CN102033513B - Computer-assisted discrete geometric programming method - Google Patents

Abstract

The invention discloses a computer-assisted discrete geometric programming method and a computer-assisted discrete geometric programming system of an open numerical control system. Geometry of a tool path curve is not Euclidean geometry but discrete geometry. The discreteness of the tool path curve is a pure discrete geometric problem. According to a basic principle of the discrete geometry, L partition of the curve is constructed through guide points according to an optimization target based on a discrete geometric structure of the curve, so non-Europeanized error of the tool path curve is eliminated, and the problem of optimization of discrete position information is solved. By the method and the system, visualization of the discrete position information and visualization of a discrete method are realized; and the system is provided with an intuitive, simple, convenient and open human-computer interface.

Description

A kind of area of computer aided geometric programming method that disperses

Technical field

The invention belongs to advanced control and advanced manufacturing field, be specifically related to the manufacturing approach and the system of discrete location information in the digital control system in open type.

Technical background

Up to now, existing digital control system adopts interpolation iteration control method to carry out digital control to mechanical system always.Interpolation precision and interpolation rate become the core technology index of existing digital control system.

The basic technical scheme of interpolation iteration control method is; Speed of feed for given cutter track (Tool Path) curve and cutter; Under the control of real time operating system; As the timesharing cycle, adopt the interpolation iterative algorithm to calculate the whole digital control informations of relevant coordinate axis in real time with interpolation cycle at given time.Said digital control information comprises the positional information of coordinate axis feeding and the related information between these positional informations.

As everyone knows, when finding the solution the coordinate figure increment of curve, interpolation is a kind of iterative algorithm in the numerical computation method.So-called interpolation algorithm in itself, is exactly from X _nThe middle X that obtains _N+1Operation rule.Since the continuity of a function, X _nIn must contain X _N+1Partial information, making full use of these information, to cause the high-order strength reduction be the low order simple operation, thereby improve the speed of interpolation algorithm greatly.For avoiding complicated high exponent arithmetic(al), some optimum interpolation iterative control algorithms can't be used.On the other hand, for some complex curves, from X _nThe middle X that obtains _N+1Operation rule be quite the difficulty.Therefore, the interpolation iterative control algorithm of high-speed, high precision becomes the core technology in the existing Numeric Control Technology.

The inventor finds that there are following four essential characteristic in interpolation iteration control method.

1, in order to improve speed of feed, existing open digital control system must adopt time-divided method (claiming the digital increments method again) to carry out the interpolation iteration control.

For straight line, according to speed of feed F and interpolation cycle T, time-divided method must disperse straight line and be some the little line segment Δ L that are referred to as the profile step-length _i: ∑ Δ L _i=L, Δ L _i=FT.

As everyone knows, be the straight line of L for long, as long as provide speed of feed F, just can accomplish processing tasks.Yet above-mentioned formula shows, because the real-time iteration that interpolation cycle causes, interpolation iteration control method is had to discrete some the little line segment Δ L of being of straight line _iThe length of little line segment Δ Li must be the integral multiple of FT.

For curve, time-divided method is at first used some little line segment Δ L _iApproach Δ L _i=FT, this is a rough interpolation.And then carry out smart interpolation, promptly to every little line segment Δ L _iCarry out closeization of data point.

Formula

e _r＝(TF) ²/(8r)

Approximate error e has been described _rAnd the relation between speed of feed F and interpolation cycle T, the radius-of-curvature r.

This formula points out, for curve interpolating, and approximate error e _rWith square being directly proportional of speed of feed F and interpolation cycle T, r is inversely proportional to radius-of-curvature.The growth of speed of feed F and interpolation cycle T will cause approximate error e _rExponential increase, in other words, approximate error e _rExtremely sensitive to time and curvature.

Therefore, in interpolation iteration control method, approximate error e _rHigh susceptibility to the time causes the time to be locked by interpolation cycle, is not a controlled external variable, but a systematic parameter.

Time becomes first essential characteristic that systematic parameter is an interpolation iteration control method, is the basic defect of giving birth in the interpolation iteration control technology.

2, in interpolation iteration control method; In each interpolation cycle by digital control information that interpolation generated; Send to kinetic control system (step-by-step control system/servo-control system) on the one hand immediately in real time and be used for the motion of Real Time Drive coordinate axis; Carry out iteration in real time generating next digital control information as the input of next interpolation cycle again on the other hand, thereby constitute the real-time iteration of digital control information.Follow the beat of interpolation cycle, digital control information constantly generates, sends, carries out, from and go round and begin again with the mode of process iteration, constitute the real-time iteration of control procedure.Therefore, through the real-time iteration of digital control information and the real-time iteration of control procedure, interpolation iteration control method is given real time implementation with the whole manufacturing process of the generation of digital control information, transmission, execution.

The real-time iteration of digital control information and the real-time iteration of control procedure (being called for short information real-time iteration and process real-time iteration, the i.e. real-time iteration of I&P) are second essential characteristic of interpolation iteration control method, are the basic defects of giving birth in the interpolation iteration control technology.

3, in interpolation iteration control method, the real-time iteration of I&P under the interpolation cycle unified command of real time operating system is a kind of focus control mode.In this control model, real time operating system is commanded all, and " arrogate all authority to oneself, and Xiao Quan is not put " carried a task right down to the grass-roots level, the bag entirely of planning, design, construct, and be " plan on the limit, the limit is designed, construct in the limit ".

The focus control mode of " limit planning, limit design, limit construction " is the 3rd essential characteristic of interpolation iteration control method, is the basic defect of giving birth in the interpolation iteration control technology.

4, in interpolation iteration control method, approximate error e _rR is inversely proportional to radius-of-curvature, with square being directly proportional of speed of feed F and interpolation cycle T.Yet workpiece profile is a geometrical issues, thereby cutter track curve and approximate error e _rWith radius-of-curvature r also geometrical issues just.What movement velocity accomplishing processing tasks as for the promptly relevant coordinate axis of center cutter with, then is the dynamics problem of a process issues and mechanical system.

In interpolation iteration control method, approximate error e _r, radius-of-curvature r, interpolation cycle T, the whole close-coupled of speed of feed F together, relate to space, time, speed, acceleration (retarded velocity), acceleration even.In other words, interpolation iteration control method is the geometry strong correlation of interpolation iterative algorithm and curve, with the whole close-coupled of dynamic characteristic of the geometric properties of workpiece profile, technology characteristics, mechanical system together.Coupled relation between this space-time of cutter track curve can abbreviate the coupling of space-time structure as.

The coupling of the space-time structure of cutter track curve is the 4th essential characteristic of interpolation iteration control method, is the basic defect of giving birth in the interpolation iteration control technology.

The inventor finds, because there is the basic defect of giving birth in above-mentioned four in the interpolation iteration control, interpolation iteration control technology is as the pervasive control method of existing digital control system in open type, aspect positional information discrete, has following problems:

1, the geometry of cutter curve is predetermined, and therefore, the kinematic relation between the coordinate axis is deterministic.Digital control system is discrete with positional information, to control the displacement (angular displacement) of relevant coordinate axis, through synthesizing of these displacements realizing the cutter track curve.The synthetic of displacement means that relevant coordinate axis must link.The discrete of positional information is the core missions of digital control system, in essence, is a geometrical issues purely.

Yet; Interpolation iteration control method has produced the coupling of the space-time structure of cutter track curve; Having ignored the discrete of digital control information fully is a discrete geometrical issues purely, and further with the whole departure process real time implementation of digital control information, causes the closure of digital control information.

2, in interpolation iteration control method; The interpolation iterative algorithm not only relates to numerical computation method but also relate to the operation rule of realizing this method on computers in real time; The real-time iteration of digital control information and the real-time iteration of departure process must relate to process scheduling and thread scheduling in the real time operating system, cause the closure of the discrete method of digital control information.

3, in interpolation iteration control method, the real time implementation of the whole departure process of digital control information must cause the closure at the interface between the subprocess such as discrete, the transmission, execution of closure and the digital control information of whole control process.

4, in interpolation iteration control method, interpolation algorithm, interpolation rate, interpolation precision are its core technology indexs.Thereby interpolation iteration control method is inseparable with figure place, frequency and the real time operating system of CPU.In other words, the progress that interpolation iteration control method causes Numeric Control Technology is progressive inseparable with the progress of chip technology and real time operating system.

(Chinese patent number: ZL200710124304.9 in patent of invention " computerized numerical system data stream association control method and architecture "; Granted publication day: on August 19th, 2009); The inventor proposed a kind of data stream association control method (Data-stream Related Control, DRC).Opposite with interpolation iteration control method, the data stream association control method is converted into a pure geometry problem with positional information discrete.The data stream association control method will be controlled the whole manufacturing process non real-timeization of the desired digital control information of determinacy kinematic relation between the mechanical system; In the PC system, produce whole digital control informations in non real-time, comprise the discrete location information of coordinate axis feeding and the related information between these discrete location information.

In the foregoing invention patent, discrete location information is the stepping type associated data stream of " 1 " or " 0 " form, does not relate to little line segment Δ L of cutter track curve ₁..., Δ L _nThe optimization problem of (being the incremental associated data stream).

Existing digital control system in open type has three kinds of pattern: PC to embed the NC pattern, NC embeds PC pattern, soft open pattern.In these three kinds of patterns, the PC system often disposes the CAD/CAM/CAPP function, becomes a programing system, is used to accomplish the planning of cutter track curve, even further accomplishes rough interpolation, and just the cutter track curve being dispersed is little line segment Δ L _i, generate said little line segment Δ L _iThe G code numerical control program send digital control system to and carry out smart interpolation.Obviously, also there are little line segment Δ L in CAD/CAM/CAPP system and other NC Programming System _iOptimization problem.

Little line segment Δ L ₁..., Δ L _nOptimization relate to the symmetry breaking of restrained forms of motion of coordinate axis and generation thereof.In this case, the geometry of cutter track curve no longer is Euclidean geometry but discrete geometry.Cutter track curve discrete thereby be a discrete geometry problem.Therefore, need the discrete geometric ultimate principle of research, thereby design the non-europeanized error that a kind of simple, efficient, open technical scheme is eliminated the cutter track curve, solve little line segment Δ L comprehensively ₁..., Δ L _nOptimization problem.

Summary of the invention

The technical matters that the present invention will solve is a kind of discrete geometric programming method of area of computer aided and system thereof of digital control system in open type to be provided, the discrete digital reflection of the opening of in the data stream association control method, optimizing for the generation of cutter track curve.

Computer Simulation has become the most far-reaching one of the computer application field the most widely of influence.In the mechanical system two, three and even the determinacy kinematic relation of multiaxis can be passed through 3 D graphical interface, with its motion process of visual picture showing, have good man computer interface.PC system for discrete control information manufacturing system; The present invention makes up discrete geometric programming method (the Computer Aided Discrete Geometry Planning of a kind of area of computer aided on 3 D graphical interface; CADGP); Similar with geometrograph, through the needed whole discrete location information of determinacy kinematic relation of multiaxis in the visual simply and intuitively technical method acquisition control mechanical system.

Technical matters of the present invention is achieved through following technical scheme.

A kind of area of computer aided geometric programming method that disperses is used to plan that the intrinsic L of cutter track curve cuts apart, and may further comprise the steps:

Discrete coordinates is planning step (S1): according to the discrete scale of setting, uses distance as the equal space line of discrete scale with the coordinate plane gridding, set up discrete coordinates and be;

Cutter track curve planning step (S2): planning cutter track curve in discrete coordinates system is k bar curve according to unique point with the cutter track curve segmentation, and every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file;

L is cut apart planning step (S3): to every curve in the said k bar curve, according to the optimization aim of setting, the intrinsic L that meets said optimization aim through guiding point pointwise structure is cut apart;

The auxiliary discrete geometric programming method of aforementioned calculation machine, in the said step (S2), the tolerance according to the workpiece profile size is adjusted into regular curve with fundamental curve, and regular curve is revised, and generates the cutter track curve of regular curve.

In the auxiliary discrete geometric programming method of aforementioned calculation machine, said step (S3) may further comprise the steps:

Step (S301), from said k bar curve, take out a curve in turn, set optimization aim;

Step (S302), be original guiding point, generate said original guiding neighborhood of a point with the starting point of said curve;

Step (S303), according to the optimization aim of setting, in said original guiding neighborhood of a point, confirm a guiding point, generate the coordinate figure increment of said guiding point and said original guiding point;

Step (S304), between said guiding point and said original guiding point, generate the straight line section;

Step (S305), for the segment of curve of said curve between said guiding point and said original guiding point, judge whether said straight-line segment is little line segment of said segment of curve;

Step (S306) is then returned step (S303) if said straight-line segment is little line segment of said segment of curve, continues to generate next guiding point;

Step (S307) is not if said straight-line segment is little line segment of said segment of curve; Then a last guiding point of said guiding point is exactly the intrinsic reflection; Said intrinsic reflection is the terminal point of said little line segment, and the coordinate figure increment of a said last guiding point and said original guiding point is exactly the coordinate figure increment of said little line segment;

Step (S308), with the original guiding point of said intrinsic reflection as the little line segment of next bar; Order repeating step (S301) is to step (S307); Generate the little line segment of next bar of said curve, until the terminal point of said curve, the intrinsic L that meets said optimization aim that generates said curve is cut apart.

In the auxiliary discrete geometric programming method of aforementioned calculation machine, said step (S305) also comprises the steps:

Step (S3051), on the cutter track orientation, generate the neighborhood of said straight-line segment;

Step (S3052), judge whether the neighborhood of said straight-line segment is the subclass of the neighborhood of said segment of curve.

In the auxiliary discrete geometric programming method of aforementioned calculation machine, the optimization aim in the said step (S301) is that distance is the shortest, and each coordinate axis is all pressed preferential direction of motion feeding in the said coordinate axis.

In the auxiliary discrete geometric programming method of aforementioned calculation machine, the optimization aim in the said step (S301) is that discretization error is minimum, and the discretization error of each guiding point was minimum during said intrinsic L was cut apart.

In the auxiliary discrete geometric programming method of aforementioned calculation machine, the optimization aim in the said step (S301) is optimum for cooperating, and the distribution of the discretization error of each guiding point in the regular curve tolerance range was consistent during said intrinsic L was cut apart.

In the auxiliary discrete geometric programming method of aforementioned calculation machine, said coordinate axis is more than three.

In the auxiliary discrete geometric programming method of aforementioned calculation machine, said discrete coordinates is to be that nonopiate discrete coordinates is.

A kind of area of computer aided geometric programming system that disperses comprises hardware platform, software platform and application software system, and said hardware platform is the PC system, and software platform is a graphical interfaces operating system; Said application software system comprises: discrete coordinates is that planning module, cutter track curve planning module, L are cut apart planning module;

Said discrete coordinates is that planning module is used for according to the discrete scale of setting, uses distance as the equal space line of discrete scale with the coordinate plane gridding, set up discrete coordinates and be;

Said cutter track curve planning module is used for the planning cutter track curve in discrete coordinates system, is k bar curve according to unique point with the cutter track curve segmentation, and every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file;

Said L is cut apart planning module and is used for every curve to said k bar curve, and according to the optimization aim of setting, the intrinsic L that meets said optimization aim through guiding point pointwise structure is cut apart;

In the auxiliary discrete geometric programming system of aforementioned calculation machine, said application software system is based upon on the middleware, adopts API API between each module.

In the auxiliary discrete geometric programming system of aforementioned calculation machine, said software platform also comprises 3 d graphic library.

In the auxiliary discrete geometric programming system of aforementioned calculation machine, said discrete coordinates is that generation module also is used to set up nonopiate discrete coordinates system.

The beneficial effect that the present invention and the contrast of existing interpolation iteration control technology are had is:

1, the geometry of cutter track curve is predetermined, and therefore, the kinematic relation between the coordinate axis is deterministic.The core missions of digital control system are that positional information is discrete, to control the displacement of relevant coordinate axis, through synthesizing of these displacements realizing the cutter track curve.The discrete of positional information is a geometrical issues purely.

Yet; Interpolation iteration control method has produced the space-time structure coupling of cutter track curve; Having ignored the discrete of positional information fully is a geometrical issues purely, and further with the whole departure process real time implementation of positional information, causes the closure of discrete location information.

In interpolation iteration control method; The interpolation iterative algorithm not only relates to numerical computation method but also relate to the operation rule of realizing this method on computers in real time; The real-time iteration of discrete location information and the real-time iteration of departure process must relate to process scheduling and thread scheduling in the real time operating system, cause the closure of the discrete method of positional information.

In interpolation iteration control method, the real time implementation of the whole departure process of positional information must cause the closure at the interface between the subprocess such as discrete, the transmission, execution of closure and the positional information of whole control process.

The present invention has removed the space-time structure coupling of cutter track curve; With the discrete geometry of cutter track curve and the technology characteristics of process, the dynamic characteristic decoupling zero of mechanical system; The geometric programming that under area of computer aided, disperses, discrete location information is open, the discrete method of discrete location information is open; Whole control process is open, and the interface between the subprocess such as discrete, the transmission of positional information, execution also is open.Therefore, with the contrast of existing interpolation iteration control technology, the present invention has solved the opening of digital control technology and the opening of digital control process fully, with the prior art contrast, has significant substantive progressive.

2, interpolation algorithm, interpolation rate, interpolation precision are the core technology indexs of prior art.The present invention allows to adopt any numerical computation method to come discrete location information; In other words, in the present invention, interpolation algorithm, interpolation rate, interpolation precision all are some pseudo problems; Thereby; With the contrast of existing interpolation iteration control technology, the present invention makes Numeric Control Technology be completely free of the restriction of interpolation algorithm, chip technology and real time operating system, for Numeric Control Technology popularize and the standardization of digital control system has substantive marked improvement.

3, in parts profile, straight line accounts for more than 70% greatly.During processing linear, generally need with straight line be divided into accelerating sections, at the uniform velocity the section and braking section.In interpolation iteration control method, for the at the uniform velocity section of straight line, must be according to formula Δ L _i=FT is further discrete some the little line segment Δ L that are referred to as the profile step-length that are of section at the uniform velocity _i, expended a large amount of computational resources thus, significantly reduced process velocity and crudy.For the at the uniform velocity section of straight line, the present invention need not further disperse and be some little line segment Δ L _iThereby, obtaining significant beneficial effect aspect raising process velocity and the crudy.

3, in interpolation iteration control method; Multi-shaft interlocked technology becomes ultra-modem technology of the prior art; And real-time control complicated that causes technological parameter; Its technical bottleneck is: along with the increase of the number of axle, the figure place of CPU, frequency must increase, and the figure place of real time operating system must increase and real-time must be stronger.

From associated data stream, the number of axle of interlock increases just increases the passage that sends associated data stream simply; Secondly, the interlock of the real-time control of technological parameter and coordinate axis does not have difference in essence.The switch that the present invention will control the technological parameter that needs real-time control is regarded as the virtual coordinates axle, and parameter value is regarded as the value of virtual coordinates axle, thereby the coordinate axis interlock and the real-time control of technological parameter are united.In the present invention; The link change amount of discrete location increment and multiparameter of needed multi-coordinate axle of multiaxis multiparameter was not only irrelevant but also irrelevant with real time operating system with discrete logarithm; With the contrast of existing interpolation iteration control technology; Thoroughly solve the complicacy of multiaxis multiparameter linkage technique, obtained significant beneficial effect.

5, prior art ignored the non-Europe characteristic and the discrete geometry thereof of cutter track curve fully, thereby the positional information that is dispersed (promptly approaching broken line) certainly leads to the non-europeanized error of cutter track curve based on Euclidean geometry.The present invention is based on discrete geometry, eliminated the non-europeanized error of discrete location information fully.

6, to cut apart be its upper bound of all approaching broken line to the intrinsic L of curve, thereby in the intrinsic L of curve was cut apart, the bar number of little line segment was minimum, and the flex point of promptly approaching broken line is minimum.The present invention is based on the discrete geometry of cutter track curve; Intrinsic L the shortest according to distance, that discretization error is minimum, the most excellent optimization aim of cooperation is constructed the cutter track curve through the guiding point pointwise is cut apart; With the prior art contrast, solved the optimization problem of discrete location information.

7, method proposed by the invention is the geometrograph based on the discrete geometry of curve under a kind of area of computer aided; Generate the discrete digital reflection of cutter track curve through the directly perceived simple visualized operation step of show clicking, for the popularization development of DRC control method provides an open platform.

Description of drawings

Fig. 1 is the synoptic diagram of quadrature discrete coordinate system;

Fig. 2 is the discrete geometric programming system module figure of area of computer aided;

Fig. 3 is the process flow diagram of the discrete geometric programming method of area of computer aided.

Embodiment

Formerly system is made the field, and speed of feed F is the technological parameter of user's appointment, refers to the speed of reference point when cutter path moves with respect to workpiece on the cutter.The desired workpiece profile of user program depends on that the track that center cutter moves with respect to workpiece is the cutter track curve.According to the requirement of processing technology, the cutter track curve generally is made up of the order of some continuous curves according to planning.

The geometry of workpiece profile is predetermined, and therefore, the kinematic relation between the coordinate axis is deterministic.The core missions of digital control system are made discrete control information exactly, and the coordinate axis that is used for the Control work machine is accomplished given determinacy mechanical motion, and pass through the synthetic realization cutter track curve of the displacement (angular displacement) of relevant coordinate axis.The synthetic of displacement means that relevant coordinate axis must link.Therefore, synthesizing of coordinate axis displacement realizing the cutter track curve through relevant, in essence, is a geometrical issues purely.

As everyone knows, in the Euclidean geometry of classics, the bearing of trend of curve is arbitrarily, and its coordinate figure then is continuous.

In digital control system, the direction of motion of coordinate axis no longer is arbitrarily, but affined, only allows to do forward and counter motion according to the specific mechanical configurations of coordinate axis.For example, the rectilinear coordinates axle can only axially be made forward feeding and feed reversing, and rotatable coordinate axis can only be rotated in the forward and reverse rotation.Therefore, in digital control system, the bearing of trend of cutter track curve (or direction of motion) is not arbitrarily, but affined.In digital control system, discreteness has replaced continuity, and the elongation of cutter track curve no longer is continuous, but discrete.Obviously, classical Euclidean geometry no longer is the geometry basis of cutter track curve.For this reason, the inventor has proposed discrete geometric idea.

Discrete Study on Geometry curve bearing of trend be tied with elongation by the geometrical invariants under the discrete situation; The structure of associated data stream and the inner link between the curve have been disclosed; Thereby for theoretical foundation has been established in the generation of associated data stream, optimization and control, for the discrete geometric programming method of the area of computer aided that the application proposed has been established technical foundation.

Be without loss of generality, the present invention is example with the two dimensional motion, sets up discrete geometric some key concepts.

(1), discrete coordinates system

Digitizing replaces continuous quantity with discrete magnitude, and this just certainly leads to error.In digital control system, must be with the certain precision discrete curve.The discretization error of this predefined permission is also referred to as discrete scale, is designated as e.

For coordinate axis, because the influence of the factors such as rigidity of gap between the mismachining tolerance of parts and rigging error, the kinematic pair and friction, unrelieved stress, mechanical system, minimum resolution of its mechanical shift existence generally is referred to as the feeding equivalent, with e _fShow it.For coordinate axis, less than e _fMechanical shift be skimble-skamble.

Generally speaking, discrete scale equals the feeding equivalent.In fine structure, discrete scale is less than the feeding equivalent.

The discrete scale of each coordinate axis can be different, and for example, the discrete scale of x axle is e _x, the discrete scale of y axle is e _y

With discrete scale that coordinate axis is discrete, distance each other is that the parallel lines of discretization error are with the coordinate plane gridding.The coordinate system of setting up thus is referred to as discrete coordinates system.Discrete scale e _x..., e _yIt is the systematic parameter of discrete coordinates system.

As shown in Figure 1, the orthogonal discrete coordinates of the direction of motion of coordinate axis system is referred to as quadrature discrete coordinate system, for example rectangular coordinate system, polar coordinate system; The mutual off plumb discrete coordinates of the direction of motion of coordinate axis system is referred to as nonopiate discrete coordinates and is.

Non-perpendicularity between the coordinate axis, nonparallelism, and the backlass of coordinate axis, pitch error etc. are the inherent features of mechanical system, also are the systematic parameters of discrete coordinates system.

(2), lattice point

In the quadrature discrete coordinate system, distance is that the equal space line of discrete scale is with the coordinate plane gridding.The intersection point of parallel equal space line is called lattice point, like intersection points such as a among Fig. 1, b, c.

The position that the discrete motion of having only lattice point to be only coordinate axis can reach.

(3), allow direction of motion, exclusion movement direction and preferential direction of motion

In digital control system, the direction of motion of coordinate axis is affined.For example, for the x/y coordinate setting table, direction of motion is ± the x direction, ± y direction and x axle and the formed+x/+y of y axle interlock ,+x/-y ,-x/+y ,-the x/-y four direction.These 8 direction of motion are referred to as the permission direction of motion of mechanical system.

In digital control system, processing is the motion process of the relative workpiece of cutter, and the extension of cutter track curve has directivity, exists counterclockwise and clockwise two kinds of bearing of trends.This directivity is referred to as the cutter track orientation.

For example, for the counterclockwise arc of the 1st quadrant, the cutter track orientation is a northwest position.

When the cutter track orientation is northwest position, have only-the x direction ,+the y direction is to allow direction of motion with-x/+y direction, other directions are the exclusion movement direction.

The tangent slope of putting on the circular arc has further retrained direction of motion.For example, for the point on the circular arc, if this some place tangent slope is greater than 1; The motion of-x direction must depart from circular arc, thereby-the x direction is the exclusion movement direction, in other words;-x direction is contained by-x/+y direction, allow direction of motion be+the y direction and-the x/+y direction; If this some place tangent slope is less than 1, the motion of+y direction must depart from circular arc, thereby+the y direction is the exclusion movement direction, in other words ,+y direction is contained by-x/+y direction, allow direction of motion be-the x direction and-the x/+y direction.

If the tangent line at this some place is near the x axle, then-the x direction is preferential direction of motion; If the tangent line at this some place is near the y axle, then+the y direction is preferential direction of motion; If the tangent line at this some place is near 45 ° of lines, then-the x/+y direction is preferential direction of motion.

(4), the reflection collection of curve

Point on the curve is called preimage, like point of the m among Fig. 1 and n point.

A lattice point if be less than or equal to discretization error with the distance of certain preimage of curve, then is called the numeral reflection of this preimage, abbreviates reflection as, like a among Fig. 1, b, c, d, all points of e.

Whole reflections of curve constitute a set, are referred to as the reflection collection of this curve.For example, be the circle of r for radius, e is a discrete scale, radius for the circle of (r-e) and radius be on the annulus between the circle of (r+e) with annulus in whole lattice points be exactly the reflection collection of this circle.

In given discrete coordinates system, the geometry of this curve is depended in the reflection collection of curve and the distribution in discrete coordinates system thereof fully.

Obviously, there are a plurality of reflections in a preimage on the curve; Otherwise,, on this curve, then have a plurality of preimages for a reflection.

For a given reflection, be referred to as the neighborhood of this reflection at the whole reflections that allow on the direction of motion distance with the preimage of this curve to be less than or equal to discretization error.For example for the reflection b among Fig. 1, if the cutter track curve is counterclockwise, its neighborhood is a point; If the cutter track curve is clockwise, its neighborhood is d point and e point, and the c point is positioned at the exclusion movement direction, is not the neighborhood of reflection b.

For given curve, its whole neighborhoods constitute a set, are referred to as this neighborhood of a curve collection.The neighborhood of a curve collection is that its reflection collection is in a sub-set that allows on the direction of motion.

(5), associated data stream

Digitizing is exactly a discretize.By discrete scale curve being dispersed is a sequence of its reflection.Coordinate figure increment between the reflection is a discrete scale, promptly equals " 1 " or " 0 ", and this reflection sequence is called the microcosmic numeral reflection of curve.For all coordinate axis, the microcosmic numeral reflection of curve to be arranged in order, the coordinate axis discrete location information of " 1 " " 0 " form that is produced is exactly the stepping type associated data stream of this curve.

The stepping type associated data stream description of curve the fine microstructures of this curve.

If the increment of each coordinate figure between the reflection is not a discrete scale but several discrete scales, this reflection sequence is called the incremental numeral and videos.For all coordinate axis, the incremental numeral reflection of curve to be arranged in order, the coordinate axis discrete location information of the coordinate figure incremental form that is produced is exactly the incremental associated data stream of this curve.

For a plurality of coordinate axis, said associated data stream constitutes the multidimensional associated data stream.

Table 1 is the synoptic diagram of 5 interlock incremental associated data streams of cutter track curve.

Table 1

In the table, the cutter track curve is the function of 5 variablees such as X, y, Z, A, B, and time T is dispersed is divided into n interval: Δ t _i, i=1 ..., n; Five of X, y, Z, A, B etc. are at Δ t _iInterior coordinate figure increment is Δ X _i, Δ y _i, Δ Z _i, Δ A _i, Δ B _i

(6), main drive shaft and universal driving shaft

Obviously, be ± 1 straight line for slope, its stepping type associated data stream is " 1 " entirely.

For other oblique lines, in its stepping type associated data stream, the data stream of certain is inevitable to be " 1 " entirely, and in other words, " 1 " is continuous, and this axle is called main drive shaft; Another data stream is inevitable not to be complete " 1 ", and in other words, " 1 " is not continuous, but about a kind of distribution of main drive shaft data stream, this axle is referred to as universal driving shaft.This just means that the main drive shaft data stream can be considered independent variable, and the universal driving shaft data stream then is the distribution of main drive shaft data stream.

For any curve, zeroaxial 45 ° of oblique lines and 135 ° of oblique lines are divided into 8 intervals with 4 quadrants.The intersection point of these two oblique lines and curve is called the unique point of curve.In unique point, curve is from interval another interval that gets into, and x axle and y axle will change active/interlock attribute.

(7), L is cut apart

For a curve in the cutter track curve, be less than or equal to some end to end small straight-line segment Δ L of discretization error with the maximum normal direction distance of this curve _iThe summation of (being called for short little line segment) is referred to as the broken line that approaches of this curve, or is called about the discrete of little line segment of this curve and cuts apart, abbreviate L as and cut apart, note be Δ L ₁..., Δ L _n

For coordinate axis, distinguish the point on coordinate axis and the axle with subscript.For example, use Δ L _{I, x}, Δ L _{I, y}Represent little line segment Δ L _iThe coordinate axis component.At Δ L _{I, x}In, first subscript " i " representes that the starting point of this little line segment is x _i, the little line segment Δ L of second subscript " x " expression _iX axle component.

To i arbitrarily, little line segment Δ L _iBe no more than discrete scale with the error of this curve.

It is the incremental associated data stream that the L of curve is cut apart pairing associated data stream, and in other words, it is exactly the incremental numeral reflection of curve that the L of curve is cut apart.

(8), geometric factor

If Δ L ₁..., Δ L _nBe the little line segment of the L of curve in cutting apart, and do not comprise unique point, Δ L _{I, x}, Δ L _{I, y}Be Δ L _iX axle, the component of y axle.

Establishing the x axle again is main drive shaft, obviously, and for all Δ L _{I, x}Axle is always main drive shaft.The data stream of universal driving shaft y is the distribution of the data stream of main drive shaft x, and therefore, the geometric properties of curve only depends on the component Δ L of universal driving shaft y _{I, y}

Curve is at point (x _i, y _i) curvature cause little line segment Δ L _iLength certainly exist a maximal value.This maximal value is referred to as curve at point (x _i, y _i) intrinsic length.As Δ L _iDuring for intrinsic length, the component Δ L of universal driving shaft y _{I, y}Be referred to as point (x _i, y _i) geometric factor, with G _{I, y}Show it, Δ L _iTerminal point then be called intrinsic reflection.G _{I, y}Integral multiple for discretization error e.

For all i, if little line segment Δ L _iLength be intrinsic length, i.e. the component Δ L of universal driving shaft y _{I, y}Be equal to little line segment Δ L _iStarting point (x _i, y _i) geometric factor G _{I, y}, this L is cut apart the intrinsic L that is curve and is cut apart, and is designated as Δ L _i(i=1 ..., n).

Obviously, for i arbitrarily, Δ L _{I, y}Length can only be less than or equal to G _{I, y}Therefore, for this curve, how much equivalent G of universal driving shaft y _{I, y}It is the inherent geometric attribute of this curve.

(9), T is cut apart

Time T is divided into is uneven in length and end to end some intervals: Δ t ₁..., Δ t _i..., Δ t _mThese Δs t _iSummation be referred to as to cut apart about the discrete of time T, abbreviate T as and cut apart, with Δ t _i(i=1 ..., m) show it, m=n-1 in the formula, n are the bar number of little line segment.

(10), the linkage of associated data stream and interlock table

The stepping type associated data stream is at each sequential point t _iThe coordinate figure increment of " 0 " or " 1 " form be referred to as the stepping type associated data stream at this sequential point t _iState; Similarly, the incremental associated data stream is at each time interval Δ t _iInterior coordinate figure increment is referred to as the incremental associated data stream at this time interval Δ t _iInterior state.

Obviously, associated data stream is a kind of state flow of discrete location information.In the state flow of associated data stream, both comprised discrete location information, comprise the related information between these discrete location information again.

Said related information has been described the linkage between the discrete location information described in the associated data stream, and promptly L is cut apart.

The linkage of associated data stream has determined relevant coordinate axis at each time interval Δ t _iInterior (or each sequential point t _i) displacement and the resultant displacement of generation thereof, reflected the geometric properties of curve, be numerically controlled essential attribute.

For given cutter track curve, discrete location information in the associated data stream and linkage thereof are the discrete geometry attributes of cutter track curve, and relevant coordinate axis with control realizes that the method for cutter track curve and process have nothing to do.

According to given data layout, set up interlock at storage space and show to describe L and cut apart.Through said interlock table, with each time interval Δ t _iInterior (or each sequential point t _i) needed displacement conversion was the spatial correlation of associated data stream at storage space when relevant coordinate axis linked.

(11), the servo-actuated property of associated data stream and servo-actuated table

The related information of said associated data stream also comprises the servo-actuated property between the adjacent states in the associated data stream.

The servo-actuated property of so-called associated data stream; Refer to the transmission speed of associated data stream; Just the time interval of associated data stream between adjacent states is exactly that T is cut apart concerning the incremental associated data stream, is exactly each sequential point t concerning the stepping type associated data stream _iBetween the time interval (also can be called T cuts apart).

The servo-actuated property of associated data stream has determined the speed of following between the said resultant displacement with the geometric properties of cutter track curve and the temporal characteristics decoupling zero of processing technology, and just the speed of feed of cutter is numerically controlled non-essential attribute.

According to given data layout, set up the servo-actuated table at storage space and describe T and cut apart.Through said servo-actuated table, convert the speed of feed of cutter the spatial correlation of associated data stream at storage space.

(12), regular curve

In manufacturing industry, tolerance is a base attribute of workpiece profile curve.Tolerance equals maximum size and the minimum absolute value that allows the algebraic difference of size of allowing.Representing maximum size and minimum two zones that straight line limited of size that allow of allowing to be called tolerance range.Generally, tolerance is half the much larger than discretization error.

Workpiece profile curve given during design is called fundamental curve.Given nominal size during design is called basic size.

For basic size, the absolute value of upper and lower deviation is unequal often.The pairing size in tolerance center is called the canonical size; For the canonical size, the absolute value of upper and lower deviation equates.

Basic size in the workpiece profile curve that when design is given is converted into the canonical size, and resulting workpiece profile curve is referred to as regular curve.In the tolerance range of regular curve, upper and lower deviation equates.

If e is a discretization error.Be referred to as the boundary line of this fundamental curve/this regular curve with the distance of fundamental curve/regular curve for ± two curves of e.

The inventor finds that discrete geometry has following eight essential characteristics.

1, discrete geometric first essential characteristic

In discrete geometry, the direction of motion of coordinate axis is affined, and for example, x axle, y axle can only be made discrete rectilinear motion forward or backwards.Because direction of motion is restrained, isotropy has been lost in the space.Therefore, in discrete geometry, the space no longer is an Euclidean space.The euclidean geometry structure of curve and the discrete geometry of curve are inconsistent.

The directivity in space is the non-europeanized of space.This is discrete geometric first essential characteristic.

2, discrete geometric second essential characteristic

Because there is the direction of motion of 8 permissions such as x axle independently moving, y axle independently moving and x axle, the interlock of y axle in the x-y coordinate setting table, thereby destroyed the uniqueness that the microcosmic numeral of curve is videoed.

The nonuniqueness of the microcosmic numeral reflection of curve, this is discrete geometric second essential characteristic.

3, discrete geometric the 3rd essential characteristic

In the microcosmic numeral reflection of curve, the universal driving shaft data stream is the function of main drive shaft data stream.

For straight line, its universal driving shaft data stream is the period profile of main drive shaft data stream.In the one-period in the universal driving shaft data stream number of " 1 " only depend on the slope of this straight line.Therefore, the periodicity of universal driving shaft data stream is discrete geometric geometrical invariants.

In the microcosmic numeral reflection of straight line, the universal driving shaft data stream is the period profile of main drive shaft data stream, and the periodicity of universal driving shaft data stream is discrete geometric geometrical invariants, and this is discrete geometric the 3rd essential characteristic.

4, discrete geometric the 4th essential characteristic

Curve can disperse and be some discrete points, constitutes the microcosmic numeral reflection of curve; It is a line segment slightly that curve also can disperse, and the incremental numeral reflection that constitutes curve promptly approaches broken line.The former discrete geometric element is a discrete point, and the latter's discrete geometric element is little line segment.

Only there are two kinds of numeral reflections in curve, and promptly the microcosmic numeral is videoed and incremental numeral reflection, and this is discrete geometric the 4th essential characteristic.

5, discrete geometric the 5th essential characteristic

The directivity in space causes discretization error relevant with direction of motion.Thereby in the numeral reflection of curve, the symmetry that exists in the curve must be destroyed, and the numeral reflection of curve has produced Broken Symmetry.

The Broken Symmetry of numeral reflection, this is discrete geometric the 5th essential characteristic.

6, discrete geometric the 6th essential characteristic

In discrete coordinates system, the directivity in space causes the data stream of x axle, y axle asymmetric, has initiatively the difference with interlock.

Coordinate axis has active/interlock attribute, and this is discrete geometric the 6th essential characteristic.

8, discrete geometric the 7th essential characteristic

As everyone knows, in Euclidean space, because the isotropy in space, the geometry of each point on the circle is identical, and the L of circle is cut apart and point (x _i, y _i) irrelevant.Yet in discrete geometry, the directivity in space causes the L of circle to be cut apart and point (x _i, y _i) relevant, point (x _i, y _i) position on circle is different, its L is cut apart also different.

Therefore, for arbitrary curve, universal driving shaft y is at point (x _i, y _i) structure factor G _{I, y}Cut apart the discrete geometric attribute in the inherence of having described curve with intrinsic L.

Universal driving shaft y is at point (x _i, y _i) structure factor G _{I, y}Cutting apart with intrinsic L is the discrete geometric attribute of curve, and this is discrete geometric the 7th essential characteristic.

8, discrete geometric the 8th essential characteristic

Cut apart Δ L at the intrinsic L of curve _i(i=1 ..., n) in, for i arbitrarily, Δ L _iBe intrinsic length, the component Δ L of its universal driving shaft y _{I, y}Be equal to point (x _i, y _i) geometric factor G _{I, y}Thereby intrinsic L is cut apart Δ L _i(i=1 ..., n) cut apart for whole L of this curve and established the upper bound.Cut apart Δ L at the intrinsic L of curve _i(i=1 ..., n) in, the bar number of little line segment is minimum, the flex point of promptly approaching broken line is minimum.

The intrinsic L of curve is cut apart Δ L _i(i=1 ..., the upper bound of n) cutting apart for whole L of this curve, this is discrete geometric the 8th essential characteristic.

9, discrete geometric the 9th essential characteristic

In discrete geometry, any curve has only these two kinds numeral reflections of microcosmic numeral reflection and incremental numeral reflection, and corresponding discrete location information is discrete point or little line segment.The cutter track curve can only root a tree name discrete location information the displacement of synthetic corresponding coordinate axle be achieved.Thereby the cutter track curve is that the corresponding coordinate axial translation is synthesized the result that the back is produced.

For the narration for simplicity, suppose that mechanical system is the x-y coordinate setting table, wherein the x axle, the y axle can only the forwards/reverse displacement.For realizing that the cutter track curve must and need only constantly change the displacement of corresponding coordinate axle.Vice versa.

Therefore, the displacement that changes the corresponding coordinate axle is a sufficient and necessary condition of realizing the cutter track curve, and this is discrete geometric the 9th essential characteristic.

Above-mentioned nine essential characteristics have been established discrete geometric basis.

The core missions of computerized numerical system are, with the digital control information decompress(ion) that is compressed in cutter track curve and the speed of feed, make the digital control information of cutter track curve, and the L that just makes the cutter track curve is cut apart with T and cut apart.

Said L is cut apart the displacement information linkage desired with it that comprises relevant coordinate axis, is used to control relevant coordinate axis interlock to produce desired resultant displacement.

The disperse basic problem of geometric programming (CADGP) of area of computer aided is for given discretization error e and optimization aim, to confirm that the intrinsic L of cutter track curve is cut apart.

Curve is different by discrete method, and then the distribution of universal driving shaft data stream is different, and the intrinsic L of curve is cut apart also different.

Because the microcosmic of curve numeral reflection is not unique, thereby can cut apart according to the intrinsic L that different optimization aim selects discrete method to generate this curve.

The discrete method of curve depends on user's technological requirement.

For example, process velocity is most important during roughing, thereby if direction of motion all is preferential direction of motion, during resulting intrinsic L was cut apart, total distance was the shortest, and this intrinsic L is divided into short distance.

Machining precision is most important during finishing, thereby, if intrinsic L cut apart in the discretization error of each reflection all minimum, this intrinsic L is divided into minimum deflection.

Cooperation between the part is very big to the dynamic property influence of mechanical system.During resulting intrinsic L is cut apart, if the distribution of the discretization error of each reflection in the regular curve tolerance range is relatively consistent, its registration property be an optimum, and this intrinsic L is divided into good cooperation.

Prior art is regarded as the curve in the Euclidean space with the cutter track curve, according to the mathematic(al) representation of curve, adopts equidistant straight line, supervisor section straight line, equal error straight line to come the L of curve construction to cut apart.Yet because the direction of motion of coordinate axis is restrained, isotropy has been lost in the space, no longer is Euclidean space, has produced Broken Symmetry.Secondly, in the prior art, adopt the digital increments method to carry out the interpolation iteration control, because the restriction of interpolation cycle, many optimized Algorithm are difficult to adopt.Prior art is based on Euclidean space, thus resulting L to cut apart inevitable be not optimum.

The present invention is based on the discrete geometry of curve, cut apart, eliminated the non-europeanized error of cutter track curve through the intrinsic L of guiding point pointwise curve construction.According to distance is the shortest, discretization error is minimum, cooperate the most excellent optimization aim, said guiding point reaches the intrinsic reflection of said curve, generates the intrinsic L that meets said optimization aim and cuts apart.On the other hand, it is the upper bound that its whole L are cut apart that the intrinsic L of curve is cut apart, thereby in the intrinsic L of curve was cut apart, the bar number of little line segment was minimum, and promptly the flex point cut apart of intrinsic L is minimum.Said intrinsic L is cut apart and is satisfied said optimization aim, and has eliminated the non-europeanized error of cutter track curve, therefore, the invention solves the optimization problem of discrete location information.

Say the geometrograph under the similar area of computer aided of process that this discrete geometry based on curve is cut apart through guiding point pointwise structure intrinsic L visually.

Clearer for the purpose, technical characterictic and the implementation result that make present embodiment, be without loss of generality, be example with two motions, be described in detail in conjunction with accompanying drawing and specific embodiment technical scheme CADGP.

Embodiment one

As shown in Figure 2 a kind of CADGP system comprises hardware platform, software platform and application software system, and its hardware platform is general PC system, and software platform is a graphical interfaces operating system.

Software platform also comprises 3 d graphic library, for example OpenGL.

OpenGL is the abbreviation of Open Graphics Library, is the 3 d graphic library that a cover is independent of operating system and hardware environment, powerful graphing capability and good cross-platform transfer ability is arranged, the graphics standard on having come true.OpenGL is widely used in numerous areas such as Computer Simulation, visualization technique, solid modelling, CAD/CAM/CAE.By means of powerful three-dimensional artificial ability and the good man computer interface of OpenGL in the PC system; The CADGP method is given the method for interface between discrete digital information, the process of making discrete digital information, the manufacturing discrete digital information process and manufacturing discrete digital information visual with good, open man-machine interface; CADGP method thereby be open is for the software implementation of digital control technology has been established solid foundation.

Said application software system comprises that discrete coordinates is that planning module, cutter track curve planning module, L are cut apart planning module.

Said application software system is based upon on the middleware, adopts API API between said each module.

Said discrete coordinates is that planning module is used for according to the discrete scale of setting, uses distance as the equal space line of discrete scale with the coordinate plane gridding, set up discrete coordinates and be;

Said cutter track curve planning module is used for the planning cutter track curve in discrete coordinates system, is k bar curve according to unique point with the cutter track curve segmentation, and every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file;

Said L is cut apart planning module and is used for every curve to said k bar curve, and according to the optimization aim of setting, the intrinsic L that meets said optimization aim through guiding point pointwise structure is cut apart.

On planing method, according to discrete geometric ultimate principle, on OpenGL, set up the quadrature discrete coordinate system, distance is that the equal space line of discrete scale is with the coordinate plane gridding; In the quadrature discrete coordinate system, generate the cutter track curve; After the user selects optimization aim according to technological requirement, for each reflection on every curve in the cutter track curve, according to its neighborhood of optimization aim pointwise structure of setting; The intrinsic L that need only just generate this curve through the directly perceived simple visualized operation step that shows click is cut apart.

As shown in Figure 3, the step of the discrete geometric programming method CADGP of said area of computer aided is following.

1, discrete coordinates is planning step S1

Said discrete coordinates is that planning step S1 is used for according to the discrete scale of setting, uses distance as the equal space line of discrete scale with the coordinate plane gridding, set up discrete coordinates and be.

System ejects the coordinate system page, and the user is through clicking " quadrature discrete coordinate system " window, and discrete coordinates is that planning step is set up the quadrature discrete coordinate system.The quadrature discrete coordinate system page is provided with " systematic parameter " window; Click " systematic parameter " window, eject " discrete scale " subitem; In the drop-down table of " discrete scale " subitem, be provided with discrete scale for each coordinate axis, the user confirms the discrete scale of quadrature discrete coordinate system according to design demand, for example, for the rectilinear coordinates axle, discrete scale is 0.01mm, 1 μ m, 1nm etc.; For rotatable coordinate axis, discrete scale is 1 degree (1 °), 1 minute (1 ') etc.

2, cutter track curve planning step S2

Said cutter track curve planning step S2 is used for the planning cutter track curve in discrete coordinates system, is k bar curve according to unique point with the cutter track curve segmentation, and every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file.

Step S201, the fundamental curve of drafting workpiece profile in the quadrature discrete coordinate system.

The user can select for use the fundamental curve of system's setting like " straight line ", " circular arc ", " nurbs curve ", " helix ", " para-curve ", " ellipse ", or creates user's oneself new curve through " creating new curve ".According to the Element Design requirement, set up the fundamental curve of parts profile.The basic size of contour curve is set, and for example, for straight line, basic size is the basic size of straight line terminal point coordinate value; For circular arc, basic size is the basic size of circular arc starting point coordinate value, the basic size of circular arc terminal point coordinate value, the basic size of central coordinate of circle value.According to said prompting, the user can import the basic size of this curve, the upper deviation, the lower deviation of input basic size.

Step S202 generates regular curve.

System can be converted into regular curve with fundamental curve; Perhaps regular curve is converted into fundamental curve.

For all curves in the workpiece profile, implement above step, workpiece profile curve in the quadrature discrete coordinate system under the generation fundamental curve pattern or the workpiece profile curve under the regular curve pattern.

Step S203, cutter compensation.

After the workpiece profile curve of fundamental curve pattern/regular curve pattern generates, in said quadrature discrete coordinate system, eject " cutter compensation " window;

In the drop-down table of said " cutter compensation " window, be provided with the options relevant such as " tool radius ", " tool length ", " transition arc radius " with processing technology; The user imports respective value;

" confirming " clicked in the input back that finishes, and the workpiece profile curve of fundamental curve pattern/regular curve pattern is carried out cutter compensation, generation cutter track curve.

Step S204, carry out the cutter track path planning according to processing technology.

Requirement according to processing technology; The user provides the information such as terminal point coordinate in the terminal point coordinate in true origin, fast feed path, the number order of confirming each segment of curve on the cutter track curve, fast return path; System be provided with " true origin ", " fast feed path ", " machining path 1 ", " machining path 2 " ..., " machining path n ", " fast return path " etc.; Carry out the cutter track path planning; Confirm the processing sequence of cutter track curve, every curve in the cutter track curve is provided with suitable speed of feed.

Step S205, according to unique point, be k bar curve with the cutter track curve segmentation, every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file.

3, L is cut apart planning step S3

Said L is cut apart planning step S3 and is used for every curve to said k bar curve, and according to the optimization aim of setting, the intrinsic L that meets said optimization aim through guiding point pointwise structure is cut apart.

The microcosmic numeral reflection of cutter track curve has disclosed the discrete geometry of curve, cuts apart the analysis tool that provides strong for the L of formation curve.

For the k bar cutter track curve after cutting apart, L is cut apart the intrinsic L that planning step S3 obtains every curve and is cut apart.

For a curve on the cutter track curve; One section circular arc for example; Origination data with this circular arc is original guiding point, according to the optimization aim of setting (for example, discretization error minimum or distance are the shortest); Confirm that in original guiding neighborhood of a point a reflection as a guiding point, generates the coordinate figure increment of this guiding point and original guiding point; Generating should guiding neighborhood of a point, in this neighborhood, confirms next guiding point, and regeneration should next one guiding point and the coordinate figure increment of original guiding point; In case reach the intrinsic reflection, this intrinsic reflection is the terminal point of the little line segment of article one, and this intrinsic reflection is exactly the coordinate figure increment of the little line segment of article one of this circular arc with the coordinate figure increment of original guiding point; With the original guiding point of this intrinsic reflection as the little line segment of next bar, generate the coordinate figure increment of the little line segment of second of this circular arc then, until the terminal point of this circular arc, thereby the intrinsic L that obtains meeting said optimization aim is cut apart.

Need in said process to judge whether each guiding point is the intrinsic reflection.The method of judging is: behind the coordinate figure increment that generates i+1 guiding point and said original guiding point, between said i+1 guiding point and said original guiding point, generate the straight line section by the cutter track orientation; For the segment of curve of said curve between said i+1 guiding point and said original guiding point, judge whether this straight-line segment is little line segment of said segment of curve, if then continue to generate next guiding point; If not, then i guiding point is the intrinsic reflection.

The concrete steps that L is cut apart planning step 3 are:

Step (S301), from said k bar curve, take out a curve in turn, set optimization aim;

Step (S302), be original guiding point, generate said original guiding neighborhood of a point with the starting point of said curve;

Step (S303), according to the optimization aim of setting, in said original guiding neighborhood of a point, confirm a guiding point, generate the coordinate figure increment of said guiding point and said original guiding point;

Step (S304), between said guiding point and said original guiding point, generate the straight line section;

Step (S305), for the segment of curve of said curve between said guiding point and said original guiding point, judge whether said straight-line segment is little line segment of said segment of curve;

Step (S306) is then returned step (S303) if said straight-line segment is little line segment of said segment of curve, continues to generate next guiding point;

Step (S307) is not if said straight-line segment is little line segment of said segment of curve; Then a last guiding point of said guiding point is exactly the intrinsic reflection; Said intrinsic reflection is the terminal point of said little line segment, and the coordinate figure increment of a said last guiding point and said original guiding point is exactly the coordinate figure increment of said little line segment;

Step (S308), with the original guiding point of said intrinsic reflection as the little line segment of next bar; Order repeating step (S301) is to step (S307); Generate the little line segment of next bar of said curve, until the terminal point of said curve, the intrinsic L that meets said optimization aim that generates said curve is cut apart.

For all curves in the said k bar curve, repeating step (S301) is to step (S308), and the intrinsic L that meets said optimization aim that generates said cutter track curve is cut apart.

In said step (S305); Judge that prior art need be calculated the maximum normal direction distance between said straight-line segment and the said segment of curve and judge whether said maximum normal direction distance is less than or equal to discretization error when whether said straight-line segment was the little line segment of said segment of curve.Yet prior art is regarded as the Euclidean curve with said segment of curve, thereby produces non-Europe error.

Because all guiding neighborhoods of a point constitute the neighborhood of said segment of curve, so on the cutter track orientation, if the neighborhood of said straight-line segment is the subclass of the neighborhood of said segment of curve, said straight-line segment then is little line segment of said segment of curve.

The present invention is based on the discrete geometry of curve, judge that through the neighborhood of more said straight-line segment and the neighborhood of said segment of curve whether said straight-line segment is little line segment of said segment of curve, has eliminated non-Europe error.

In the application operating, need only click " incremental numeral reflection " window, then obtain the incremental associated data stream of this curve.

The optimization aim that sets can be chosen as: " distance is the shortest ", " discretization error is minimum ", " cooperating optimum " etc.; In said optimization aim, click definite optimization aim through window.

In parts profile, straight line accounts for more than 70% greatly.During processing linear, generally need with straight line be divided into accelerating sections, at the uniform velocity the section and braking section.In interpolation iteration control method, for the at the uniform velocity section of straight line, must be according to formula Δ L _i=FT is further discrete some the little line segment Δ L that are referred to as the profile step-length that are of section at the uniform velocity _i, expended a large amount of computational resources thus, significantly reduced process velocity and crudy.For the at the uniform velocity section of straight line, the present invention need not further disperse and be some little line segment Δ L _i

Embodiment two

Generally all orthogonal coordinate system in mechanical system.So-called orthogonal coordinate system is the mutually perpendicular coordinate system of coordinate axis, for example, and rectangular coordinate system, polar coordinate system etc.High-accuracy processing requires very high to the verticality between the coordinate axis, the depth of parallelism.In the Installation and Debugging process of lathe; Testing tools such as usage level appearance, standard square chi, leveling ruler, parallel light tube; Move each coordinate axis, the relevant adjustment component of adjustment reaches designing requirement with geometric accuracies such as the verticality between the assurance coordinate axis, the depth of parallelisms repeatedly.This needs high-accuracy adjustment component and high-accuracy adjustment instrument and abundant adjustment experience and perfect technical scheme.The data stream association control method is no longer regarded geometric accuracies such as verticality, the depth of parallelism as the error of mechanical system, but the same as the stroke of coordinate axis, is regarded as the systematic parameter of coordinate system.Therefore, the data stream association control method adopts non-orthogonal coordinate system to eliminate geometric errors such as non-perpendicularity, nonparallelism.

So-called non-orthogonal coordinate system is exactly the mutual off plumb coordinate system of coordinate axis.

The discrete scale of maintenance coordinate system is constant, orthogonal coordinate axis and coordinate line in the quadrature discrete coordinate system is obtained nonopiate discrete coordinates by the non-perpendicularity distortion be.

CADGP method in the nonopiate discrete coordinates system is with embodiment one difference, and step 1 is set up in the discrete coordinates system, and discrete coordinates is that generation module is set up nonopiate discrete coordinates system.In nonopiate discrete coordinates is, subwindows such as " discrete scale ", " non-perpendicularity " can be set, wherein " non-perpendicularity " subwindow is used for the non-perpendicularity of user's input coordinate axle.

What need further specify is, modern CAD/CAM/CAPP system has been widely used in numerical control programming, is used to accomplish the planning of cutter track curve, even further accomplishes rough interpolation, just is little line segment Δ L with the cutter track curve is discrete _i, generate about said little line segment Δ L _iThe G code numerical control program send digital control system to and carry out smart interpolation.Therefore, also there are little line segment Δ L in CAD/CAM/CAPP system and other NC Programming System _iOptimization problem.Obviously, the present invention is applicable to CAD/CAM/CAPP system and other NC Programming System fully.

Above content is the further explain that combines concrete preferred implementation that the discrete geometric programming method of area of computer aided is done.The present invention is an example with two motions, and the technical scheme of implementing the discrete geometric programming method and system of area of computer aided has been described, can not assert that practical implementation of the present invention is confined to these explanations.Those of ordinary skill for technical field under the present invention; Under the prerequisite that does not break away from the present invention's design; Can also make the discrete geometric programming method of area of computer aided that some simple deduction or replace are used to make up three and even multiaxial motion, all should be regarded as belonging to protection scope of the present invention.

Claims (8)

1. the discrete geometric programming method of an area of computer aided is used to plan that the intrinsic L of cutter track curve cuts apart, and it is characterized in that, may further comprise the steps:

Discrete coordinates is planning step (S1): according to the discrete scale of setting, uses distance as the equal space line of discrete scale with the coordinate plane gridding, set up discrete coordinates and be;

Cutter track curve planning step (S2): planning cutter track curve in discrete coordinates system is k bar curve according to unique point with the cutter track curve segmentation, and every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file;

L is cut apart planning step (S3): to every curve in the said k bar curve, according to the optimization aim of setting, the intrinsic L that meets said optimization aim through guiding point pointwise structure is cut apart,

Said step (S3) may further comprise the steps:

Step (S301), from said k bar curve, take out a curve in turn, set optimization aim;

Step (S302), be original guiding point, generate said original guiding neighborhood of a point with the starting point of said curve;

Step (S303), according to the optimization aim of setting, in said original guiding neighborhood of a point, confirm a guiding point, generate the coordinate figure increment of said guiding point and said original guiding point;

Step (S304), between said guiding point and said original guiding point, generate the straight line section;

Step (S305), for the segment of curve of said curve between said guiding point and said original guiding point, judge whether said straight-line segment is little line segment of said segment of curve;

Step (S306) is then returned step (S303) if said straight-line segment is little line segment of said segment of curve, continues to generate next guiding point;

Step (S307) is not if said straight-line segment is little line segment of said segment of curve; Then a last guiding point of said guiding point is exactly the intrinsic reflection; Said intrinsic reflection is the terminal point of said little line segment, and the coordinate figure increment of a said last guiding point and said original guiding point is exactly the coordinate figure increment of said little line segment;

Step (S308), with the original guiding point of said intrinsic reflection as the little line segment of next bar; Order repeating step (S301) is to step (S307); Generate the little line segment of next bar of said curve, until the terminal point of said curve, the intrinsic L that meets said optimization aim that generates said curve is cut apart.

2. the area of computer aided as claimed in claim 1 geometric programming method that disperses; It is characterized in that: in the said step (S2), the tolerance according to the workpiece profile size is adjusted into regular curve with fundamental curve; Regular curve is revised, generated the cutter track curve of regular curve.

3. the area of computer aided as claimed in claim 2 geometric programming method that disperses, it is characterized in that: said step (S305) also comprises the steps:

Step (S3051), on the cutter track orientation, generate the neighborhood of said straight-line segment;

Step (S3052), judge whether the neighborhood of said straight-line segment is the subclass of the neighborhood of said segment of curve.

4. the area of computer aided as claimed in claim 3 geometric programming method that disperses, it is characterized in that: the optimization aim in the said step (S301) is that distance is the shortest, each coordinate axis is all pressed preferential direction of motion feeding in the said coordinate axis.

5. the area of computer aided as claimed in claim 3 geometric programming method that disperses is characterized in that: the optimization aim in the said step (S301) is that discretization error is minimum, and the discretization error of each guiding point was minimum during said intrinsic L was cut apart.

6. the area of computer aided as claimed in claim 3 geometric programming method that disperses; It is characterized in that: the optimization aim in the said step (S301) is optimum for cooperating, and the distribution of the discretization error of each guiding point in the regular curve tolerance range was consistent during said intrinsic L was cut apart.

7. like the discrete geometric programming method of any described area of computer aided in the claim 1～6, it is characterized in that: said coordinate axis is more than three.

8. the area of computer aided as claimed in claim 7 geometric programming method that disperses is characterized in that: said discrete coordinates system is nonopiate discrete coordinates system.

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