CN102662351A - 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 big, is realizing that tool has great advantage aspect gap dividing movement, the bigger motion lift.Cylindrical cam belongs to space cam, can be divided into translating follower cylindrical cam and oscillating follower cylinder cam according to the mode of motion of driven member.Can adopt the CNC milling machine processing column cam contour that has a rotary table; For example having on the vertical numerical control milling machine of 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 influences the cylindrical cam machining precision in the cylindrical cam processing comprises 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, Because numerically-controlled machine mechanical part, servo-drive more complicated; And relate to machinery, electric, control and the variation of parameter in motion process; Lathe respectively links, and actual dynamic performance is difficult to accomplish to mate fully between the feed shaft, and the raising that this has directly influenced 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 the bee-line of current actual cutter location to 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.

Retrieval is found to existing technical literature, 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 processed with the turning axle interlock.Like Syh-Shiuh Yeh etc. 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 links that the distance of current interpolated point place tangent line is approximately profile errors on the cutter rail curve to instructing with actual cutter location of certain sampling period; Liu Yi etc. are at academic journal " system emulation journal " (2009; 21 (11): in the paper of delivering 3381-3386) " based on the optimal profile control and the emulation thereof of work coordinate system "; Proposition through on desired trajectory, setting up the Frenet coordinate system as work coordinate system, comes the approximate contours error with the normal component of location following error in work coordinate system when three linear axis link; 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 "; To a linear axis and a turning axle interlock processing; Propose a kind of expression formula, but this profile errors model description is comparatively abstract in Camshaft Grinding machining profile error under polar coordinate system.

In sum; In the processing of cylindrical cam part by numerical control,, describe intuitively and high-precision calculating profile errors and profile errors compensation rate how in each sampling period; A axle, X axle, Y axle servo actuator are compensated control; For strengthening matching degree between each feed shaft, it is significant to improve contour accuracy, has 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 deficiency that can overcome prior art, profile errors describe directly perceived, computational accuracy is high, profile errors compensation control is simply towards the three-shaft linkage profile errors compensating control method of cylindrical cam processing.Its technical scheme is:

To A axle, X axle, the interlock of Y axle, in the interpolation process, carry out profile errors calculating and profile errors compensation, it is characterized in that may further comprise the steps:

1) in each sampling period to cylindrical cam contour line cutter path interpolation processing, on the one hand, under lathe coordinate system, detect current each worktable physical location through A axle, X axle, Y axle position transducer separately, obtain actual cutter location R (R _A, R _x, R _y) coordinate, calculate the tracking error of A axle, X axle, Y axle, be designated as E respectively _A, E _x, E _yOn the other hand, with actual cutter location R (R under the lathe coordinate system _A, R _x, R _y) be transformed under the 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 on the 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 interpolated point P _a, P _bLine P _aP _bDistance be approximately profile errors ε ', profile errors ε ' decomposed along X axle, Y axle, Z axle obtain ε _x', ε _y', ε _z';

3) with rectangular coordinate system in space Oxyz bottom profiled error ε ' (ε _x', ε _y', ε _z') be transformed under the lathe coordinate system, obtain the profile errors ε (ε of A axle, X axle, Y axle correspondence _A, ε _x, ε _y), be respectively

ε _x=ε _x', ε _y=ε _y';

4) use A axle, X axle, the Y axle feed system scale-up factor K in the tracking error PID positioner separately _PA, K _Px, K _Py, calculate along the profile errors compensation rate of A axle, X axle, Y axle, 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 errors degree of compensation power, value between 0.9～1.1; Then with profile errors compensation rate C _{ε A}, C _{ε x}, C _{ε y}In A axle, X axle, the position control amount of Y axle of being added to respectively, and the servo actuator that stack result outputs to A axle, X axle, Y axle carried out profile errors compensation control to tracking error.

The present invention compares with existing method; Advantage is: with A turning axle, X linear axis, Y linear axis interlock processing column cam the time; Except lathe coordinate system; Also set up rectangular coordinate system in space Oxyz, profile errors abstract under the lathe coordinate system has been transformed under the Oxyz coordinate system describes, it is directly perceived that profile errors is described; Under rectangular coordinate system in space Oxyz, be approximately profile errors with the distance of current actual cutter location two nearest interpolated point lines to the tracking cutter path curve, so the profile errors computing method are simple, computational accuracy is high; Introduce scale factor, and use scale-up factor in each tracking error positioner, make profile errors compensation rate computing method simple, effective.

Description of drawings

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

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

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

Fig. 4 is that the three-shaft linkage profile errors towards cylindrical cam processing of the present invention calculates the 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 cylindrical cam contour line cutter path.

Fig. 7 is interpolation profile Error Graph when following the tracks of cutter path shown in Figure 6.

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

Embodiment

To with A axle, X axle, Y axle interlock processing column cam, do to describe in further detail below in conjunction with Fig. 1～4 couple the present invention:

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

In each sampling period to cylindrical cam contour line cutter path interpolation processing, under lathe coordinate system, detect current each worktable physical location through A axle, X axle, Y axle position transducer (like circle grating, grating chi etc.) separately, obtain actual cutter location R (R _A, R _x, R _y) coordinate, instruct the some subtraction calculations to obtain the tracking error of A axle, X axle, Y axle with the interpolation of A axle, X axle, Y axle, be designated as E respectively _A, E _x, E _yOn the other hand, with actual cutter location R (R under the lathe coordinate system _A, R _x, R _y) coordinate transformation under the rectangular coordinate system in space Oxyz, obtain 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 to go up two nearest interpolated point P apart from current actual cutter location R ' _a, P _b, establish R ' M ⊥ P _aP _b,, profile errors ε ' is obtained ε along X axle, Y axle, the decomposition of Z axle then at Oxyz coordinate system bottom profiled error ε ' ≈ R ' M _x', ε _y', ε _z'.

3) with rectangular coordinate system in space Oxyz bottom profiled error ε ' (ε _x', ε _y', ε _z') be transformed under the lathe coordinate system, obtain the profile errors ε (ε of A axle, X axle, Y axle correspondence _A, ε _x, ε _y), be respectively

${\mathrm{\ϵ}}_A=\mathrm{arctg}\frac{{{\mathrm{\ϵ}}_z}^{\′}}{{{\mathrm{\ϵ}}_y}^{\′}}---\left(4\right)$

ε _x＝ε _x′ (5)

ε _y＝ε _y′ (6)

4) establish that scale-up factor is K in the A axle feed system tracking error PID positioner _PA, integral coefficient is K _IA, differential coefficient is K _DAIf scale-up factor is K in the X axle feed system tracking error PID positioner _Px, integral coefficient is K _Ix, differential coefficient is K _DxIf scale-up factor is K in the Y axle feed system tracking error PID positioner _Py, integral coefficient is K _Iy, differential coefficient is K _DyThen easy for calculation is established and is respectively C in this sampling period A axle, X axle, Y axle tracking error position control amount separately _EA, C _Ex, C _EyUse A axle, X axle, the Y axle feed system scale-up factor K in the 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, calculates along the profile errors compensation rate of A axle, X axle, Y axle between 0.9～1.1:

C _εA＝ε _A·K _pA (7)

C _εx＝ε _x·K _px·w (8)

C _εy＝ε _y·K _py·w (9)

Then that 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 axle is (C _Ex+ C _{ε x}), the stack result of Y axle is (C _Ey+ C _{ε y}), the servo actuator that at last stack result is outputed to A axle, X axle, Y axle respectively carries out profile errors compensation control.

The present invention can obtain to realize in the digital control system of A axle shown in Figure 5, X axle, Y axle three-shaft linkage numerical control motion platform: constitute the upper and lower computer structure by industrial computer and Programmable DSPs motion control card; Realize data communication through USB; Sampling period equals interpolation cycle, is T=4ms.X axle, Y axle all drag working table movement with AC servo motor and ball guide screw nat, each sampling period with grating chi testing platform physical location; The A axle drags worktable with AC servo motor and over-type worm gear pair and rotatablely moves, and uses circle grating testing platform physical location in each sampling period.Realize that in the Programmable DSPs motion control card acceleration and deceleration control, interpolation algorithm, tracking error position control, profile errors calculate and compensate control etc.

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

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

Comparative illustration, the profile errors to A axle, X axle, the interlock of Y axle 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 axle, the Y axle.The present invention is suitable for turning axle and linear axis interlock control occasion, can in the digital control system of cylindrical cam processing and numerically-controlled machine, use and popularization.

Claims (1)

1. three-shaft linkage profile errors compensating control method towards cylindrical cam processing; To A axle, X axle, the interlock of Y axle, in the interpolation process, carry out profile errors calculating and profile errors compensation, it is characterized in that may further comprise the steps: 1) in each sampling period to cylindrical cam contour line cutter path interpolation processing; On the one hand; Under lathe coordinate system, detect current each worktable physical location through A axle, X axle, Y axle position transducer separately, obtain actual cutter location R (R _A, R _x, R _y) coordinate, calculate the tracking error of A axle, X axle, Y axle, be designated as E respectively _A, E _x, E _yOn the other hand, with actual cutter location R (R under the lathe coordinate system _A, R _x, R _y) be transformed under the 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 _A2) under rectangular coordinate system in space Oxyz, find on the 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 interpolated point P _a, P _bLine P _aP _bDistance be approximately profile errors ε ', profile errors ε ' decomposed along X axle, Y axle, Z axle obtain ε _x', ε _y', ε _z'; 3) with rectangular coordinate system in space Oxyz bottom profiled error ε ' (ε _x', ε _y', ε _z') be transformed under the lathe coordinate system, obtain the profile errors ε (ε of A axle, X axle, Y axle correspondence _A, ε _x, ε _y), be respectively

ε _x=ε _x', ε _y=ε _y'; 4) use A axle, X axle, the Y axle feed system scale-up factor K in the tracking error PID positioner separately _PA, K _Px, K _Py, calculate along the profile errors compensation rate of A axle, X axle, Y axle, 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 errors degree of compensation power, value between 0.9～1.1; Then with profile errors compensation rate C _{ε A}, C _{ε x}, C _{ε y}In A axle, X axle, the position control amount of Y axle of being added to respectively, and the servo actuator that stack result outputs to A axle, X axle, Y axle carried out profile errors compensation control to tracking error.

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