CN101976060B - NURBS (Non-Uniform Rational B-Spline) interpolation method based on machine tool dynamics and curve characteristics - Google Patents
NURBS (Non-Uniform Rational B-Spline) interpolation method based on machine tool dynamics and curve characteristics Download PDFInfo
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Abstract
The invention discloses an NURBS (Non-Uniform Rational B-Spline) interpolation method based on machine tool dynamics and curve characteristics, which adopts a constraint equation ZHYS considering integrative factors of machine tooling for controlling the feeding speed and the acceleration of the interpolation algorithm. The method consists of three links: pre-interpolation, prospective information processing and real-time interpolation, and comprises the following steps of: carrying out trigonometric function speed smoothing processing according to the corresponding speed mode; storing corresponding data after the trigonometric function speed smoothing processing; adopting the trigonometric function speed smoothing processing according to prospective information if entering an acceleration-deceleration region; and adopting a speed self-adapting method for calculation if not entering the acceleration-deceleration region, thus finally obtaining the coordinates and the feeding speed of interpolation points. The method of the invention has the advantages that the interpolation is always in the safe range of a machine tool, the whole interpolation movement process is smooth and stable through the trigonometric function speed smoothing processing, in addition, the tangential acceleration and the continuity of the tangential acceleration in the speed change region can be ensured, andthe NURBS interpolation method has the important significance on the development of a high-speed and high-precision numerical control system.
Description
Technical field
The invention belongs to CNC technology, especially numerically-controlled machine or revolute robot's movement control technology field.
Background technology
The principal feature of non-uniform rational B-spline (Non-Uniform Rational B-Spline is called for short nurbs curve) is with accurately expression quafric curve and quadric mathematical method are unified each other with the B spline method of describing the free type curve and surface.In view of power and the potentiality of NURBS aspect shape definition.Be about to unique method for expressing that NURBS is defined as free type curve, curved surface in the industrial products geometric definition STEP standard of the formal promulgation of International Standards Organization (ISO) in 1991.The a large amount of free profiles of industries such as aviation, shipbuilding, automobile, mould adopt nurbs curve to describe, and research NURBS interpolation technique is for the class, level and the competitiveness that improve the domestic numerical control system, and the blockade on new techniques of breaking developed country has significant meaning.
Being regarded as the interpolation of NURBS parametric line in the world is one of significant function of modern high-grade digital control system; The high-grade digital control systems of minority such as at present external FANUC30i, Sinumerik840D and Mitsubishi are supported the NURBS interpolation; The Axium Power digital control system of NUM company is supported polynomial interpolator and NURBS interpolation, the domestic digital control system that does not also have ripe support NURBS interpolation.Mainly there is following problem in the NURBS interpolation algorithm in the present High-speed machining: constant feeding interpolation is difficult to satisfy simultaneously high speed and high-precision requirement, and variable-speed feeding speed possibly cause bigger speed and acceleration change, influence processing stationarity and machining precision; The bigger acceleration of sudden change influence in the interpolation process is considered not enough, and in fact in High-speed machining, bigger acceleration possibly cause that cutter trembles even breaking; Lathe acceleration and deceleration performance is considered not enough, only considered along the influence of tangential, path and normal acceleration usually, do not consider that each speed or acceleration decompose the influence of lathe on each; Acceleration and deceleration control method computation process is complicated, and the real-time of interpolation is not high.People such as Chen Jincheng
[1] Chen Jincheng, Xu Zhiming, Zhong Tingxiu, Jiang Houzong. kinematics and the dynamical property analysis [J] of lathe during along the curve High-speed machining. mechanical engineering journal, 2002,38 (l): 31-34.
[2]?Zhi?Ming?Xu,?Jin?Cheng?Chen,?Zheng?Jin?Feng.?Performance?evalution?of?a?real-time?interpolation?algorithm?for?NURBS?curves.?International?Journal?of?Advanced?Manufacturing?Technology,2002,20:270-276.
[3] Chen Jincheng, Xu Zhiming, Xu Zhengfei; Zhong Tingxiu; Jiang Houzong. based on the High-speed machining smooth motion profile study on algorithm of adaptive [J] of segmentation cubic spline curve. mechanical engineering journal, 2002,38 (5): 61-65.) from constant speed of feed interpolation; With the nurbs curve is example; Studied the constraint condition of lathe acceleration and deceleration performance to speed of feed, the value that speed of feed is described is relevant with the condition of the virtual rating of drive motor and Processing Curve, and obtains the maximum safe speed of feed equation of constraint of curve.
The scholar of the Central China University of Science and Technology has carried out dynamics based on triumphant grace equation to the electric rotating machine feed system,
[4] Liu Kezhao. based on the research [D] of the direct interpolation of nurbs curve of Machine Tool Dynamics characteristic. the Central China University of Science and Technology, 2004.
[5] Liu Kezhao, Peng Fangyu, Wu Hao, Hu Jianbing. based on the direct interpolation of the nurbs curve of Machine Tool Dynamics characteristic [J]. lathe and hydraulic pressure, 2004,11:19-22.
[6] Peng Fangyu; Appoint jade-like stone, Luo Zhongcheng, Li Bin. nurbs curve Machine Tool Dynamics characteristic self-adaptive direct patches benefit [J]; Central China University of Science and Technology's journal (natural science edition); Adopt secondary genetic algorithm nurbs curve curvature peak values calculate at 2005,33 (7): 80～83., and become the feeding interpolation algorithm when having designed on this basis.But speed is not carried out smoothing processing.
The patent of invention (number of patent application is 200910113894.4) of people such as Pan Hai Hong of Guangxi University application is the nurbs curve self-adapting subsection interpolation method of real time forward looking whole-process acceleration and deceleration control.In this patent of invention, interpolation algorithm has following characteristics: the one, and adopted matrix form to represent nurbs curve, improved the counting yield of nurbs curve equation; The 2nd, interpolation algorithm is divided into prediction pre-service and real-time interpolation two parts; In the prediction pre-service, calculate the speed of feed that satisfies the interpolation precision requirement through the speed adaptive method; And according to curvature of curve with curve segmentation, utilize D curve acceleration and deceleration control method that the speed of each section is planned then.The real-time interpolation part is calculated interpolated point then according to prediction information.Owing to have above-mentioned two characteristics, so this algorithm motion smoothing property and accuracy of interpolation real-time and deceleration point position prediction in the interpolation process of having compared the limited raising of other algorithms.
Summary of the invention
Above shortcoming in view of prior art; The purpose of this invention is to provide a kind of NURBS interpolating method based on Machine Tool Dynamics and curve characteristic; Make it synthetically consider the actual conditions of lathe the moving interpolation, again further smoothing processing speed from lathe with by interpolation curve two aspects.
The objective of the invention is to realize through following means.
NURBS interpolating method based on Machine Tool Dynamics and curve characteristic; Derive speed of feed and the acceleration that equation of constraint is controlled interpolation algorithm according to lathe property and curve characteristic, method is made up of three links: interpolation in advance, prediction information processing and real-time interpolation; The interpolation link adopts the speed adaptive adjustment algorithm in advance; Prediction information processing link is at first divided the acceleration and deceleration district according to the interpolated point speed of feed, respectively the acceleration and deceleration district is judged then, carries out the function rate smoothing according to the velocity mode of correspondence and handles; It is characterized in that said equation of constraint adopts the equation of constraint ZHYS that considers the machine tooling comprehensive key element; And
(1) in advance the interpolation link adopts the speed adaptive adjustment algorithm, preserves interpolated point information and the substitution of interpolated point information is calculated interpolated point maximum tangential acceleration sequence based on the equation of constraint ZHYS of Machine Tool Dynamics and curve characteristic;
(2) prediction information processing link is at first divided the acceleration and deceleration district according to the interpolated point speed of feed; Respectively the acceleration and deceleration district is judged then; Velocity mode according to correspondence carries out the processing of trigonometric function rate smoothing, preserves the corresponding data after the trigonometric function rate smoothing is handled;
(3) the real-time interpolation link is carried out real-time speed adaptive interpolation calculating to prediction information, if get into the acceleration and deceleration district, then according to prediction information, adopts the trigonometric function rate smoothing to handle; If do not get into the acceleration and deceleration district, then adopt the speed adaptive method to calculate, thereby finally obtain the coordinate and the speed of feed of interpolated point.
Adopt method of the present invention; Interpolation is in the safe range of lathe all the time; The trigonometric function rate smoothing is handled and is made whole moving interpolation process smoothly stable; And guarantee that tangential acceleration and tangential acceleration are continuous in the velocity variations district, the development of high speed and super precision digital control system there is important meaning.
Description of drawings
Fig. 1 is a general structure process flow diagram of the present invention
Fig. 2 is the process flow diagram of definite processing module of accelerating region and deceleration area
Fig. 3 is the speed planning pattern
Fig. 4 is the speed displacement intersection in imaginary acceleration and deceleration district
Fig. 5 is the process flow diagram of trigonometric function rate smoothing processing module
Fig. 6 is by three nurbs curves of interpolation in the instance
Fig. 7 is by the curvature of curve figure of three nurbs curves of interpolation in the instance
Fig. 8 is the rate curve comparison diagram of two kinds of interpolating methods in the instance
Fig. 9 is the accelerating curve comparison diagram of two kinds of interpolating methods in the instance
Figure 10 is the error comparison diagram of two kinds of interpolating methods in the instance.
Embodiment
Below in conjunction with accompanying drawing and embodiment the present invention is described further.
The inventive method has taken into full account the constraint to interpolating method of Machine Tool Dynamics and curve characteristic; Interpolation is in the safe range of lathe all the time; The trigonometric function rate smoothing is handled and is made whole moving interpolation process smoothly stable simultaneously, and guarantees in the velocity variations district continuity of tangential acceleration and tangential acceleration; Be all very strong numerical control interpolation control method of a kind of practicality and adaptability, this method has important use to be worth to the high speed and super precision digital control system.
For realizing above-mentioned target, technical scheme of the present invention is following:
Based on Machine Tool Dynamics and curve characteristic, the NURBS interpolating method that adopts the trigonometric function rate smoothing to handle shown in accompanying drawing 1, may further comprise the steps:
Set up equation of constraint ZHYS link:
(1) pass through the motor-driven characteristic, the Milling Force modeling, friction force and machine tool motion state etc. is carried out modeling;
(2) simultaneously obtaining of nurbs curve condition parameter derived, set up equation of constraint based on the Machine Tool Dynamics curve characteristic.
Preparatory interpolation link:
(1), calculates the radius-of-curvature of current point by current interpolated point parameter;
(2), estimate speed of feed in next interpolation cycle by the relation between error and radius-of-curvature;
(3) get little person in the speed of feed and instruction speed of feed as the speed of feed discreet value;
(4) calculate the interpolation step-length;
Arrow is cut by the unit of (5) trying to achieve interpolated point, and the secondary method of unit is vowed parameters such as the master of unit method arrow;
(6) calculate interpolated point tangential peak acceleration, can form the interpolated point argument sequence, preserve interpolation step-length sequence, the knot vector sequence, speed of feed sequence and maximum tangential acceleration sequence are as prediction information.
Prediction information processing link:
(1) speed in the interpolated point speed of feed sequence is judged, the speed of feed sequence is divided into velocity-stabilization district and velocity variations district (being the acceleration and deceleration districts);
(2) processing of trigonometric function rate smoothing is divided into three kinds of speed planning patterns and handles, the velocity variations district is sorted out respectively, handle according to the Planning Model of correspondence.
(3) line up according to the size of starting point knot vector and peripheral node vector successively in each acceleration and deceleration district.
The real-time interpolation link:
Adopt the speed adaptive adjustment algorithm to calculate interpolated point,,, adopt corresponding trigonometric function rate smoothing to handle then according to prediction information if interpolation gets into the acceleration and deceleration district.If interpolation does not get into the acceleration and deceleration district, then adopt the speed adaptive method to calculate.Coordinate and the speed of feed that generates interpolated point calculated in interpolation.
Comprise following steps:
(1) compares Calculation of curvature radius or speed of feed by the information in current interpolated point parameter and the prediction information;
(2) calculate the interpolation step-length;
(3) obtain the parameter of interpolated point.
The equation of constraint ZHYS of described Machine Tool Dynamics of the inventive method and curve characteristic is:
Wherein,
is each coordinate direction moving-member gross mass;
is circular constant;
Each receives the restriction of self dynamic response to
for lathe, has intrinsic peak acceleration;
In the formula
Where
is the moving speed of each axis.
is each output torque of going up motor;
is each nominal torque that goes up motor;
is each rated power of going up motor;
is that each goes up rotating speed of motor, and
is each rated speed that goes up motor.
Wherein
（5）
Wherein
Wherein
(8)
Wherein
（10）
Wherein
Wherein
Wherein
（22）
Wherein
, (23)
And note
;
,
The said preparatory interpolation link of the inventive method comprises following steps:
(1), calculates the radius-of-curvature
of current point by current interpolated point parameter
.
(2) by the relation between error and radius-of-curvature; Estimate speed of feed in next interpolation cycle, calculate speed of feed
:
(3) get little person in speed of feed
the and instruction speed of feed
as the speed of feed discreet value; Be designated as
, promptly
(4) calculate interpolation step-length
.
is interpolation cycle in the formula
(5) calculate next interpolated point parameter
.
(6) by interpolated point parameter
; Arrow
is cut by the unit that calculates this interpolated point; Unit is secondary, and method is vowed
, and the master of unit method is vowed parameters such as
.
(7) arrow
is cut by unit; Unit is secondary, and method is vowed
; The master of unit method is vowed
; Speed of feed
and lathe; The equation of constraint ZHYS of parameter substitution Machine Tool Dynamicses such as motor and curve characteristic obtains this interpolated point tangential peak acceleration
.
When interpolating method from curve when starting point calculates terminal point; Each parameter of interpolated point just can be formed corresponding sequence; Preserve interpolation step-length sequence
; Knot vector sequence
, speed of feed sequence
and maximum tangential acceleration sequence
are as prediction information.
Interpolation step-length sequence
adds up and can further try to achieve the discrete function of displacement and knot vector.
The concrete steps of the said prediction information processing of the inventive method link are:
(1) speed in the interpolated point speed of feed sequence is judged, the speed of feed sequence is divided into velocity-stabilization district and velocity variations district (also crying the acceleration and deceleration district).
Comprised the speed of feed sequence in the prediction information that interpolation is tried to achieve in advance.In the speed of feed sequence; Judge that whether the speed of feed value is less than the instruction speed of feed; If speed of feed is less than the instruction speed of feed; Then extract the corresponding interpolation sequence number of this speed of feed value (sequence number of this interpolated point when the interpolation sequence number is preparatory interpolation; Be
value in the sequence
), knot vector value, speed of feed value and maximum tangential acceleration value.A velocity variations district is formed in the continuous zone of sequence number.
In the velocity variations zone, be deceleration area in the front of speed minimum value; In the speed minimum value is accelerating region at the back.In like manner, try to achieve the speed maximal value after, can confirm speed maximal value front for accelerating region; Speed maximal value back be deceleration area, the flow process of definite processing module of accelerating region and deceleration area is shown in accompanying drawing 2.
Obtain the velocity series of accelerating region and deceleration area; And after obtaining this zone knot vector sequence and maximum tangential acceleration sequence accordingly; Rough handling through prediction information; The sequence of each parameter that preparatory interpolation is tried to achieve is divided into the little sequence of plurality of sections according to speed, and is classified as accelerating region or deceleration area.These information will be used for the trigonometric function rate smoothing and handle.
(2) processing of trigonometric function rate smoothing is divided into three kinds of speed planning patterns and handles, the velocity variations district is sorted out respectively, handle according to the Planning Model of correspondence.
Trigonometric function structure acceleration and deceleration curves makes system have very high acceleration and deceleration flexibility.Its speed constructed fuction is following:
Satisfying velocity boundary conditions is:
,
The speed constructed fuction is carried out integration can obtain displacement function:
（29）
Differentiate can obtain acceleration function to the speed constructed fuction:
Satisfying the acceleartion boundary condition is:
,
Velocity function confirm to depend on
;
and
; With the unknown number of these three variablees, it is found the solution as speed planning.
Analyze actual processing situation, generally have three kinds of multi-form accelerating regions and deceleration area, the present invention is divided into three kinds of patterns with speed planning, shown in accompanying drawing 3.
(1) the speed planning pattern 1.Shown in accompanying drawing 3 (a).
Play spot speed in the speed planning pattern 1 and terminal velocity remains unchanged; Therefore
,
can be obtained by the velocity series in acceleration and deceleration district.
In order to make in the whole trigonometric function speed planning; Accekeration can not surpass the limit acceleration value of lathe; Should make the minimum value of the amplitude of acceleration
, that is:
smaller or equal to maximum tangential acceleration sequence in this acceleration and deceleration district
By
, can get
Can confirm the speed constructed fuction according to
, promptly obtain the arbitrary speed in the acceleration and deceleration district.
3. the knot vector of accelerating region and deceleration area is confirmed
Because acceleration is planned according to trigonometric function; Therefore planning back average acceleration value has diminished; And velocity variable remains unchanged; Can know that according to
displacement will increase.
Because displacement and knot vector
are to concern one to one; Under the situation that total displacement increases, knot vector should extend out accordingly.A point vector
of accelerating region is constant, and terminal point vector
should increase; The point vector
that rises of deceleration area reduces, and terminal point vector
remains unchanged.
Will
and
into the displacement function can be obtained after the planned total displacement:
?.
According to displacement and knot vector
corresponding relationship; Can calculate starting point
value and terminal point
value in acceleration and deceleration district; During as interpolation next time, whether get into the sign in acceleration and deceleration district.
In program; Storage speed Planning Model numbering; Play spot speed
; Terminal velocity
; Trigonometric function angular velocity
; Starting point knot vector
and peripheral node vector
promptly can be used as the prediction control information in an acceleration and deceleration district.
(2) the speed planning pattern 2.Shown in accompanying drawing 3 (b).
The spot speed that rises of accelerating region remains unchanged in the speed planning pattern 2, and the terminal velocity of deceleration area remains unchanged, and the planning of accelerating region and the planning of deceleration area are similar, and therefore the planning of accelerating region only is discussed.Playing spot speed
can be obtained by the velocity series in acceleration and deceleration district.
In order to make in the whole trigonometric function speed planning; Accekeration can not surpass the limit acceleration value of lathe; Should make the minimum value of the amplitude of acceleration
, that is:
smaller or equal to the maximum tangential acceleration sequence in this acceleration and deceleration district.
By the acceleration function
can be obtained:
Total displacement remains unchanged in the speed planning pattern 2.Displacement can be calculated through knot vector u sequence.
Will
displacement function can get into accelerated Chief displacement:
With
substitution
, can try to achieve:
Then
is:
Can be according to displacement and knot vector u corresponding relationship in the hope of starting point
value and the terminal point
of accelerating region; Storage speed Planning Model numbering; Play spot speed
; Terminal velocity
; Trigonometric function angular velocity
; Starting point knot vector
and peripheral node vector
promptly can be used as the prediction control information in an acceleration and deceleration district.
(3) speed planning mode 3
Shown in accompanying drawing 3 (c), in first kind of speed planning pattern, if accelerating region and the overlapping phenomenon of deceleration area successively will be carried out extra processing.
If
is for accelerating region plays spot speed,
accelerating region terminal velocity;
deceleration area plays spot speed,
the deceleration area terminal velocity;
is midrange speed.If the corresponding displacement of
point is 0;
point corresponding displacement is
(with respect to
point);
point corresponding displacement be
(with respect to
point),
some correspondence displacement is
(with respect to
point).In order to simplify calculating; Adopt the method for approximate treatment; With
;
;
;
is regarded as the coordinate points that two-dimensional coordinate is fastened; And with
and
;
and
is linked to be straight line; Wherein
some displacement with respect to
for
that intersection point is
is shown in accompanying drawing 4.
Through finding the solution the intersection point of two straight lines, can obtain
.
Can the speed planning mode 3 be changed into speed planning pattern 2 like this handles.
plays spot speed for accelerating region;
accelerating region plays spot speed and deceleration area terminal velocity,
the deceleration area terminal velocity.
At last in program; Storage speed Planning Model numbering; Play spot speed
; Terminal velocity
; Trigonometric function angular velocity
; Starting point knot vector
and peripheral node vector
promptly can be used as the prediction control information in an acceleration and deceleration district.
After handling prediction information, owing to comprised the starting point in each acceleration and deceleration district in the prediction information, information such as terminal point, therefore, the velocity series that preparatory interpolation is tried to achieve, knot vector sequence and maximum tangential acceleration sequence can be left out, to reduce the consumption of internal memory.Be depicted as the process flow diagram that the trigonometric function rate smoothing is handled like accompanying drawing 5.
Deceleration area in accordance with the starting node vector
and the end node vector
size line up.
The concrete steps of the said real-time interpolation link of the inventive method are:
Adopt the speed adaptive adjustment algorithm to calculate interpolated point,,, adopt corresponding trigonometric function rate smoothing to handle then according to prediction information if interpolation gets into the acceleration and deceleration district.If interpolation does not get into the acceleration and deceleration district, then adopt the speed adaptive method to calculate.Coordinate and the speed of feed that generates interpolated point calculated in interpolation.
Comprise following steps:
(1) compares by the information in current interpolated point parameter
and the prediction information; If current interpolated point parameter
not between the starting point knot vector
and peripheral node vector
in certain acceleration and deceleration district, is calculated the radius-of-curvature
of current point by
.Otherwise;
confirms that present interpolated point is positioned at the position in acceleration and deceleration district according to the interpolated point parameter; Calculate speed of feed
by the speed constructed fuction, and skip to step (4).
(2) by the relation between error and radius-of-curvature; Estimate speed of feed in next interpolation cycle, speed of feed
.
(3) get little person in speed of feed
the and instruction speed of feed
as speed of feed, i.e.
.
(4) by the
calculate interpolation step length
.
(5) calculate next interpolated point parameter
and
by
;
,
.
Embodiment
Choose three nurbs curves as simulation example, curve shape is shown in accompanying drawing 6, and its curvature curve is shown in accompanying drawing 7.Adopting two kinds of methods to carry out interpolation, is respectively that the speed adaptive method reaches the NURBS interpolating method based on Machine Tool Dynamics and curve characteristic.Algorithm use MATLAB writes; Interpolation cycle is
; Interpolation precision is
, and the instruction speed of feed is
.
Lathe parameter is following: the maximum normal acceleration that lathe can bear is
.Leading screw pitch
(each axial filament bar pitch equates); Each axial filament thick stick moment of inertia
;
;
; Each goes up moving-member quality
;
;
; The coefficient of sliding friction
, the velocity coefficient of force of sliding friction
.
The cutting parameter coefficient is following:
,
.
It is following that each goes up the parameter of electric machine: rated speed
;
;
; Rated power
;
;
; Moment of inertia
;
,
.
Accompanying drawing 8 is respectively with two kinds of algorithms with accompanying drawing 9 and carries out rate curve and the acceleration correlation curve that interpolation obtains.Visible from Fig. 8, the speed adaptive algorithm has reduced speed automatically in the bigger place of curvature, but curve sudden change, not buffering.NURBS interpolating method based on Machine Tool Dynamics and curve characteristic is then regulated the speed in the bigger place of curvature, and meanwhile, has set up buffer zone, and speed is changed according to the trigonometric function curve.As can beappreciated from fig. 9, after speed being planned according to trigonometric function based on the NURBS interpolating method of Machine Tool Dynamics and curve characteristic, make acceleration change mild, not sudden change.The accelerating curve of speed adaptive algorithm then has the part of sudden change, and the acceleration extreme value is bigger, and the acceleration capacity of lathe is had relatively high expectations.Can find out that from the error comparison diagram of Figure 10 the error of the interpolated point of two kinds of algorithms is all in limited range.
The present invention has proposed a kind of NURBS interpolating method based on Machine Tool Dynamics and curve characteristic on the former study basis.On the one hand, the equation of setting up based on Machine Tool Dynamics and curve characteristic retrains speed, has synthetically considered the ability of lathe the moving interpolation from lathe with by interpolation curve two aspects.On the other hand, adopted the structure trigonometric function to come speed is carried out smoothing processing, made moving interpolation more steady.
The present invention is a creationary novel interpolating method, compared with prior art, has originality and technique effect aspect following two:
(1) considered the influence of Machine Tool Dynamics and curve characteristic to interpolation.
When Processing Curve; Because the geometrical properties such as arrow, method arrow, curvature, amount of deflection of cutting on the cutter path constantly change; Even cutter keeps constant speed of feed to process; The speed that is assigned on each kinematic axis also constantly changes, and each kinematic axis of lathe is in the continuous acceleration and deceleration state all the time.In High-speed machining lathe each can't bear because of changing at a high speed the inertial force that brings.And that present most NURBS interpolating method is considered lathe acceleration and deceleration performance is not enough, only considers along the influence of tangential, path and normal acceleration usually, does not consider that each speed or acceleration decompose the influence of lathe on each.The inventive method has been set up equation of constraint to the interpolation curve with corresponding lathe and has been controlled speed of feed and acceleration in the NURBS interpolation, makes machine tool motion guarantee safety and not reduce under the prerequisite of crudy, improves sport efficiency.
(2) improve topworks's motion smoothing property in the interpolation overall process.
Though S type curve acceleration and deceleration control method can guarantee that acceleration is continuous, acceleration is discontinuous, can in the interpolation process, produce to impact, and S type curve acceleration and deceleration control method computation process is complicated.And the present invention adopts the trigonometric function rate smoothing to handle; Make the velocity variations in the whole interpolation process level and smooth; Acceleration is continuous, and acceleration is also continuous, thereby has avoided acceleration and acceleration is excessive that system is impacted; Improved the flatness of topworks's motion, and compared its computation process with S type curve acceleration and deceleration control method and want simple.
Claims (1)
1. based on the NURBS interpolating method of Machine Tool Dynamics and curve characteristic; Derive speed of feed and the acceleration that equation of constraint is controlled interpolation algorithm according to lathe property and curve characteristic, method is made up of three links: interpolation in advance, prediction information processing and real-time interpolation; The interpolation link adopts the speed adaptive adjustment algorithm in advance; Prediction information processing link is at first divided the acceleration and deceleration district according to the interpolated point speed of feed, respectively the acceleration and deceleration district is judged then, carries out the function rate smoothing according to the velocity mode of correspondence and handles; It is characterized in that said equation of constraint adopts the equation of constraint ZHYS that considers the machine tooling comprehensive key element; And
(1) in advance the interpolation link adopts the speed adaptive adjustment algorithm, preserves interpolated point information and the substitution of interpolated point information is calculated interpolated point maximum tangential acceleration sequence based on the equation of constraint ZHYS of Machine Tool Dynamics and curve characteristic;
The interpolation link comprises following steps in advance:
(a), calculate the radius-of-curvature ρ (i) of current point by current interpolated point parameters u (i);
(b) by the relation between error and radius-of-curvature, estimate speed of feed in next interpolation cycle, calculate speed of feed v
f(i):
(c) get speed of feed v
f(i) and instruction speed of feed v
cIn little person as the speed of feed discreet value, be designated as pre_v (i), promptly
pre_v(i)＝min{v
f(i)，v
c}
(d) calculate interpolation step-length L (i);
L(i)＝v
f(i)T
T is an interpolation cycle in the formula
(e) calculate next interpolated point parameters u (i+1);
(f) by interpolated point parameters u (i+1), arrow
unit secondary method arrow
master of unit method arrow
parameter is cut by the unit that calculates this interpolated point;
(g) arrow
unit secondary method
master of unit method of vowing is cut by unit and vow
speed of feed discreet value pre_v (i); The equation of constraint ZHYS of lathe parameter and parameter of electric machine substitution Machine Tool Dynamics and curve characteristic obtains this interpolated point tangential peak acceleration Max_acc (i);
When interpolating method from curve when starting point calculates terminal point, each parameter of interpolated point just can be formed corresponding sequence, preserves interpolation step-length sequence L, knot vector sequence u, speed of feed sequence pre_v and maximum tangential acceleration sequence Max_acc are as prediction information;
(2) prediction information processing link is at first divided the acceleration and deceleration district according to the interpolated point speed of feed; Respectively the acceleration and deceleration district is judged then; Velocity mode according to correspondence carries out the processing of trigonometric function rate smoothing, preserves the corresponding data after the trigonometric function rate smoothing is handled; The step of prediction information processing link comprises:
(a) speed in the interpolated point speed of feed sequence is judged, the speed of feed sequence is divided into velocity-stabilization district and velocity variations district;
(b) processing of trigonometric function rate smoothing is divided into three kinds of speed planning patterns and handles, the velocity variations district is sorted out respectively, handle according to the Planning Model of correspondence;
(c) line up according to the size of starting point knot vector and peripheral node vector successively in each acceleration and deceleration district;
(3) the real-time interpolation link is carried out real-time speed adaptive interpolation calculating to prediction information, if get into the acceleration and deceleration district, then according to prediction information, adopts the trigonometric function rate smoothing to handle; If do not get into the acceleration and deceleration district, then adopt the speed adaptive method to calculate, thereby finally obtain the coordinate and the speed of feed of interpolated point; Comprise following steps:
(a) compare Calculation of curvature radius or speed of feed by the information in current interpolated point parameter and the prediction information;
(b) calculate the interpolation step-length;
(c) obtain the parameter of interpolated point;
The equation of constraint ZHYS of described Machine Tool Dynamics and curve characteristic is:
Wherein, the desirable x of all subscript i, y, z;
m
iBe each coordinate direction moving-member gross mass;
N
iFor each coordinate direction machine tool guideway acts on the anchorage force on the moving-member;
J
Mi, J
SiBe respectively the servomotor of each coordinate axis and the moment of inertia of leading screw;
p
iHelical pitch for each axial filament thick stick;
G is an acceleration of gravity;
π is a circular constant;
N
iBe the worktable pressure;
a
ImaxEach receives the restriction of self dynamic response for lathe, has intrinsic peak acceleration;
a
tBe the tool motion tangential acceleration, also be the feeding acceleration;
T
IMFor each goes up the output torque of motor; τ
x, τ
y, τ
zFor arrow is cut by tool motion unit, n
x, n
y, n
zFor the master of the unit method of tool motion is vowed.
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