CN102591257A - Parameter curve cutter path oriented numerical control system contour error control method - Google Patents

Abstract

The invention provides a parameter curve cutter path oriented numerical control system contour error control method which comprises the following steps of: 1) calculation of the contour error; 2) calculation and control of the contour error compensation quantity, and is characterized in that: in the step 1), in each sampling period for performing curve interpolation on the parameter curve cutter path, the contour error epsilon is calculated according to the current actual cutter location point and the interpolation point on the tracked parameter curve cutter path, namely the shortest distance from the current actual cutter location point to the tracked parameter curve cutter path is calculated; in the step 2), the components of the contour error epsilon along the X axis, Y axis and Z axis are calculated, and the contour error compensation quantities are obtained by proportional control and superposed with the location control quantities for the following error on the X axis, Y axis and Z axis respectively; and then the result is output to a servo execution mechanism to perform contour error compensation control. The method provided by the invention has the advantages that: the contour error calculation precision is high, the contour error compensation method is simple and effective, and the contour precision can be obviously improved.

Description

Digital control system profile errors control method towards the parametric line cutter path

Technical field

The present invention relates to a kind of error compensation control method, particularly relate to a kind of digital control system profile errors control method towards the parametric line cutter path.

Background technology

In machinery manufacturing industry, the profile of many complex parts can be described (like SPL, Bezier curve, B-spline curves, nurbs curve etc.) with parametric line, can describe the cutter path of these parts of processing accordingly with parametric line.For the parametric line cutter path, advanced digital control system adopts curve interpolating method more.With respect to carrying out linear interpolation again with straight-line segment approximating parameter curve cutter path, when adopting curve interpolating method, all interpolated points and can improve machining precision and process velocity all on the parametric line cutter path in theory simultaneously.On the other hand, for these complex parts, often use the multi-axis numerical control machine tooling.Profile errors refers to that current actual cutter location instructs the bee-line of curve to institute's cutter path of following the tracks of in the digital control processing; Profile errors is caused by multiple factor; Like geometric errors such as pitch error, orthogonal axes out of plumb, backlasses; The hot error that thermal deformation causes, cutting force error and servocontrol error etc.Syh-Shiuh Yeh etc. are at academic journal " IEEE/ASME TRANSACTIONS ON MECHATRONICS " (2002; 7 (1): in the paper of delivering 44-50) " Estimation of the Contouring Error Vector for the Cross-Coupled Control Design "; Point out that actual dynamic performance is difficult to accomplish to mate fully between each feed shaft of numerically-controlled machine; This has directly influenced the raising of contour accuracy; Being the major reason that causes profile errors, proposing in part processing, profile errors to be calculated and carry out real-Time Compensation, is the effective way of raising system contour accuracy.

Existing technical literature retrieval is found; Xu Zhixiang etc. are at academic journal " machine science and technology " (2006; 25 (12): in the paper of delivering 1451-1453) " a kind of multi-shaft crossed coupling control method " based on the NURBS interpolator; Proposition is the interpolation instruction point according to the some of the actual tool position of each feedback and storage in each sampling period, finds from the nearest interpolated point in actual tool position, and distance between two points is approximately profile errors; Computing method are simple, but the profile errors model accuracy is not too high in this method.Syh-Shiuh Yeh etc. are at academic journal " IEEE TRANSACTIONS 0N CONTROL SYSTEMS TECHNOLOGY " (2003; 11 (3): in the paper of delivering 375-382) " Analysis and Design of Integrated Control for Multi-Axis Motion Systems "; Actual cutter location of certain sampling period distance of current interpolated point place tangent line to the instruction cutter rail curve is approximately profile errors; Be called profile errors " tangent line method of approximation ", this method is lower in speed of feed, the contour curvature of following the tracks of hour desirable a degree of precision.Myung-Hoon LEE etc. are at academic journal " JSME International Journal " (2004; 47 (1): in the paper of delivering P144-149) " A multi-axis contour error controller for free form curves "; To parametric line a kind of control method based on the profile errors vector is proposed; In each sampling period, adopt dichotomy and Newton iteration method to find the solution Nonlinear System of Equations and calculate profile errors.The problem that this method exists is that Newton iteration method is very high to the requirement of initial value, and calculated amount is bigger, is difficult to satisfy the requirement of digital control system real-time sometimes.Myung-Hoon LEE also proposes in this article except each tracking error PID positioner; The profile errors that obtains for approximate treatment; Design a cover PID controller in addition and calculate the profile errors compensation rate, but the controlled variable of this PID controller is difficult to adjust.

In sum, in part by numerical control processing, for the cutter path of describing with parametric line; How in each sampling period, high precision and simple as far as possible profile errors and the profile errors compensation rate calculated compensate control to each feed shaft servo actuator; For strengthening matching degree between each feed shaft; Improve contour accuracy, realize that the multiaxis Collaborative Control is significant, become the technical matters that those skilled in the art are badly in need of solving.

Summary of the invention

The purpose of this invention is to provide a kind of high, simple digital control system profile errors control method of profile errors compensation control of deficiency, profile errors computational accuracy that can overcome prior art towards the parametric line cutter path.Its technical scheme is:

Adopt following steps: 1) profile errors calculates; 2) the profile errors compensation rate is calculated and control; It is characterized in that: in the step 1); In each sampling period of the parametric line cutter path being carried out curve interpolating processing, obtain current actual cutter location R through the position transducer detection separately of X axle, Y axle, Z axle, find again on the parametric line cutter path apart from two nearest interpolated point P of current actual cutter location R _a, P _b, establish interpolated point P _a, P _bCorresponding parameter of curve is respectively u _a, u _b, establish parameter of curve

The point on the corresponding parametric line cutter path be P _c, profile errors ε ≈ RP then _cStep 2) in, the profile errors ε that step 1) is calculated decomposes along X axle, Y axle, Z axle direction of feed, obtains ε respectively _x, ε _y, ε _zUse X axle, Y axle, the Z axle feed system scale-up factor K in the tracking error PID positioner separately _Px, K _Py, K _Pz, calculate profile errors compensation rate, C along X axle, Y axle, Z axle _{ε x}=ε _xK _Px, C _{ε y}=ε _yK _Py, C _{ε z}=ε _zK _PzThen with profile errors compensation rate C _{ε x}, C _{ε y}, C _{ε z}In X axle, Y axle, the position control amount of Z axle to tracking error of being added to respectively, the servo actuator that at last stack result is outputed to X axle, Y axle, Z axle carries out profile errors compensation control.

The present invention compared with prior art, its advantage is:

1, the profile errors computing method are simple, and computational accuracy is high.

2, profile errors compensation rate computing method are simple, effective.

Description of drawings

Fig. 1 is the digital control system profile errors control method process flow diagram towards the parametric line cutter path of the present invention.

Fig. 2 is the digital control system profile errors computing method synoptic diagram towards the parametric line cutter path of the present invention.

Fig. 3 is that the digital control system profile errors towards the parametric line cutter path of the present invention calculates the compensation program process flow diagram.

Fig. 4 adopts three-shaft linkage numerical control motion platform hardware structure diagram of the present invention.

Fig. 5 is one section parametric line cutter path of describing with NURBS.

Fig. 6 is interpolation profile Error Graph when following the tracks of parametric line cutter path shown in Figure 5.

Among the figure: P _a, interpolated point P _b, interpolated point P _k, interpolated point L, cutter path P _c, some R, actual cutter location A～I on the cutter path be the control vertex of cutter path

Embodiment

Do below in conjunction with Fig. 1～3 couple the present invention and to describe in further detail:

Step 1); In each sampling period of the parametric line cutter path being carried out curve interpolating processing; According to the interpolated point on current actual cutter location and the institute's tracking parameter curve cutter path; Calculate profile errors, promptly calculate the bee-line of current actual cutter location to institute's tracking parameter curve cutter path.Specifically as shown in Figure 2, establish with the NURBS parametric line and describe this cutter path L, cutter path L goes up every bit and does

$P\left(u\right)=\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{B}_{i,k}\left(u\right)W_i{V}_i}{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{B}_{i,k}\left(u\right)W_i}---\left(1\right)$

V wherein _iBe control vertex, W _iBe weight factor, B _{I, k}(u) be k B spline base function.Corresponding each parameter of curve u has P (u)=(x (u), y (u), z (u)) ', promptly goes up a bit corresponding with cutter path L.It is to be noted; Which type of parametric line form that don't work (like SPL, Bezier curve, B-spline curves, nurbs curve etc.) is described cutter path; Each parameter of curve u all with cutter path on a bit corresponding; And when using curve interpolating, all interpolated points all on cutter path, so among Fig. 2 with the NURBS parametric line describe cutter path be have general.

K interpolation sampling period, establishing at this moment, interpolated point is P _kLearn that through each feed shaft position probing feedback actual cutter location is R, from 10 interpolated points in past, promptly from (P _K-9, P _K-8P _k) the middle search apart from putting two nearest interpolated points of R, be made as interpolated point P _a, interpolated point P _bIf interpolated point P _a, interpolated point P _bCorresponding parameter of curve is respectively u _a, u _b, promptly satisfy

$P_a=P\left(u_a\right)=\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{B}_{i,k}\left(u_a\right)W_i{V}_i}{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{B}_{i,k}\left(u_a\right)W_i},$ $P_b=P\left(u_b\right)=\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{B}_{i,k}\left(u_b\right)W_i{V}_i}{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{B}_{i,k}\left(u_b\right)W_i}.$

If parameter of curve

The point on the corresponding parametric line cutter path L be P _c, promptly

$P_c=P\left(\frac{u_a+u_b}{2}\right)=\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{B}_{i,k}\left(\frac{u_a+u_b}{2}\right)W_i{V}_i}{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{B}_{i,k}\left(\frac{u_a+u_b}{2}\right)W_i}---\left(2\right)$

Then, make profile errors in this sampling period

ε≈RP _c (3)

Promptly use RP _cBe similar to the bee-line of current actual cutter location R to cutter path L.

Step 2), the profile errors ε that step 1) is calculated decomposes along X axle, Y axle, Z axle direction of feed, obtains ε respectively _x, ε _y, ε _zUse X axle, Y axle, the Z axle feed system scale-up factor K in the tracking error PID positioner separately _Px, K _Py, K _Pz, calculate profile errors compensation rate, C along X axle, Y axle, Z axle _{ε x}=ε _xK _Px, C _{ε y}=ε _yK _Py, C _{ε z}=ε _zK _PzThen with profile errors compensation rate C _{ε x}, C _{ε y}, C _{ε z}In X axle, Y axle, the position control amount of Z axle to tracking error of being added to respectively, the servo actuator that at last stack result is outputed to X axle, Y axle, Z axle is controlled.Specifically calculate shown in the compensation program process flow diagram: after reading in n the cutter path job sequence section of describing with parametric line,, obtain interpolated point P through the curve interpolation in the k sampling period like the digital control system profile errors towards the parametric line cutter path among Fig. 3 _k, detect each feed shaft position simultaneously and obtain actual cutter location R, carry out two aspects then and calculate:

(1) by actual cutter location R and current interpolated point P _kObtain tracking error E=RP _kIf X feed shaft tracking error PID positioner coefficient is K _Px, K _Ix, K _Dx, Y feed shaft tracking error PID positioner coefficient is K _Py, K _Iy, K _Dy, Z feed shaft tracking error PID positioner coefficient is K _Pz, K _Iz, K _Dz, then after the PID position control, the tracking error position control amount C of the X axle that is easy to get, Y axle, Z axle _Ex, C _Ey, C _Ez

(2) calculate profile errors ε with formula (3), profile errors ε is obtained ε along X axle, Y axle, the decomposition of Z axle _x, ε _y, ε _zUse the scale-up factor K in X axle, Y axle, the Z axle tracking error PID positioner _Px, K _Py, K _Pz, obtain the profile errors compensation rate C of X axle, Y axle, Z axle through proportional control _{ε x}, C _{ε y}, C _{ε z}:

C _εx＝ε _x·K _px (4)

C _εy＝ε _y·K _py (5)

C _εz＝ε _z·K _pz (6)

The profile errors compensation rate along X axle, Y axle, Z axle that above-mentioned two steps are calculated superposes to the position control amount of tracking error with X axle, Y axle, Z axle respectively, with stack result (C _Ex+ C _{ε x}), (C _Ey+ C _{ε y}), (C _Ez+ C _{ε z}) output to each feed shaft servo actuator respectively and control, both can realize that cutter presses the command speed motion, make cutter convergence instruction profile simultaneously again, improve contour accuracy.

The present invention obtains to realize in the digital control system of three-shaft linkage numerical control motion platform shown in Figure 4: constitute the upper and lower computer structure by industrial computer and SEED-DEC2812 motion control card; Realize data communication through USB2.0; X axle, Y axle, Z axle feed system all adopt the little inertia servomotor of Panasonic; Sampling period equals interpolation cycle, is T=4ms.Realize detection with the grating chi to X axle, Y axle, Z axle direction of feed physical location.Core DSP process chip is TMS320-F2812 in the SEED-DEC2812 motion control card, has the USB2.0 communication interface, and dominant frequency is 150MHz, and development environment is CCS2.0.Realize that in the SEED-DEC2812 motion control card nurbs curve interpolation, profile errors calculate and compensate control, tracking error position control, acceleration and deceleration control etc.

Fig. 5 is one section cutter path of describing with the NURBS parametric line.Wherein,

Control vertex is: A (0,0,0), B (125,0,3), C (250,0,10), D (350,25,40), E (250,50,30), F (125,50,40), G (0,50,10), H (0,25,3), I (0,0,0); Its mid point A and some I overlap;

Weight factor is: (1,1.2,1.1,1,0.9,11,0.8,1,1);

Knot vector is: (0,0,0,0,0.3266,0.4667,0.6018,0.7655,0.9333,1,1,1,1).

Profile Error Graph when Fig. 6 follows the tracks of parametric line cutter path shown in Figure 5 for interpolation.At first, in the SEED-DEC2812 motion control card, realize " tangent line method of approximation " profile errors compensation method, cutter path shown in Figure 5 is followed the tracks of in interpolation, and profile errors is shown in data2 among Fig. 6, and the largest contours error is about 0.064mm; Then; Realize that in the SEED-DEC2812 motion control card profile errors proposed by the invention calculates compensation method, under same working environment, cutter path shown in Figure 5 is followed the tracks of in interpolation; Profile errors is shown in datal among Fig. 6, and the largest contours error is about 0.042mm.

Comparative illustration, profile errors proposed by the invention are calculated compensation method can realize effectively compensation to profile errors, improves contour accuracy, strengthens matching degree between each feed shaft, reduces the unmatched influence of actual dynamic performance between each kinematic axis.This invention can use in digital control system and numerically-controlled machine and promote, and is particularly significant for the digital control processing of cutter path of describing with parametric line and part.

Claims (1)

1. digital control system profile errors control method towards the parametric line cutter path; Adopt following steps: 1) profile errors calculates; 2) the profile errors compensation rate is calculated and control, it is characterized in that: in the step 1), in each sampling period of the parametric line cutter path being carried out curve interpolating processing; Obtain current actual cutter location R through the position transducer detection separately of X axle, Y axle, Z axle, find again on the parametric line cutter path apart from two nearest interpolated point P of current actual cutter location R _a, P _b, establish interpolated point P _a, P _bCorresponding parameter of curve is respectively u _a, u _b, establish parameter of curve

The point on the corresponding parametric line cutter path be P _c, profile errors ε ≈ RP then _cStep 2) in, the profile errors ε that step 1) is calculated decomposes along X axle, Y axle, Z axle direction of feed, obtains ε respectively _x, ε _y, ε _zUse X axle, Y axle, the Z axle feed system scale-up factor K in the tracking error PID positioner separately _Px, K _Py, K _Pz, calculate profile errors compensation rate, C along X axle, Y axle, Z axle _{ε x}=ε _xK _Px, C _{ε y}=ε _yK _Py, C _{ε z}=ε _zK _PzThen with profile errors compensation rate C _{ε x}, C _{ε y}, C _{ε z}In X axle, Y axle, the position control amount of Z axle to tracking error of being added to respectively, the servo actuator that at last stack result is outputed to X axle, Y axle, Z axle carries out profile errors compensation control.

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