CN106647637A - Trigonometric function acceleration and deceleration control method for high-quality machining - Google Patents
Trigonometric function acceleration and deceleration control method for high-quality machining Download PDFInfo
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- CN106647637A CN106647637A CN201510737207.1A CN201510737207A CN106647637A CN 106647637 A CN106647637 A CN 106647637A CN 201510737207 A CN201510737207 A CN 201510737207A CN 106647637 A CN106647637 A CN 106647637A
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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
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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- G05B2219/34085—Software interpolator
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Abstract
The invention relates to a trigonometric function acceleration and deceleration control method for high-quality machining. The method comprises a pre-interpolation stage and a real-time spline interpolation stage. In the preprocessing stage, a path to be machined is quickly interpolated, key information is recorded, and the trigonometric function speed equation in each acceleration and deceleration section is calculated. In the real-time spline interpolation stage, the real-time feed rate of a cutter is calculated according to the recorded information and the speed equations in the preprocessing stage, and then, next interpolation parameter is calculated in real time using a Newton iteration method, and real-time spline interpolation is carried out. The method is simple in control. Continuous change of speed, acceleration and jerk in the process of machining is realized, and fluctuation in feed rate is reduced. Therefore, the machining precision is guaranteed, overshoot caused by high-speed machining is eased, and flexible acceleration and deceleration control on a servo shaft is achieved. The method is suitable for high-quality processing.
Description
Technical field
The present invention relates to Computerized Numerical Control processing technology field, specifically a kind of triangle letter for high-quality processing
Number Acceleration-deceleration Control Method.
Background technology
Numeric Control Technology is the basis of modern advanced manufacturing technique and core, and a state is reflected to a great extent
The manufacturing technology level of family, is an important symbol for weighing the modernization of industry.
Realize that High-speed machining and high finishing are two important goals of digital control system.The speed of processing is directly closed
The efficiency of processing is tied to, and machining accuracy then directly influences crudy.With modern science and technology and life
The development of product, machining proposes higher and higher speed and required precision with fields of measurement.At high speed,
In high precision, high-quality digital control processing proposes higher wanting to the computing capability and control ability of digital control system
Ask, be mainly manifested in two aspects:First digital control system arithmetic speed is fast, and requires that Digit Control Machine Tool is anti-
Should be fast, i.e., each coordinate motion part can reach given speed within the extremely short time, and can be in high-speed cruising
In rapidly and accurately stop at precalculated position, shorten time;On the other hand require that process motion is flat
Surely, impact, step-out, the excess of stroke or vibration are not produced, high accuracy, high-quality processing is realized.The control of acceleration and deceleration
System and planning are the important component parts of digital control system trajectory planning, are also the key technology of Development of CNC
One of.Therefore, speed planning is the important step in high speed, high accuracy, high-quality digital control processing.
At present, in digital control processing field, conventional velocity planning algorithm includes space rate law of planning, S curve
Speed planning method, cubic polynomial speed planning method etc..Traditional linear acceleration and deceleration control method amount of calculation is little,
Control is simple, but there is the mutation of acceleration in acceleration or deceleration, it is easy to cause lathe to produce vibration,
Have impact on crudy.S curve velocity planning algorithm once accelerate or accelerator in, its rate equation
Two sections or three sections calculating of segmentation, control it is more complicated, and its acceleration in an accelerating sections or
Braking section is mutated four times, in processed complex parts, may cause trembling for cutter.Cubic polynomial speed
Degree planning algorithm control is simple, can realize the consecutive variations of acceleration, but its acceleration is remained and do not connected
Continuous, during an acceleration and deceleration, its acceleration mutation still can be mutated twice, and institute is in this way same
Sample is unfavorable for that high-quality is processed.
The content of the invention
For above-mentioned weak point present in prior art, the technical problem to be solved in the present invention is to provide one
Plant the trigonometric function Acceleration-deceleration Control Method for high-quality processing.
The technical scheme that adopted for achieving the above object of the present invention is:A kind of triangle for high-quality processing
Function Acceleration-deceleration Control Method, including pretreatment stage and real-time interpolation stage;
The pretreatment stage is comprised the following steps:Data point to be processed is carried out with centripetalization parametric technique
Normalization;High speed interpolation is carried out to path to be processed and key message is recorded;
During the high speed interpolation, feed speed is calculated using the approximate method of circular arc;In each step interpolation
The length in the path of interpolation is recorded afterwards;Record the initial of each plus/minus speed process and the speed that terminates and
Corresponding interpolation parameters value;Calculate the peak acceleration and maximum acceleration, triangle of each plus/minus speed section
Function speed planning equation, and the theoretical plus/minus speed distance of plus/minus speed section is calculated according to displacement equation, obtain
The start parameter of plus/minus speed during real-time interpolation;Acceleration and deceleration whole story parameter, trigonometric function rate equation coefficient are protected
In being stored to acceleration and deceleration array;
The real-time interpolation stage comprises the following steps:According to the data in acceleration and deceleration array, calculate current
Real-time speed at point;Using first order Taylor calculating parameter initial value, with calculating after Newton iterative method
The exact value of interpolation parameters, substitutes into parameter curve equation, calculates next interpolated point, so as to carry out in real time
Interpolation.
The centripetalization parametric technique is:
Wherein, PkAnd Pk-1Represent the kth+1 and k-th data point in path to be processed, UkAnd Uk-1Point
Biao Shi not data point PkAnd Pk-1Corresponding normalized parameter, U0Represent first data point P0Corresponding normalizing
Change parameter, n represents the number of data point.
The approximate method of the employing circular arc calculates feed speed, specially:
Wherein, uiFor current interpolated point piCorresponding interpolation parameters, T for digital control system interpolation cycle, ρiFor
Interpolation parameters uiThe radius of curvature at place, EcFor the largest chord high level error of processing request, F is the volume of digital control system
Journey feed speed.
Length S in the path of the interpolationiInterpolation parameters u is incorporated into for pretreatmentiThe path passed by during place,
Calculated by following formula:
Wherein, Si-1To be incorporated into interpolation parameters ui-1When the path passed by, T for digital control system interpolation cycle,
V(ui) it is interpolation parameters uiThe feed speed at place, V (ut) it is interpolation parameters utThe feed speed at place.
Peak acceleration A and maximum acceleration J of the plus/minus speed section, by comparing | Ve-Vs| and
Relation calculate:
IfThen A=Amax, J=Jmax;
IfThen A=Amax,
IfThen J=Jmax,
Wherein, AmaxFor the peak acceleration of digital control system, JmaxFor the maximum acceleration of digital control system, Vs
For the initial velocity of plus/minus speed section, VeFor the end speed of plus/minus speed section.
The expression formula of the trigonometric function speed planning equation acceleration section is:
The expression formula of braking section is:
Wherein, A is the peak acceleration of plus/minus speed section;J is the maximum acceleration of plus/minus speed section;When t is
Between, start time is 0;Va(t) and VdT () is respectively the speed of accelerating sections and braking section;V0It is plus/minus speed section
Initial velocity.
The displacement equation be trigonometric function speed planning equation is quadratured after the equation that obtains, specially:
The displacement S of accelerating sectionsaT () expression formula is:
The displacement S of braking sectiondT () expression formula is:
Wherein, A is the peak acceleration of plus/minus speed section;J is the maximum acceleration of plus/minus speed section;S0For
Initial displacement;V0It is the initial velocity of plus/minus speed section;T is the time, and start time is 0.
The theoretical plus/minus speed distance is referred under conditions of requirement on machining accuracy is met, from the initial of plus/minus speed
Speed VsPlus/minus speed is to end speed VeRequired theoretical path;
Theoretical acceleration distance saComputing formula be:
sa=Sa(ta)-Sa(0)
Theoretical deceleration distance sdComputing formula be:
sd=Sd(td)-Sd(0)
Wherein, Sa(ta) for accelerating sections displacement, taFor acceleration time, Sd(td) for braking section displacement, tdTo subtract
The fast time, and
Wherein, A is the peak acceleration of plus/minus speed section;J is the maximum acceleration of plus/minus speed section.
Data in the array according to acceleration and deceleration, calculate the real-time speed at current point, specially:It is false
If current interpolation parameters is ui, the interpolation moment is ti, plus/minus speed section x being presently in, then real-time speed
ViCalculating process it is as follows:
If 1) ui<AD [x] .us, keeps cutter to move with uniform velocity, Vi=Vi-1;
If 2) AD [x] .us≤ui<AD [x] .ue, then accelerating sections Vi=Va(ti), braking section Vi=Vd(ti);
If 3) ui-1<AD [x] .ue, ui>AD [x] .ue, then x=x+1, Vi=Vi-1;
If 4) when slowing down, ui<AD [x] .ue and V (ui)≤AD [x] .ve, then Vi=Vi-1;
Wherein, AD [x] is the xth section of acceleration and deceleration array obtained after pretreatment terminates, AD [x] .us, AD [x] .ue
The respectively beginning and end interpolation parameters of the accelerating and decelerating part.
The first order Taylor is:
Wherein, C (u) be SPL equation, u be SPL parameter, uiFor current interpolation parameters, ViFor
uiThe speed at place, ui+1For next interpolation parameters, T is interpolation cycle.
The standard iterative formula of described Newton iteration method is:
Wherein, ξkAnd ξk+1It is ui+1Respectively iteration k time with k+1 time after result;F (ξ) is equationof structure, F'(ξk)
It is its first derivative, the expression formula of F (ξ) is:
F (ξ)=| | C (ξ)-C (ui)||-ViT
Wherein, C (ui) for SPL in uiThe value at place, C (ξ) is value of the SPL at ξ, under ξ is represented
One interpolation parameters ui+1, ViFor uiThe speed at place, T is interpolation cycle.
The present invention has advantages below and beneficial effect:
1. processing flexibility is good, and smoothness is high.The rate curve of the inventive method is trigonometric function curve and line
Property polynomial combination, acceleration and jerk curve are trigonometric function curve, in each plus/minus speed stage
The consecutive variations of speed, acceleration and acceleration can be realized, so as to realize flexible feed speed control.
2. machining accuracy is high.The inventive method calculates feeding speed in pretreatment stage using the approximate method of circular arc
Degree, it is contemplated that the restriction of action error, interpolation parameters is calculated in real time during real-time interpolation with Newton iteration method, is subtracted
Little feed speed fluctuation, so as to ensure that machining accuracy.
3. execution efficiency is high.Pretreatment stage is used to collect the related data and calculating speed of the curve to be processed
Equation, the real-time interpolation stage need to only use the data of pretreatment stage and carry out real-time spline interpolation, and computing is simple.
4. highly versatile.The inventive method can not only be applied in various SPL interpolation interpolations, and
The feed speed control in various interpolating methods (linear interpolation, circular interpolation etc.) can be applied.
Description of the drawings
Fig. 1 is the implementing procedure figure of the inventive method;
Fig. 2 is SPL to be processed;
Fig. 3 is to calculate action error schematic diagram using circular arc approximation method;
Fig. 4 is speed, acceleration and the jerk curve of the inventive method moderating process;
Fig. 5 is the rate curve obtained using present invention processing " butterfly " nurbs curve;
Fig. 6 is the accelerating curve obtained using present invention processing " butterfly " nurbs curve;
Fig. 7 is the jerk curve obtained using present invention processing " butterfly " nurbs curve;
Fig. 8 is the action error curve obtained using present invention processing " butterfly " nurbs curve;
Fig. 9 is the rectangular area in embodiment in " butterfly " curve of comparative selection;
Figure 10 is inventive algorithm and S curve, velocity contrast's curve of cubic polynomial velocity planning algorithm;
Figure 11 is inventive algorithm and S curve, the acceleration correlation curve of cubic polynomial velocity planning algorithm;
Figure 12 is inventive algorithm and S curve, the acceleration contrast song of cubic polynomial velocity planning algorithm
Line.
Specific embodiment
Below in conjunction with the accompanying drawings and embodiment the present invention is described in further detail.
Embodiment:The inventive method is carried out into simulating, verifying on PC, programming software used is Microsoft
Visual Studio 2010, using C language coding, the SPL selected here is NURBS
(Non-Uniform Rational B-Spline) curve.
The major technique interpolation parameters of test environment is as follows:
Operating system:Microsoft Windows XP
CPU:Pentium(R)Dual-Core
Dominant frequency:2.93GHz
Internal memory:4G
Digital control system interpolation parameters is as follows:
Feed rate F=250mm/s;
Peak acceleration Amax=5000mm/s2;
Maximum acceleration Jmax=400000mm/s3;
Largest chord high level error Ec=0.001mm;
Interpolation cycle T=3ms;
The present embodiment by taking the processing of representative workpiece program " butterfly " type curve as an example, as shown in Figure 2.
The present invention is used for the speed planning of spline interpolation in digital control processing, its whole interpolation flow chart such as Fig. 1 institute
Show.
The inventive method includes pretreatment and real-time spline interpolation two parts.
By taking moderating process as an example, pre- interpolation has steps of:
Treat Processing Curve to be pre-processed:First the data to be processed are clicked through with centripetalization parametric method
Row normalization, feed speed is determined with the approximate method of circular arc according to the largest chord high level error of requirement on machining accuracy
(its schematic diagram is as shown in Figure 3), and the length in interpolation path will be recorded after each interpolation.In addition note is needed
Each plus/minus speed process initial and the speed for terminating and corresponding parameter value under record, then calculate each add/
The peak acceleration of braking section and maximum acceleration, so as to calculate the trigonometric function speed of each accelerating and decelerating part
Metric draws equation, after asking it first derivative and second dervative, can respectively obtain acceleration and acceleration
Equation (speed of moderating process, acceleration and jerk curve are as shown in Figure 4).To rate equation quadrature
After point, the displacement equation of each accelerating and decelerating part is calculated;The theory of plus/minus speed section is calculated according to displacement equation
Plus/acceleration and deceleration distance, the start parameter of plus/minus speed when finally obtaining real-time interpolation.In Interpolation Process, need by
The information such as acceleration and deceleration whole story parameter, trigonometric function rate equation coefficient are saved in acceleration and deceleration array in AD [].
After pretreatment terminates, accelerating and decelerating part array AD [n] is obtained, n is the number of plus/minus velocity shooting.
Real-time interpolation:According to the data in acceleration and deceleration array, the real-time speed at current point is calculated, then
Using first order Taylor calculating parameter initial value, with the exact value that interpolation parameters is calculated after Newton iterative method,
Parameter curve equation is substituted into, next interpolated point is calculated, so as to carry out real-time interpolation.
Real-time spline interpolation:Speed, initial parameter, rate equation information first in plus/minus speed array,
Calculate in parameter current uiReal-time feed speed V at placei, then calculated in real time using the first order Taylor method of development
In real time the iterative initial value of next one interpolation parameters, then calculates the exact value of interpolation parameters with Newton iteration method,
Parametric equation is substituted into, next interpolated point is calculated, real-time spline interpolation is carried out.
The formula of described centripetalization parametric method is:
In formula, PkAnd Pk-1The kth+1 and k-th data point of machining path, U are wanted in expressionkAnd Uk-1Point
P is not representedkAnd Pk-1Corresponding normalized parameter, U0Represent first data point P0Corresponding parameter, n tables
The number at registration strong point, i.e., the common n point from 0 to n-1.
The approximate method of the employing circular arc calculates feed speed V (ui) expression formula be:
Wherein, uiFor current interpolated point piCorresponding interpolation parameters, T for digital control system interpolation cycle, ρiFor
Parameter uiThe radius of curvature at place, EcFor the largest chord high level error of processing request, F is being programmed into for digital control system
To speed.
Length S in the path of described record interpolationiParameter u is incorporated into for pretreatmentiThe road passed by during place
Footpath, is calculated by below equation:
Wherein, Si-1To be incorporated into parameter ui-1When the path passed by, V (ui) it is parameter uiThe feed speed at place, V (ut)
For parameter utThe feed speed at place.
The initial velocity of described accelerator refers to the speed for accelerating to start, it is assumed that in parameter uiPlace's acceleration is opened
Begin, then the initial velocity value V (u for acceleratingi) should meet:
V(ui-1)≤V(ui)<V(ui+1)
The end speed of described accelerator refer to acceleration terminate after speed, it is assumed that in parameter ujPlace accelerates
Start, then the initial velocity value V (u for acceleratingj) should meet:
V(ui-1)<V(uj), V (uj+1)≤V(uj)
The initial velocity of described moderating process refers to the speed for starting of slowing down, it is assumed that in parameter uxPlace's deceleration is opened
Begin, then the initial velocity value V (u for slowing downx) should meet:
V(ux-1)≤V(ux),V(ux)>V(ux+1)
The end speed of described moderating process refer to deceleration terminate after speed, it is assumed that in parameter uySlow down at place
Terminate, then the velocity amplitude V (u of end of slowing downy) should meet:
V(uy-1)<V(uy)≤V(uy+1)
Peak acceleration A and maximum acceleration J during the plus/minus speed, by comparing | Ve-Vs| andRelation calculate:
IfThen A=Amax, J=Jmax;
IfThen A=Amax,
IfThen J=Jmax,
Wherein AmaxFor the peak acceleration of digital control system, JmaxFor the maximum acceleration V of digital control systemsIt is
The initial velocity of plus/minus speed section, VeThe end speed of plus/minus speed section.
The expression formula of the trigonometric function rate equation acceleration section is:
The expression formula of braking section is:
Wherein, t is the time, and start time is 0;Va(t) and VdT () is respectively the speed of accelerating sections and braking section
Equation;V0It is the initial velocity of accelerating sections or braking section;A is the peak acceleration during acceleration and deceleration;J is
Maximum acceleration during acceleration and deceleration.
The displacement equation refers to the equation obtained after quadraturing to trigonometric function rate equation, is mainly used in meter
Calculate and calculate theoretical plus/minus speed distance, the displacement S of accelerating sectionsaT () expression formula is:
Braking section SdT the displacement expression formula of () is:
Wherein, S0For initial displacement, t is the time, and start time is that 0, A is the maximum during plus/minus speed
Acceleration;J is the maximum acceleration during plus/minus speed.
The theoretical plus/minus speed distance is referred under conditions of requirement on machining accuracy is met, from the initial of plus/minus speed
Speed VsPlus/minus speed is to end speed VeRequired theoretical path.Theoretical acceleration distance saComputing formula be:
sa=Sa(ta)-Sa(0)
Theoretical deceleration distance sdComputing formula be:
sd=Sd(td)-Sd(0)
Wherein, taIt is the acceleration time, tdFor deceleration time, computing formula is:
In formula, A is the peak acceleration during plus/minus speed;J is most greatly accelerating during plus/minus speed
Degree.
The start parameter of plus/minus speed, refers to when real-time spline interpolation is carried out during the real-time interpolation, and cutter is moved
When moving the interpolation parameters, plus/minus speed is proceeded by;By taking moderating process as an example, it is assumed that be currently u from parameteri,
The speed of cutter is in parameter ujPlace reaches minimum of a value, start parameter u of decelerationdCalculate by the following method:
1) theoretical deceleration distance s is calculated with displacement equationd;
2) find interpolation parameters successively forward, find interpolation parameters uk, its corresponding interpolation path SkIt is full
Foot:
Sj-Sk≥sd
3) relatively more current interpolation parameters uiAnd ukSize, if ui<uk, then ud=ui, otherwise ud=uk;
Wherein, SjAnd SkIt is respectively that cutter is incorporated into parameter u from 0jAnd ukThe when path passed by.
Described acceleration and deceleration array AD [] have recorded the data of the accelerating and decelerating part for needing to preserve in pretreatment, its shape
Formula is:
The calculating process of the real-time speed during the real-time interpolation is:
Assume that current interpolation parameters is ui, the interpolation moment is ti, plus/minus speed section x being presently in, then
ViCalculating process it is as follows:
If 1) ui<AD [x] .us, keeps cutter to move with uniform velocity, Vi=Vi-1;
If 2) AD [x] .us≤ui<AD [x] .ue, then accelerating sections Vi=Va(ti), braking section Vi=Vd(ti);
If 3) ui-1<AD [x] .ue, ui>AD [x] .ue, then x=x+1, Vi=Vi-1;
If 4) when slowing down, ui<AD [x] .ue and V (ui)≤AD [x] .ve, then Vi=Vi-1;
Wherein, AD [x] is the xth section of acceleration and deceleration array obtained after pretreatment terminates, AD [x] .us, AD [x] .ue
The respectively beginning and end interpolation parameters of plus/minus speed section.
The expression formula of the first order Taylor method of development is:
In formula, C (u) be SPL equation, u be SPL parameter, uiFor current interpolation parameters, ViFor
uiThe speed at place, ui+1For next interpolation parameters, T is interpolation cycle.
The standard iterative formula of described Newton iteration method is:
Wherein, ξkAnd ξk+1It is ui+1Respectively iteration k time with k+1 time after result;F (ξ) is equationof structure, and F ' is (ξ)
It is its first derivative, the expression formula of F (ξ) is:
F (ξ)=| | C (ξ)-C (ui)||-ViT
In formula, C (u) be SPL equation, C (ui) for SPL in uiThe value at place, C (ξ) is SPL
Value at ξ, ξ represents next interpolation parameters ui+1。
Using inventive algorithm, machining simulation is carried out to " butterfly " curve shown in Fig. 2, the SPL
Publicly-owned 51 data points.Feed speed curve, accelerating curve and jerk curve difference that experiment is obtained
As shown in Fig. 5~7, error curve is as shown in Figure 8.In order to illustrate the trigonometric function acceleration and deceleration of the inventive method
The characteristics of control method, five section S curve velocity planning algorithms, cubic polynomial speed of the emulation experiment to commonly use
Degree planning algorithm as a comparison, is processed to the curve shown in Fig. 2, and selects the rectangle region in Fig. 9
Domain region as a comparison, the inventive method and S curve, the speed of cubic polynomial velocity planning algorithm, plus
Speed and jerk curve are to such as shown in Figure 10~12.
By analysis, can obtain as drawn a conclusion:
1. the inventive method can meet the requirement of machining accuracy, and ensure to add the feed speed in man-hour, accelerate
Degree and acceleration are limited less than the maximum of digital control system.From figure 8, it is seen that to buttferfly-type
After curve machining simulation, the action error curve for obtaining all is limited in the maximum action of requirement on machining accuracy and misses
Differ within 1 μm;From Fig. 5~7 as can be seen that the feed speed curve of inventive algorithm is distributed in digital control system
Programming feed rate F in, acceleration and acceleration are also without peak acceleration A more than systemmaxWith
Acceleration JmaxLimit, this reduces to a certain extent the vibrations of lathe.
2. the inventive method control is fairly simple, and execution efficiency is high, and can guarantee that lathe operates steadily.Pre- place
The reason stage is used to record the critical data and calculating speed equation of Processing Curve, and the speed of inventive algorithm
Equation is link definition.During the real-time interpolation stage, only using the data of pretreatment stage carries out real-time batten
Interpolation, it is simple to operate.From fig. 5, it can be seen that cutter is all moving with uniform velocity within the most of the time, only
Have carries out deceleration control to ensure machining accuracy around the corner.Avoiding problems start because of frequently system,
Stop caused vibration and affect the situation of work procedure finished surface smoothness decline.
3. the inventive method can improve the flexible feed speed control of digital control system processing, make the operation of lathe more
Plus it is steady.From Figure 10~12 as can be seen that during acceleration and deceleration, the rate curve of inventive algorithm, plus
Rate curve and jerk curve are all continually varyings, and S curve velocity planning algorithm and three times it is multinomial
The jerk curve of the algorithm of formula speed planning is all discontinuous, and during an acceleration or deceleration, S is bent
The acceleration of line algorithm can be mutated 4 times, and cubic polynomial algorithm has been mutated twice.Due to the acceleration of cutter
Degree reflects the stressing conditions of lathe, and acceleration reflect lathe response speed and traveling comfort it
Between relation.The rate equation of inventive algorithm is the combination of trigonometric function formula and linear polynomial, acceleration
Equation and acceleration equation are trigonometric function formula, be all it is continuous, so inventive algorithm can reduce because
Start for system, stop caused machine vibration, so as to improve crudy.
Claims (11)
1. it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, it is characterised in that including pre-
Processing stage and real-time interpolation stage;
The pretreatment stage is comprised the following steps:Data point to be processed is carried out with centripetalization parametric technique
Normalization;High speed interpolation is carried out to path to be processed and key message is recorded;
During the high speed interpolation, feed speed is calculated using the approximate method of circular arc;In each step interpolation
The length in the path of interpolation is recorded afterwards;Record the initial of each plus/minus speed process and the speed that terminates and
Corresponding interpolation parameters value;Calculate the peak acceleration and maximum acceleration, triangle of each plus/minus speed section
Function speed planning equation, and the theoretical plus/minus speed distance of plus/minus speed section is calculated according to displacement equation, obtain
The start parameter of plus/minus speed during real-time interpolation;Acceleration and deceleration whole story parameter, trigonometric function rate equation coefficient are protected
In being stored to acceleration and deceleration array;
The real-time interpolation stage comprises the following steps:According to the data in acceleration and deceleration array, calculate current
Real-time speed at point;Using first order Taylor calculating parameter initial value, with calculating after Newton iterative method
The exact value of interpolation parameters, substitutes into parameter curve equation, calculates next interpolated point, so as to carry out in real time
Interpolation.
2. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method,
Characterized in that, the centripetalization parametric technique is:
Wherein, PkAnd Pk-1Represent the kth+1 and k-th data point in path to be processed, UkAnd Uk-1Point
Biao Shi not data point PkAnd Pk-1Corresponding normalized parameter, U0Represent first data point P0Corresponding normalizing
Change parameter, n represents the number of data point.
3. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method,
Characterized in that, the approximate method of the employing circular arc calculates feed speed, specially:
Wherein, uiFor current interpolated point piCorresponding interpolation parameters, T for digital control system interpolation cycle, ρiFor
Interpolation parameters uiThe radius of curvature at place, EcFor the largest chord high level error of processing request, F is the volume of digital control system
Journey feed speed.
4. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method,
Characterized in that, length S in the path of the interpolationiInterpolation parameters u is incorporated into for pretreatmentiWalk during place
The path crossed, is calculated by following formula:
Wherein, Si-1To be incorporated into interpolation parameters ui-1When the path passed by, T for digital control system interpolation cycle,
V(ui) it is interpolation parameters uiThe feed speed at place, V (ut) it is interpolation parameters utThe feed speed at place.
5. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method,
Characterized in that, peak acceleration A and maximum acceleration J of the plus/minus speed section, by comparing | Ve-Vs|
WithRelation calculate:
IfThen A=Amax, J=Jmax;
If Then A=Amax,
If Then J=Jmax,
Wherein, AmaxFor the peak acceleration of digital control system, JmaxFor the maximum acceleration of digital control system, Vs
For the initial velocity of plus/minus speed section, VeFor the end speed of plus/minus speed section.
6. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method,
Characterized in that, the expression formula of the trigonometric function speed planning equation acceleration section is:
The expression formula of braking section is:
Wherein, A is the peak acceleration of plus/minus speed section;J is the maximum acceleration of plus/minus speed section;When t is
Between, start time is 0;Va(t) and VdT () is respectively the speed of accelerating sections and braking section;V0It is plus/minus speed section
Initial velocity.
7. it is according to claim 1 it is a kind of for high-quality processing trigonometric function feed speed control side
Method, it is characterised in that the displacement equation be trigonometric function speed planning equation is quadratured after the side that obtains
Journey, specially:
The displacement S of accelerating sectionsaT () expression formula is:
The displacement S of braking sectiondT () expression formula is:
Wherein, A is the peak acceleration of plus/minus speed section;J is the maximum acceleration of plus/minus speed section;S0For
Initial displacement;V0It is the initial velocity of plus/minus speed section;T is the time, and start time is 0.
8. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method,
Characterized in that, the theoretical plus/minus speed distance is referred under conditions of requirement on machining accuracy is met, from plus/minus
The initial velocity V of speedsPlus/minus speed is to end speed VeRequired theoretical path;
Theoretical acceleration distance saComputing formula be:
sa=Sa(ta)-Sa(0)
Theoretical deceleration distance sdComputing formula be:
sd=Sd(td)-Sd(0)
Wherein, Sa(ta) for accelerating sections displacement, taFor acceleration time, Sd(td) for braking section displacement, tdTo subtract
The fast time, and
Wherein, A is the peak acceleration of plus/minus speed section;J is the maximum acceleration of plus/minus speed section.
9. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method,
Characterized in that, the data in the array according to acceleration and deceleration, calculate the real-time speed at current point, tool
Body is:Assume that current interpolation parameters is ui, the interpolation moment is ti, plus/minus speed section x being presently in, then in fact
Shi Sudu ViCalculating process it is as follows:
If 1) ui<AD [x] .us, keeps cutter to move with uniform velocity, Vi=Vi-1;
If 2) AD [x] .us≤ui<AD [x] .ue, then accelerating sections Vi=Va(ti), braking section Vi=Vd(ti);
If 3) ui-1<AD [x] .ue, ui>AD [x] .ue, then x=x+1, Vi=Vi-1;
If 4) when slowing down, ui<AD [x] .ue and V (ui)≤AD [x] .ve, then Vi=Vi-1;
Wherein, AD [x] is the xth section of acceleration and deceleration array obtained after pretreatment terminates, AD [x] .us, AD [x] .ue
The respectively beginning and end interpolation parameters of the accelerating and decelerating part.
10. it is according to claim 1 it is a kind of for high-quality processing trigonometric function feed speed control side
Method, it is characterised in that the first order Taylor is:
Wherein, C (u) be SPL equation, u be SPL parameter, uiFor current interpolation parameters, ViFor
uiThe speed at place, ui+1For next interpolation parameters, T is interpolation cycle.
A kind of 11. trigonometric function feed speed control sides for high-quality processing according to claim 1
Method, it is characterised in that the standard iterative formula of described Newton iteration method is:
Wherein, ξkAnd ξk+1It is ui+1Respectively iteration k time with k+1 time after result;F (ξ) is equationof structure, F'(ξk)
It is its first derivative, the expression formula of F (ξ) is:
F (ξ)=| | C (ξ)-C (ui)||-ViT
Wherein, C (ui) for SPL in uiThe value at place, C (ξ) is value of the SPL at ξ, under ξ is represented
One interpolation parameters ui+1, ViFor uiThe speed at place, T is interpolation cycle.
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