CN102662351B - Three-axis linkage contour error compensation control method for cylinder cam machining - Google Patents

Abstract

The invention relates to a three-axis linkage contour error compensation control method for cylinder cam machining. The method carries out contour error calculation and compensation during an interpolation machining process according to the linkage of axis A, axis X and axis Y, and is characterized in that the method comprises the steps of in each sampling cycle detecting the actual location of the worktable of axis A, axis X and axis Y in a machine tool coordinate system; converting into a space rectangular coordinate system and approximating the distance between the actual cutter location point and the line connecting with the two closest interpolation points on the tool path of the cylindrical cam contour at contour errors; converting into the machine tool coordinate system to obtain the corresponding contour errors of axis A, axis X and axis Y; and introducing a scaling factor, acquiring the contour error compensation quantities through proportional control, separately stacking the contour error compensation quantities with the location control quantities of shaft A, shaft X and shaft Y to follow errors, and outputting to a servo actuator. The method provided by the invention has the advantages that during axis A, axis X and axis Y linkage machining contour error description is intuitive, calculation precision is high, and contour error compensation method is simple and effective.

Description

Three-shaft linkage profile errors compensating control method towards cylindrical cam processing

Technical field

The present invention relates to a kind of profile errors compensating control method, particularly relate to a kind of three-shaft linkage profile errors compensating control method towards cylindrical cam processing.

Background technology

Cylindrical cam mechanism is compared with planar cam mechanism, and volume is little, compact conformation, good rigidly, running is reliable, driving torque is large, has great advantage realizing tool aspect gap dividing movement, larger motion lift.Cylindrical cam belongs to space cam, according to the mode of motion of driven member, can be divided into translating follower cylindrical cam and oscillating follower cylinder cam.Can adopt the CNC milling machine processing column cam contour with a rotary table, for example, on the vertical numerical control milling machine with rotary table, can use X feed shaft, A turning axle interlock processing translating follower cylindrical cam, with X feed shaft, Y feed shaft, A turning axle interlock processing oscillating follower cylinder cam.The source of error that affects Machining Accuracy of Cylinder Cam in cylindrical cam processing comprises the machine tool structure errors such as leading screw gap, guide rail are not straight, thermal deformation, the error that the dynamic perfromance of drive system, controller and external disturbance cause etc.Wherein, due to numerically-controlled machine machinery part, servo driving more complicated, and relate to machinery, electric, control and the variation of parameter in motion process, the lathe actual dynamic performance between feed shaft that respectively links is difficult to accomplish to mate completely, the raising that this has directly affected contour accuracy is the major reason that causes profile errors.Research shows, in part processing, profile errors calculated and carries out real-Time Compensation, and be the effective way of raising system contour accuracy.Profile errors refers to that current actual cutter location is to the bee-line of the cutter path curve of following the tracks of.In linear axis interlock occasion, profile errors is described directly perceived, is convenient to calculate and compensation; But in linear axis and turning axle interlock occasion, the description of profile errors and calculating compensation be difficulty comparatively.

To existing technical literature, retrieval is found, the existing achievement in research profile errors coupling control method when two or three linear axis interlocks that focuses mostly on, but the rare research of computing method, compensation method of profile errors when linear axis is processed with turning axle interlock.If Syh-Shiuh Yeh etc. is at academic journal < < IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY > > (2003,11 (3): in the paper of delivering 375-382) " Analysis and Design of Integrated Control for Multi-Axis Motion Systems ", propose when three linear axis interlocks actual cutter location of certain sampling period to be approximately profile errors to the distance of current interpolated point place tangent line on instruction cutter rail curve; Liu Yi etc. are at academic journal < < Journal of System Simulation > > (2009,21 (11): in the paper of delivering 3381-3386) " optimal profile based on work coordinate system is controlled and emulation ", proposition by setting up Frenet coordinate system as work coordinate system when three linear axis interlocks on desired trajectory, and the normal component by location following error in work coordinate system carrys out approximate contours error; The people such as Gong Shihua are at academic journal < < electric automatization > > (2010,32 (4): in the paper of delivering 11-13) " adaptive control of Camshaft Grinding machining profile error ", for a linear axis and a turning axle interlock processing, propose a kind of expression formula in Camshaft Grinding machining profile error under polar coordinate system, but this profile errors model description is comparatively abstract.

In sum, in the processing of cylindrical cam part by numerical control, how in each sampling period, describe intuitively and high-precision calculating profile errors and profile errors compensation rate, A axle, X-axis, Y-axis servo actuator are compensated to control, for strengthening matching degree between each feed shaft, improve contour accuracy significant, become those skilled in the art and be badly in need of the technical matters solving.

Summary of the invention

The object of this invention is to provide a kind of can overcome the deficiencies in the prior art, profile errors describe directly perceived, computational accuracy is high, the three-shaft linkage profile errors compensating control method towards cylindrical cam processing is controlled simply in profile errors compensation.Its technical scheme is:

For A axle, X-axis, Y-axis interlock, in interpolation process, carry out profile errors calculating and profile errors compensation, it is characterized in that comprising the following steps:

1) in each sampling period to cylindrical cam contour line cutter path interpolation processing, on the one hand, under lathe coordinate system, through A axle, X-axis, Y-axis position transducer separately, detect current each axle worktable physical location, obtain actual cutter location R (R _a, R _x, R _y) coordinate, calculate the tracking error of A axle, X-axis, Y-axis, be designated as respectively E _a, E _x, E _y; On the other hand, by actual cutter location R (R under lathe coordinate system _a, R _x, R _y) be transformed under rectangular coordinate system in space Oxyz, obtain corresponding actual cutter location R ' (R _x', R _y', R _z') coordinate, wherein R _x'=R _x, R _y'=R _y, R _z'=R _ytgR _a;

2), under rectangular coordinate system in space Oxyz, find in cylindrical cam contour line cutter path apart from current actual cutter location R ' (R _x', R _y', R _z') two nearest interpolated point P _a, P _b, actual cutter location R ' is arrived to interpolated point P _a, P _bline P _ap _bapart from being approximately profile errors ε ', profile errors ε ' is decomposed and obtains ε along X-axis, Y-axis, Z axis _x', ε _y', ε _z';

3) by rectangular coordinate system in space Oxyz bottom profiled error ε ' (ε _x', ε _y', ε _z') be transformed under lathe coordinate system, obtain A axle, X-axis, profile errors ε (ε corresponding to Y-axis _a, ε _x, ε _y), be respectively ε _x=ε _x', ε _y=ε _y';

4) use A axle, X-axis, the Y-axis feed system Proportional coefficient K in tracking error PID positioner separately _pA, K _px, K _py, calculate the profile errors compensation rate along A axle, X-axis, Y-axis, C _{ε A}=ε _ak _pA, C _{ε x}=ε _xk _pxw, C _{ε y}=ε _yk _pyw, wherein the scale factor of w for introducing, is used for controlling profile error compensation degree strong and weak, value between 0.9～1.1; Then by profile errors compensation rate C _{ε A}, C _{ε x}, C _{ε y}be added to A axle, X-axis, Y-axis respectively in the position control amount of tracking error, and the servo actuator that stack result outputs to A axle, X-axis, Y-axis carried out to profile errors compensation and control.

The present invention compared with the conventional method, advantage is: when with A turning axle, X linear axis, Y linear axis interlock processing column cam, except lathe coordinate system, also set up rectangular coordinate system in space Oxyz, profile errors abstract under lathe coordinate system is transformed under Oxyz coordinate system and is described, profile errors is described directly perceived; Under rectangular coordinate system in space Oxyz, with current actual cutter location to two interpolated point lines nearest on followed the tracks of cutter path curve apart from being approximately profile errors, so profile errors computing method are simple, computational accuracy is high; Introduce scale factor, and use scale-up factor in each axle tracking error positioner, make profile errors compensation rate computing method simple, effective.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Lathe coordinate system and rectangular coordinate system in space figure when Fig. 2 is cylindrical cam processing of the present invention.

Fig. 3 be of the present invention towards cylindrical cam processing at rectangular coordinate system in space bottom profiled error calculation method schematic diagram.

Fig. 4 is that the three-shaft linkage profile errors towards cylindrical cam processing of the present invention calculates compensation program process flow diagram.

Fig. 5 adopts three-shaft linkage numerical control motion platform hardware structure diagram of the present invention.

Fig. 6 is one section of cylindrical cam contour line cutter path.

Profile Error Graph when Fig. 7 is cutter path shown in interpolation tracing figure 6.

In figure: R ', actual cutter location P _a, interpolated point P _b, interpolated point P _c, interpolated point L, cutter path

Embodiment

For the processing column cam that links by A axle, X-axis, Y-axis, below in conjunction with Fig. 1～4, couple the present invention is described in further detail:

1) as shown in Figure 2, when with A axle, X-axis, Y-axis interlock processing column cam, X linear axis is vertical with Y linear axis, and A axle is the turning axle around X-axis, with this, sets up lathe coordinate system; In the rectangular coordinate system in space Oxyz setting up, except X linear axis, the Y linear axis of interlock processing, also virtual Z linear axis, and X-axis, Y-axis, Z axis meet right hand rectangular cartesian coordinate system.

In each sampling period to cylindrical cam contour line cutter path interpolation processing, under lathe coordinate system, through A axle, X-axis, Y-axis position transducer (as circle grating, grating scale etc.) separately, detect current each axle worktable physical location, obtain actual cutter location R (R _a, R _x, R _y) coordinate, obtain the tracking error of A axle, X-axis, Y-axis with the interpolation instruction point subtraction calculations of A axle, X-axis, Y-axis, be designated as respectively E _a, E _x, E _y; On the other hand, by actual cutter location R (R under lathe coordinate system _a, R _x, R _y) coordinate transformation is under rectangular coordinate system in space Oxyz, obtains corresponding actual cutter location R ' (R _x', R _y', R _z') coordinate, wherein

R _x′＝R _x (1)

R _y′＝R _y (2)

R _z′＝R _y·tgR _A (3)

2) as shown in Figure 3, under rectangular coordinate system in space Oxyz, establishing certain cylindrical cam contour line cutter path is L, and current actual cutter location is R ', finds cylindrical cam contour line cutter path L upper apart from two nearest interpolated point P of current actual cutter location R ' _a, P _b, establish R ' M ⊥ P _ap _b, at Oxyz coordinate system bottom profiled error ε ' ≈ R ' M, profile errors ε ' is decomposed and obtains ε along X-axis, Y-axis, Z axis _x', ε _y', ε _z'.

3) by rectangular coordinate system in space Oxyz bottom profiled error ε ' (ε _x', ε _y', ε _z') be transformed under lathe coordinate system, obtain A axle, X-axis, profile errors ε (ε corresponding to Y-axis _a, ε _x, ε _y), be respectively

${\mathrm{\&epsiv;}}_A=\mathrm{arctg}\frac{{{\mathrm{\&epsiv;}}_z}^{\&prime;}}{{{\mathrm{\&epsiv;}}_y}^{\&prime;}}---\left(4\right)$

ε _x＝ε _x′ (5)

ε _y＝ε _y′ (6)

4) establishing scale-up factor in A axle feed system tracking error PID positioner is K _pA, integral coefficient is K _iA, differential coefficient is K _dA; If scale-up factor is K in X-axis feed system tracking error PID positioner _px, integral coefficient is K _ix, differential coefficient is K _dx; If scale-up factor is K in Y-axis feed system tracking error PID positioner _py, integral coefficient is K _iy, differential coefficient is K _dy; Easily calculate in this sampling period A axle, X-axis, Y-axis tracking error position control amount separately, establish and be respectively C _eA, C _ex, C _ey; Use A axle, X-axis, the Y-axis feed system Proportional coefficient K in tracking error PID positioner separately _pA, K _px, K _py, and introduce profile errors compensating proportion zoom factor w, wherein w, according to actual compensation effect value between 0.9～1.1, calculates the profile errors compensation rate along A axle, X-axis, Y-axis:

C _εA＝ε _A·K _pA (7)

C _εx＝ε _x·K _px·w (8)

C _εy＝ε _y·K _py·w (9)

Then the wide error compensation amount of each arbor wheel and tracking error position control amount is superimposed, the stack result of A axle is (C _eA+ C _{ε A}), the stack result of X-axis is (C _ex+ C _{ε x}), the stack result of Y-axis is (C _ey+ C _{ε y}), the servo actuator that finally stack result is outputed to respectively to A axle, X-axis, Y-axis carries out profile errors compensation and controls.

The present invention can obtain realization in the digital control system of the A axle shown in Fig. 5, X-axis, Y-axis three-shaft linkage numerical control motion platform: by industrial computer and Programmable DSPs motion control card, form upper and lower computer structure, by USB, realize data communication, sampling period equals interpolation cycle, is T=4ms.X-axis, Y-axis all drag working table movement with AC servo motor and ball guide screw nat, in each sampling period, use grating scale testing platform physical location; A axle drags worktable rotary motion by AC servo motor and over-type worm gear pair, in each sampling period, uses circle grating testing platform physical location.In Programmable DSPs motion control card, realize that acceleration and deceleration control, interpolation algorithm, tracking error position control, profile errors calculating and compensation are controlled etc.

Fig. 6 is one section of cylindrical cam contour line cutter path, uses parametric line formal description: under the lathe coordinate system of A axle, X-axis, Y-axis interlock, be described as $\left\{\begin{array}{c}x=100t\\ y=35\cos 2\mathrm{\&pi;t},(0\&le;t\&le;1)\\ A=2\mathrm{\&pi;t}\end{array}\right.;$ Under the rectangular coordinate system in space Oxyz setting up shown in Fig. 2, be described as $\left\{\begin{array}{c}x=100t\\ y=35\cos 2\mathrm{\&pi;t},(0\&le;t\&le;1)\\ z=35\sin 2\mathrm{\&pi;t}\end{array}\right..$

Profile Error Graph when Fig. 7 is outline line cutter path shown in interpolation tracing figure 6.Wherein, in Fig. 7, in order not take, profile errors proposed by the invention calculates data1, profile Error Graph during compensating control method, and largest contours error is 0.112mm left and right.When adopting profile errors calculating proposed by the invention, compensating control method (making w=1.05), error curve of outline is as shown in data2 in Fig. 7, and largest contours error is 0.065mm left and right.

Comparative illustration, the profile errors for A axle, X-axis, Y-axis interlock proposed by the invention calculates, compensating control method is very effective, can improve contour accuracy, reduces profile errors, strengthens matching degree between A axle, X-axis, Y-axis.The present invention is suitable for turning axle and occasion is controlled in linear axis interlock, application and popularization in the digital control system that can process at cylindrical cam and numerically-controlled machine.

Claims (1)

1. the three-shaft linkage profile errors compensating control method towards cylindrical cam processing, for A axle, X-axis, Y-axis interlock, in interpolation process, carry out profile errors calculating and profile errors compensation, it is characterized in that each sampling period of cylindrical cam contour line cutter path interpolation processing including following steps: 1) under lathe coordinate system, through A axle, X-axis, Y-axis position transducer separately, detect current each axle worktable physical location, obtain actual cutter location R (R _a, R _x, R _y) coordinate, on the one hand, calculate the tracking error of A axle, X-axis, Y-axis, be designated as respectively E _a, E _x, E _y, through PID positioner, obtain tracking error position control amount C _eA, C _ex, C _ey; On the other hand, by actual cutter location R (R under lathe coordinate system _a, R _x, R _y) be transformed under rectangular coordinate system in space Oxyz, obtain corresponding actual cutter location R'(R _x', R _y', R _z') coordinate, wherein R _x'=R _x, R _y'=R _y, R _z'=R _ytgR _a; 2), under rectangular coordinate system in space Oxyz, find in cylindrical cam contour line cutter path apart from current actual cutter location R'(R _x', R _y', R _z') two nearest interpolated point P _a, P _b, by actual cutter location R' to interpolated point P _a, P _bline P _ap _bapart from being approximately profile errors ε ', profile errors ε ' is decomposed and obtains ε along X-axis, Y-axis, Z axis _x', ε _y', ε _z'; 3) by rectangular coordinate system in space Oxyz bottom profiled error ε ' (ε _x', ε _y', ε _z') be transformed under lathe coordinate system, obtain A axle, X-axis, profile errors ε (ε corresponding to Y-axis _a, ε _x, ε _y), be respectively ε _x=ε _x', ε _y=ε _y'; 4) use A axle, X-axis, the Y-axis feed system Proportional coefficient K in tracking error PID positioner separately _pA, K _px, K _py, calculate the profile errors compensation rate along A axle, X-axis, Y-axis, C _{ε A}=ε _ak _pA, C _{ε x}=ε _xk _pxw, C _{ε y}=ε _yk _pyw, wherein the scale factor of w for introducing, is used for controlling profile error compensation degree strong and weak, value between 0.9～1.1; Then by profile errors compensation rate C _{ε A}, C _{ε x}, C _{ε y}be added to A axle, X-axis, Y-axis respectively in the position control amount of tracking error, and the servo actuator that stack result outputs to A axle, X-axis, Y-axis carried out to profile errors compensation and control.

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