CN104635621A - XY workbench over-quadrant heave compensation method based on field buses - Google Patents

Abstract

The invention relates to an XY workbench over-quadrant heave compensation method based on field buses. The method includes researching the workbench speed reversing friction features, establishing an over-quadrant heave compensation parameter learning model, determining the position, heaving height and width, lasting time and produced maximum follow error caused by the over-quadrant heaving situation through mathematical deduction, providing a zero-speed symmetric friction compensation method for engineering implementation, performing compensation in the lasting time of the workbench over-quadrant heaving to reduce the workbench over-quadrant heaving, and reducing the friction error. According to the simulation result, the lasting time of the over-quadrant heaving can be shortened significantly, the width and height of the over-quadrant heave can be decreased, the friction error can be reduced, and the ideal effect can be achieved.

Description

Fieldbus Based XY worktable crosses quadrant doming compensation method

Technical field

The present invention relates to a kind of Fieldbus Based XY worktable servo feed system, cross quadrant doming compensation method, what be specially a kind of servo drive system crosses quadrant doming compensation method.

Background technology

The high speed of numerically-controlled machine, high precision performance are the main development directions of following numerically-controlled machine.In numerically-controlled machine, relative motion can be produced between servomotor and ball-screw in feed drive system motion process, feed servo-system determines the machining precision of digital control system, surface quality and production efficiency to a great extent, therefore, the kinematic accuracy of feed drive system is approximately the precision of numerically-controlled machine, the normal accuracy adopting circular interpolation to evaluate feed drive system motion.Feed drive system, when low-speed motion, particularly counter motion, acts on the control of the frictional influence kinematic accuracy of feed drive system, is one of principal element causing high speed, high-precision numerical control machine feed servo-system profile errors.

Various friction force is there is between the worktable of numerically-controlled machine and ball-screw, the servo feed system of CNC machine, eliminate in CNC system after guide screw lead and gap equal error in employing closed-loop control, frictional error when resulting from each axle reversing of motion just becomes the main cause of profile errors.Worktable needs the stiction overcome to be far longer than kinetic force of friction in motion process when setting in motion, thus can produce a larger tracking error when worktable setting in motion.Equally, produce a larger tracking error when stiction direction changes, there will be spike phenomenon and cause contour accuracy to be deteriorated.Different friction conditions and mechanical rigid, at quadrant switching point place, the actual speed participating in each axle of moving interpolation is different, and machine spindle all accurately can not navigate to command value each time.Therefore the physical location of each axle is not desirable programming route, especially crossing quadrant place, creates profile errors.Carrying out in circular interpolation process, crossing quadrant place friction phenomenon and show particularly evident.Crossing the place of quadrant, a coordinate axis is moved with maximum speed, and another coordinate axis accelerates to positive speed from negative speed, when its speed zero passage, the direction of friction force also changes thereupon, thus produce large tracking error, there is obvious spike phenomenon, namely cross the protruding phenomenon of quadrant.

In order to eliminate the protruding phenomenon of quadrant, reducing the negative effect of friction, control method can be taked to reduce the error rubbing and produce, but be more the method adopting friciton compensation.

Research at present for friction compensation method has a lot, as according to bidimensional mixed friction model prediction friction, carries out feedforward compensation; By the frictional error measured in advance, join in position command as compensating instruction and compensate; Adopt GMS model to add interference observer and carry out friciton compensation.Although existing friction compensation method achieves good effect, these methods all more complicated, are not easy to realize.The present invention is by the research of rubbing characteristics time reverse to the speed of table, position that the protruding phenomenon of quadrant produces, duration and consequent maximum tracking error was determined by mathematical derivation, a kind of zero-speed symmetrical expression friction compensation method being convenient to Project Realization is proposed, cross in the quadrant protruding phenomenon duration at worktable and it is compensated, to making worktable eliminate the protruding phenomenon of quadrant, reduce frictional error.The method that shows simulation result can shorten the quadrant protruding duration significantly, reduces width and the height of quadrant projection, and reduces frictional error, reach comparatively ideal effect.

Summary of the invention

The technical problem to be solved in the present invention is: cross the protruding phenomenon of quadrant what cross that quadrant place produces when carrying out counter motion for feed drive system, the present invention proposes a kind of zero-speed symmetrical expression friction compensation method, cross in the quadrant protruding phenomenon duration at worktable and it is compensated, significantly shorten the quadrant protruding duration, reduce width and the height of quadrant projection, reduce frictional error.

The technical scheme that the present invention is adopted for achieving the above object is: a kind of Fieldbus Based XY worktable crosses quadrant doming compensation method, comprises the following steps:

CNC obtains mechanical data by SSBIII bus from servo-drive system, set up quadrant doming compensation parameter learning model, and parameter is sent to servo-drive system by SSBIII bus;

Servo-drive system employing zero-speed symmetrical expression is crossed the protruding friction compensation method of quadrant and is carried out real-Time Compensation to crossing quadrant projection.

Described quadrant doming compensation parameter learning model of setting up is:

Calculated quadrant height of projection cross quadrant ledge width w=s*cos θ;

Compensation start position is:

$x_c=\sqrt{r^2-{(r-h)}^2}=\sqrt{4r\sqrt{r^2+{\left(\frac{s}{2}\right)}^2}-{4r}^2-{\left(\frac{s}{2}\right)}^2},y_c=r-h=2r-\sqrt{r^2+{\left(\frac{s}{2}\right)}^2}$

Wherein, s is the actual displacement that worktable is in pre-sliding phase, and described pre-sliding phase is that worktable drops to v by speed ₀start again to rise to v to speed ₀the time that process experiences, in this process, worktable passed through quadrantal points, and r is predetermined circular motion orbital radius, and θ was the angle of the line place coordinate axis in quadrantal points and the line compensating terminal and mistake quadrantal points and the predetermined circular motion track center of circle;

Compensate terminal and compensate starting point about crossing quadrantal points and predetermined circular motion track circle center line connecting place coordinate axis symmetry.

The model that described zero-speed symmetrical expression crosses the protruding friction compensation method of quadrant is:

Wherein, F _fricfor crossing the protruding friciton compensation moment of quadrant, Δ T is the time that worktable is in pre-sliding phase, and described pre-sliding phase is that the speed of worktable drops to v ₀moment T ₀arrived speed more again rose to v to passing through quadrantal points motion ₀moment T ₁, coulomb friction moment F _cfor the maximal value of friciton compensation, σ is stiffness coefficient.

The present invention has the following advantages and beneficial effect:

1. the quadrant doming compensation method of crossing that the present invention proposes realizes simple, can effectively determine compensation point position, when suppressing low speed worktable cross the protruding phenomenon of quadrant, obtain good system low speed control characteristic;

2. the quadrant doming compensation method of crossing of the present invention's proposition can shorten the quadrant protruding duration significantly;

3. what the present invention proposed crosses width and the height that quadrant doming compensation method obviously can reduce quadrant projection, reduces frictional error.

Accompanying drawing explanation

Fig. 1 is the system construction drawing based on motion control bus;

Fig. 2 was the protruding phenomenon partial enlarged drawing of quadrant;

Fig. 3 is Frictional model;

Fig. 4 is the feed servo drive system Controlling model comprising compensating module;

Fig. 5 is for compensating front rate curve and given speed curve comparison figure;

Fig. 6 is for compensating rear rate curve and given speed curve comparison figure;

Fig. 7 is for compensating front position graph of errors;

Fig. 8 is for compensating rear site error curve.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Set up worktable and cross quadrant doming compensation parameter learning model, be in the duration in quadrant protruding stage and relative displacement interior during this period of time according to worktable, and obtained the time that worktable is in pre-sliding phase.According to the relation of the total driving force of worktable and force of sliding friction, adopt Stribeck Frictional model, design pre-sliding friction compensation model, obtain zero degree symmetrical expression friction compensation method.

Specific implementation step of the present invention is:

In order to the protruding error of compensated quadrant, set up quadrant doming compensation parameter learning model, according to the displacement of worktable actual motion, predetermined circular motion orbital radius and worktable rotational angle, the position of the height of quadrant projection, width and precompensation point must be.

Cross quadrant height of projection cross quadrant ledge width w=s*cos θ, compensate terminal and compensate starting point about crossing quadrantal points and predetermined circular motion track circle center line connecting place coordinate axis symmetry, the position compensating starting point is:

$x_c=\sqrt{r^2-{(r-h)}^2}=\sqrt{4r\sqrt{r^2+{\left(\frac{s}{2}\right)}^2}-{4r}^2-{\left(\frac{s}{2}\right)}^2},y_c=r-h=2r-\sqrt{r^2+{\left(\frac{s}{2}\right)}^2}.$

Wherein, s is that worktable is in pre-sliding phase (worktable drops to v by speed ₀moment passed through quadrantal points and moves to speed and again rise to v ₀moment) actual displacement, r is predetermined circular motion orbital radius, and θ was quadrantal points and the line compensating terminal and the angle of line place coordinate axis crossing quadrantal points and the predetermined circular motion track center of circle.

In order to suppress the protruding phenomenon of quadrant, we needed to know that worktable was in the time in quadrant protruding stage.Worktable is v in speed ₀moment produced quadrant phenomenon, if the speed of table is v ₀moment is T ₀, and the moment that worktable departed from quadrant phenomenon is T ₁, in the meantime, worktable is in pre-sliding phase, makes χ _bfor T ₀to T ₁the relative displacement of period.Again because this time is very short, can suppose that acceleration is constant a, then:

${\mathrm{\χ}}_b={\∫}_{T_0}^{T_1}{\∫}_{T_0}^t\mathrm{adt}---\left(1\right)$

According to Dahl model, can obtain

${\mathrm{\χ}}_b=\frac{F_c}{\mathrm{\σ}}---\left(2\right)$

Wherein F _cfor Coulomb friction moment, σ is stiffness coefficient.

Δ T is made to be the time (T that worktable is in pre-sliding phase ₁-T ₀), then:

${\mathrm{\χ}}_b=\frac{1}{2}a{\mathrm{\ΔT}}^2=\frac{F_c}{\mathrm{\σ}}---\left(3\right)$

Can obtain:

$\mathrm{\ΔT}=\sqrt{\frac{{2F}_c}{\mathrm{\σ}}}---\left(4\right)$

Cross the protruding phenomenon of quadrant for what suppress worktable, improve the precision of worktable, we only need the pre-sliding phase at worktable, carry out quadrant doming compensation time namely speed is v0.In other moment, be compensated for as 0, according to above-mentioned gained, compensate as follows:

Because add suddenly a moment can cause system oscillation, should avoid adding discontinuous control inputs.Therefore F _fricit should be a continuous print function.For ease of describing compensation model, we suppose T without loss of generality ₀moment is then interval [T ₀, T ₀+ Δ T] can be described as because whole course work platform is in from sliding friction to pre-sliding friction again to the process of sliding friction, in order to suppress the protruding phenomenon of quadrant excessively of worktable, we need to compensate it make worktable be in sliding phase always or reduce the time that worktable is in pre-sliding phase.The driving force of worktable is then in one from reducing gradually, the process then increased gradually again, and in order to reach the effect suppressing the protruding phenomenon of quadrant, after needing to make compensation, total driving force and force of sliding friction keep the state balanced.Then friciton compensation should be in an elder generation increases gradually, the process then reduced gradually.Pre-sliding friction compensation model can be expressed as:

$\begin{array}{cc}{F}_{\mathrm{pre}}\left(t\right)=F\·\cos \left(\frac{\mathrm{\π}}{\mathrm{\Δt}}t\right)& -\frac{\mathrm{\ΔT}}{2}\≤t\≤\frac{\mathrm{\ΔT}}{2}\end{array}----\left(6\right)$

? arrive period, be in for making worktable the time that sliding friction stage or minimizing are in the pre-sliding friction stage, so the maximal value compensated is F _c(Coulomb friction moment), therefore | F| value is F _c.In motion process, friction force is relevant with the direction of motion, and therefore when compensating, F is also connected with direction of motion.When worktable is in positive movement process, F equals F _c, when worktable is in counter motion process, F equals-F _c.

In sum, can obtain zero-speed symmetrical expression friction compensation method is:

Fig. 1 is the servo feed system structural drawing that the present invention is based on SSBIII fieldbus.This system is made up of CNC system, high-precision SSIII fieldbus, XY worktable (comprise two identical servo drive system ServoX, ServoY) and ball-screw; Position order interpolation, Speed and acceleration feedforward information are sent to the servo drive system of each axle by CNC respectively by SSBIII bus, positional information, the servomotor anglec of rotation and moment information are fed back to CNC by fieldbus by the servo drive system of X, Y-axis, and CNC controls position and the velocity close-loop control that servo drive system completes single shaft; Required compensating parameter is passed to servo drive system by fieldbus by CNC, and servo drive system employing zero-speed symmetrical expression is crossed the protruding friction compensation method of quadrant and carried out real-Time Compensation to crossing quadrant projection.

Fig. 2 was the protruding partial enlarged drawing of quadrant phenomenon.O point is predetermined circular motion track origin, and A point was quadrantal points, C ₁point for worktable produced quadrant projection phenomenon moment (compensation starting point), C ₂put as worktable departed from the protruding phenomenon moment (compensation terminal) of quadrant, AC ₂for A point is to C ₂the actual motion track of point, s is that worktable is in pre-sliding phase (worktable drops to v by speed ₀the C in moment ₁point passed through quadrantal points A point and moves to speed and again rise to v ₀the C in moment ₂point) actual displacement, cross quadrant fillet curve symmetrical about coordinate axis OA, then θ is straight line AC ₂with the angle in coordinate axis OA direction, r is predetermined circular motion orbital radius, is v in the speed of table ₀in the moment, compensating crossing quadrant projection, compensating terminal C ₂with compensation starting point C ₁symmetrical about coordinate axis OA, be v in the speed of table ₀in the moment, compensate crossing quadrant projection.

Cross quadrant height of projection cross quadrant ledge width w=s*cos θ, compensate starting point C ₁position is: $x_c=\sqrt{r^2-{(r-h)}^2}=\sqrt{4r\sqrt{r^2+{\left(\frac{s}{2}\right)}^2}-{4r}^2-{\left(\frac{s}{2}\right)}^2},y_c=r-h=2r-\sqrt{r^2+{\left(\frac{s}{2}\right)}^2}.$

Fig. 3 is Frictional model, have employed Stribeck model, wherein T ₀for the speed of table drops to v ₀moment, and T ₁for the speed of table rises to v again ₀moment.Because whole course work platform is in from sliding friction to pre-sliding friction again to the process of sliding friction, in order to suppress the protruding phenomenon of quadrant excessively of worktable, need to compensate it, make worktable be in sliding phase always or reduce the time that worktable is in pre-sliding phase.The driving force of worktable is then in one from reducing gradually, the process then increased gradually again, and in order to reach the effect suppressing the protruding phenomenon of quadrant, after needing to make compensation, total driving force and force of sliding friction keep the state balanced.Then cross quadrant doming compensation should be in an elder generation and increase gradually, the process then reduced gradually.Be in for making worktable the time that sliding friction stage or minimizing are in the pre-sliding friction stage, then the maximal value of friciton compensation is F _c(force of sliding friction).In motion process, friction force is relevant with the direction of motion, and therefore compensation F and direction of motion are connected.When worktable is in positive movement process, F equals F _c, when worktable is in counter motion process, F equals-F _c.

Zero-speed symmetrical expression friction compensation method is:

Emulation experiment is carried out for above-mentioned quadrant doming compensation method of crossing.As shown in Figure 4, given speed signal is v=0.01sin (π t).K _ppfor position loop gain (50000), K _vpfor speed ring gain (40), K _cpfor current loop gain (2), L is motor inductance (52.7mH), R _mfor motor resistance (1.04 Ω), K _efor counter electromotive force of motor (0.18Vs/rad), K _tfor motor torque constant (0.82Nm/A), J is to electric machine rotation inertia (0.00299kgm ²), K _bsfor guide screw lead (1.59mm/rad), K is leading screw rigidity (410000N/m), m be worktable quality (48.8kg), B is worktable damping (15000Ns/m), F _ffor friction force (N).F _cfor force of sliding friction (18.9272N), F _sfor stiction (26.9487N), V _sfor rotating speed (0.0172m/s), B is worktable damping (56.6223Ns/m).We suppose guide screw lead, and gap equal error is eliminated, and only compensate for the friction on worktable.Fig. 5 is for speed before compensation and given speed curve comparison figure, Fig. 6 are for compensating rear rate curve and given speed curve comparison figure.Fig. 7 is for compensating front position graph of errors, and Fig. 8 is the site error curve after compensating.Can find out when velocity reversal (1s), due to the impact of friction, cause worktable to occur the protruding phenomenon of quadrant, thus cause this moment site error to increase suddenly.And after compensating, the site error in this moment significantly reduces, and achieves good effect.Can be found by Fig. 5 and Fig. 6, before compensation, the time that worktable was in the protruding phenomenon of quadrant is 0.05 second, and after compensating, the duration is 0.02 second, significantly reduces.Therefore when zero-speed symmetrical expression friction compensation method effectively can suppress low speed worktable cross the protruding phenomenon of quadrant, reduce the time that worktable was in the protruding phenomenon of quadrant, obtain good system low speed control characteristic.

Claims (3)

1. Fieldbus Based XY worktable crosses a quadrant doming compensation method, it is characterized in that, comprises the following steps:

CNC obtains mechanical data by SSBIII bus from servo-drive system, set up quadrant doming compensation parameter learning model, and parameter is sent to servo-drive system by SSBIII bus;

Servo-drive system employing zero-speed symmetrical expression is crossed the protruding friction compensation method of quadrant and is carried out real-Time Compensation to crossing quadrant projection.

2. Fieldbus Based XY worktable according to claim 1 crosses quadrant doming compensation method, it is characterized in that, described quadrant doming compensation parameter learning model of setting up is:

Calculated quadrant height of projection cross quadrant ledge width w=s*cos θ;

Compensation start position is:

$x_c=\sqrt{r^2-{(r-h)}^2}=\sqrt{4r\sqrt{r^2+{\left(\frac{s}{2}\right)}^2}-{4r}^2-{\left(\frac{s}{2}\right)}^2},y_c=r-h=2r-\sqrt{r^2+{\left(\frac{s}{2}\right)}^2}$

Wherein, s is the actual displacement that worktable is in pre-sliding phase, and described pre-sliding phase is that worktable drops to v by speed ₀start again to rise to v to speed ₀the time that process experiences, in this process, worktable passed through quadrantal points, and r is predetermined circular motion orbital radius, and θ was the angle of the line place coordinate axis in quadrantal points and the line compensating terminal and mistake quadrantal points and the predetermined circular motion track center of circle;

Compensate terminal and compensate starting point about crossing quadrantal points and predetermined circular motion track circle center line connecting place coordinate axis symmetry.

3. Fieldbus Based XY worktable according to claim 1 crosses quadrant doming compensation method, it is characterized in that, the model that described zero-speed symmetrical expression crosses the protruding friction compensation method of quadrant is:

Wherein, F _fricfor crossing the protruding friciton compensation moment of quadrant, Δ T is the time that worktable is in pre-sliding phase, and described pre-sliding phase is that the speed of worktable drops to v ₀moment T ₀arrived speed more again rose to v to passing through quadrantal points motion ₀moment T ₁, coulomb friction moment F _cfor the maximal value of friciton compensation, σ is stiffness coefficient.