMaximum acceleration a max Cannot be achieved, and there is no uniform deceleration section, the maximum acceleration a that can be achieved at this time l And (3) recalculating: />
6. Performing real-time interpolation, and calculating the feeding speed in real time according to the obtained interpolation parameters, the feeding speed, the trigonometric function acceleration and deceleration equation and other information, wherein the specific steps are as follows:
assume that the current interpolation parameter is x i The current acceleration/deceleration section is ADL [ x ]]Then:
(1) When x is i ＜ADL[x]Xs, the cutter continues to move at a uniform speed;
(2) When ADL [ x ]].xs＜x i ＜ADL[x]Xe, calculating the real-time feeding speed according to a speed equation;
(3) When x is i-1 ＜ADL[x].xe，x i ＞ADL[x]And xe, adding 1 to x, and keeping the cutter to do uniform motion.
(4) If x occurs during deceleration i ＜ADL[x]Xe and V (x) i )≤ADL[x]And (e) continuously keeping the cutter to do uniform motion during xe.
Wherein ADL [ x ]]ADL [ x ] for the x-th segment of the acceleration/deceleration array obtained before real-time interpolation].xs、ADL[x]Xe is the initial and final interpolation parameters of the acceleration and deceleration section, V (x) i ) For interpolation parameter x i At a speed.
The invention has the advantages and effects that: (1) The continuity of acceleration, jerk and even higher order curves can be ensured, flexible acceleration and deceleration control is realized, the processing speed is changed stably, and the smoothness of the surface of a workpiece is improved; (2) The calculated amount is small, so that the fluctuation of the feeding speed in real-time interpolation is effectively reduced, and the oscillation of a machine tool is reduced; (3) The cutter can be ensured to stably run at the sharp angle or inflection point, and the numerical control requirements of high speed and high precision can be simultaneously met on the premise of not exceeding the maximum speed, acceleration and jerk.
While the invention has been described with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (9)

  1. An nurbs curve adaptive look-ahead interpolation method, comprising:
    obtaining interpolation parameters of each interpolation point by adopting a second-order Taylor expansion type;
    finding out an extremely low speed point according to the curvature change condition, and segmenting a curve;
    the feeding speed is adaptively adjusted by using constraint conditions of curve bow height error, normal maximum acceleration, jerk, self-characteristics of a machine tool and dynamics characteristics of the machine tool, and the method specifically comprises the following steps:
    the feeding speed under the arch height error constraint is as follows:
    wherein ER is the maximum bow height error, ρ i The curvature radius is T, and the interpolation period is T;
    the feeding speed under the normal maximum acceleration and the jerk is as follows:
    wherein A is nmax For maximum normal acceleration, J nmax Maximum normal jerk;
    the feed speed based on the characteristics of the machine tool itself is:
    wherein: v (V) i 、A i 、J i Feed speed, acceleration and jerk for the ith interpolation period, V max 、A max 、J max For maximum speed, acceleration and jerk, V i+1 、A i+1 、J i+1 Interpolation cycle speed, acceleration, and jerk for the i+1th;
    the feed speed based on the machine dynamics is:
    wherein F is lim For maximum cutting force, K c For the cutting force correction factor, a o For the cutting depth, f is the feeding amount of each tooth, and alpha, beta and gamma are parameters related to the workpiece material, the cutter and the cutting condition of the cutter;
    the self-adaptive feeding speed adjusting mode comprises the following steps:
    wherein F is the maximum speed during processing;
    path planning is carried out through a trigonometric function acceleration and deceleration control algorithm to obtain acceleration and deceleration start and end parameters, and the parameters are recorded into an acceleration and deceleration array;
    according to the obtained deceleration section information, performing look-ahead interpolation to obtain acceleration section information and acceleration and deceleration distances;
    and calculating the feeding speed in real time for interpolation through the obtained interpolation parameters, the feeding speed and the trigonometric function acceleration and deceleration equation.
  2. 2. The NURBS curve adaptive look-ahead interpolation method of claim 1, wherein the interpolation parameters of each interpolation point are obtained by using a second-order taylor expansion, specifically:
    wherein x is i As the current interpolation point, the interpolation parameter corresponding to P (x), T is the interpolation period, and v (T) is the feed synthesis speed; a k-order NURBS curve consists of control vertex d i Weight factor omega i Sum node vector u= (x) i ,x i+1 ...x i+k ) The definition is that the formula is as follows:
    wherein: x is an independent variable, d i (i=0, 1..n) is the control vertex, ω 0 ,ω n ＞0，ω i ≥0，N i,k (x) Is a B spline basis function;
    the B spline basis function formula is as follows:
    in three dimensions, NURBS curve expression is:
    P(x)＝x(x)m+y(x)n+z(x)p(0≤x≤1)
    wherein m, n, p are unit vectors of x, y, z axes respectively, the feed combining speed v (t) is:
  3. 3. the NURBS curve adaptive look-ahead interpolation method of claim 1, wherein the finding of the very low speed point according to the curvature change condition and the segmentation of the curve are specifically: if v (i-1) > v (i), v (i+1) > v (i), v (i) is a very low speed point, and a curve between two adjacent very low speed points is an interpolation section.
  4. 4. The NURBS curve adaptive look-ahead interpolation method of claim 1, wherein a path is planned by a trigonometric function acceleration/deceleration control algorithm to obtain acceleration/deceleration start/end parameters, and the parameters are recorded in an acceleration/deceleration array, specifically:
    the speed equation for the acceleration and deceleration phase is:
    the velocity equation for the ramp-up phase is:
    V 2 (t)＝v 1 -a max (t-t 1 )t 1 ＜t≤t 2
    the speed equation of the acceleration and deceleration phase:
    t 2 ＜t≤t 3
    wherein t is time and the starting time is 0; v (V) 1 (t)、V 2 (t) and V 3 (t) is a speed formula of an acceleration and deceleration stage, a uniform acceleration stage and an acceleration and deceleration stage respectively; v s For initial speed v e To end the speed v 1 At t 1 A feed speed at a moment; the duration of the acceleration and deceleration stage is 0-t 1 The duration of the ramp-up phase is t 1 ～t 2 The duration of the acceleration and deceleration stage is t 2 ～t 3 。
  5. 5. The NURBS curve adaptive look-ahead interpolation method of claim 4, wherein, according to the obtained deceleration section information, look-ahead interpolation obtains acceleration section information and acceleration-deceleration distance, specifically: let the current working position of the tool be p i The interpolation section is P i P i+1 To ensure the next interpolation point p of the tool i+1 When moving, the feeding speed can be reduced to a specified speed on the premise of ensuring the processing precision, and the judgment is carried out by adopting the prospective distance:
    judging the reference speed v k And the magnitude of maximum speed allowed by curve segment V, if V k < V, described in p i The speed is not over-run, and the speed is not required to be reduced at the current point;
    obtaining the next interpolation point p i+1 Interpolation parameter x at i+1 The interpolation is performedParameter x i+1 The method comprises the steps of obtaining by adopting second-order Taylor expansion calculation;
    comparison p i And p i+1 Is of a size of (2); if p is i ＜p i+1 Description p i A starting position at a deceleration stage; otherwise, p is i+1 As a starting point for the deceleration phase.
  6. 6. The NURBS curve adaptive look-ahead interpolation method of claim 5, wherein the reference velocity v is determined k The specific formula of the maximum speed V allowed by the curve segment is as follows:
    v k ＝min(F,v k-1 +A max T)
    wherein v is k-1 Is p i-1 Reference speed at.
  7. 7. The NURBS curve adaptive look-ahead interpolation method of claim 5, wherein the interpolation point p is followed i Velocity v at i Decelerating to the interpolation point p j Velocity v at j The required theoretical path is the deceleration distance S d Obtaining a theoretical deceleration distance S d Then, the interpolation parameters are sequentially searched forward until the interpolation parameter x is found k The method comprises the following steps: l (L) j -l k ≥S d Wherein l is j Interpolation of tool to point p j The length of the path travelled by the tool, l k Interpolation of tool to point p i+1 The length of the path travelled by the time; comparison p i And p i+1 If p is of the size of i ＜p i+1 Description p i At the start position of the deceleration stage, otherwise, p i+1 As a starting point for the deceleration phase; the path length travelled is determined by equation S (t).
  8. 8. The NURBS curve adaptive look-ahead interpolation method of claim 7, wherein the tool interpolation to point p is obtained i+1 Path length of travel k Before, whether the deceleration stage contains a uniform deceleration stage is judged, and the judgment method is as follows:
    if it isMaximum acceleration a max The method can achieve that the deceleration stage is divided into an acceleration and deceleration stage, a uniform deceleration stage and a deceleration and deceleration stage;
    if it isThere is no uniform deceleration phase but its maximum acceleration a max The method can achieve that the deceleration stage is divided into an acceleration and deceleration stage and a deceleration and deceleration stage;
    if it isMaximum acceleration a max Cannot be achieved, and there is no uniform deceleration section, the maximum acceleration a that can be achieved at this time l And (3) recalculating: />
  9. 9. The NURBS curve adaptive look-ahead interpolation method of claim 2, wherein the interpolation is performed by calculating the feed speed in real time by using the obtained interpolation parameters, the feed speed and the trigonometric function acceleration and deceleration equation, specifically: let the current interpolation parameter be x i The current acceleration/deceleration section is ADL [ i ]]Then:
    when x is i ＜ADL[i]Xs, the cutter continues to move at a uniform speed;
    when ADL [ i ]].xs＜x i ＜ADL[i]Xe, calculating the real-time feeding synthetic speed according to a speed equation v (t);
    when x is i-1 ＜ADL[i].xe，x i ＞ADL[i]Xe, adding 1 to x, and keeping the cutter to do uniform motion;
    if x occurs during deceleration i ＜ADL[i]Xe and V (x) i )≤ADL[i]When xe, continuously keeping the cutter to do uniform motion;
    wherein ADL [ i ]]For an acceleration/deceleration array obtained before real-time interpolationSection i, ADL [ i ]].xs、ADL[i]Xe is the initial and final interpolation parameters of the acceleration and deceleration section, V (x) i ) For interpolation parameter x i At a speed.
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CN114237161B (en) * 2021-11-16 2023-07-21 华南理工大学 Industrial robot NURBS curve interpolation method based on digital filtering
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105629882A (en) * 2014-11-07 2016-06-01 中国科学院沈阳计算技术研究所有限公司 Trigonometric function speed planning method used for spline interpolation
CN107291047A (en) * 2017-07-14 2017-10-24 福建工程学院 A kind of positive and negative two-way nurbs curve interpolating method based on multi-constraint condition
CN110471368A (en) * 2019-08-30 2019-11-19 长安大学 A kind of prediction interpolating method that High Speed NC Machine Tools process velocity is adaptive
CN111123840A (en) * 2018-10-31 2020-05-08 发那科株式会社 Numerical controller

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105629882A (en) * 2014-11-07 2016-06-01 中国科学院沈阳计算技术研究所有限公司 Trigonometric function speed planning method used for spline interpolation
CN107291047A (en) * 2017-07-14 2017-10-24 福建工程学院 A kind of positive and negative two-way nurbs curve interpolating method based on multi-constraint condition
CN111123840A (en) * 2018-10-31 2020-05-08 发那科株式会社 Numerical controller
CN110471368A (en) * 2019-08-30 2019-11-19 长安大学 A kind of prediction interpolating method that High Speed NC Machine Tools process velocity is adaptive

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
Design of jerk bounded feedrate with ripple effect for adaptive nurbs interpolator;M.Sekar;Int J Adv Manuf Technol;全文 *
Summary of spline Curve Interpolation;Gai Rongli;ICMCCE;全文 *
Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming;Wei Fan.Xiao;Int J Adv Manuf Technol;全文 *
多约束条件的NURBS曲线自适应前瞻插补算法;盖荣丽;郑州大学学报（理学版）;第54卷(第3期);全文 *
多约束综合控制的NURBS曲线插补算法及其刀补研究与实现;李业鹏;中国优秀硕士学位论文全文数据库 工程科技I辑;全文 *
空间自由曲线机器人匀速运动控制方法研究;郭光远;中国优秀硕士学位论文全文数据库 信息科技辑;全文 *

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