CN108803481B - Free form surface ball-end mill paths planning method and system based on Fermat helix - Google Patents
Free form surface ball-end mill paths planning method and system based on Fermat helix Download PDFInfo
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- CN108803481B CN108803481B CN201810853512.0A CN201810853512A CN108803481B CN 108803481 B CN108803481 B CN 108803481B CN 201810853512 A CN201810853512 A CN 201810853512A CN 108803481 B CN108803481 B CN 108803481B
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/35—Nc in input of data, input till input file format
- G05B2219/35349—Display part, programmed locus and tool path, traject, dynamic locus
Abstract
The invention discloses a kind of free form surface ball-end mill paths planning methods and system based on Fermat helix, the described method comprises the following steps: the free form surface of connection is received, is calculated apart from scalar field, it is described to meet uniform residual altitude constraint apart from scalar field；The isopleth in scalar field is extracted, connection Fermat helix is generated；Under the constraint of maximum residual altitude, the connection Fermat helix of generation is smoothed.The present invention is based on Fermat helixes to generate the ball head knife finishing track that successive and smooth, zone boundary is related, residual altitude is evenly distributed, processing efficiency can be obviously improved under the premise of meeting processing quality for the free form surface of arbitrary topology connection.
Description
Technical field
The present invention relates to milling machine finishing track planning technology fields, and in particular to a kind of freedom based on Fermat helix
Curved surface ball-end mill paths planning method and system, are applied to Milling Motion in Three-axes NC or Five-axis numerical control milling machine 3+2 operating mode adds
Work free form surface.
Background technique
Milling machine be in numerical control processing (Numerical Control Machining) it is a kind of with milling cutter to a variety of surfaces of workpiece
The lathe processed, the curved surface for being suitble to processing more complicated.Processing flow is usually roughing, finishing and back chipping.
Roughing generally uses large scale milling cutter head, and quickly removal is largely not belonging to the boule portions of target shape,
Obtain the approximate shapes of target component；The approximate shapes are actually an approximate iso-metric offset face of target component.Finishing
With the milling cutter head of smaller size, the clout that target workpiece is not belonging in approximate shapes is removed.Due to finishing tip size and
This body structure of parts to be machined limitation, undressed part may be still left after finishing, need to the clean-up machining stage carry out into
The cleaning of one step.
Most common milling machine includes: the three-head milling machine for being generally used for processing flat surface impression structure and height field free curved surface,
Five axis milling machines of processable complex free curved surface.Five axis milling machines can be divided into 3+2 operating mode and 5 axis linkage work according to the course of work
Operation mode.Wherein the operating mode of 3+2 refers to that cutter takes dead axle to process during processing a certain panel region, milling process
In only three shifting axles linkage (also known as " dead axle processing "), other two rotation axis is motionless.Five-axle linkage operating mode is
Referring to cutter, five kinematic axis move synchronously milling during the cutting process.
All there is tool-path planning in each stage of CNC milling machine process, wherein the knife in finishing passes
Tool planning is even more important, because finishing directly affects the quality on the surface of shaping workpiece, and when in whole process
Between accounting it is big.The present invention pays close attention to the tool-path planning problem in free form surface finishing passes, and finishing generallys use bulb
Knife processing, it is insensitive to machine direction to be primarily due to ball head knife, that is to say, that ball-end mill exists relative to the direction of free form surface
Arbitrarily change in a certain range, does not influence it and cut range.Main target constraint: 1) machining path is successive；2) road is processed
Diameter is smooth, reduces zig zag；3) under the premise of meeting the maximum residual altitude that user specifies, residual altitude is uniform on free form surface
Distribution.Wherein, processing residual altitude refers to the height of remaining residue part after two adjacent cutter track cuttings.On free form surface etc.
The path of geodesic distance distribution can not generate equally distributed residual altitude.In order to obtain equally distributed residual altitude, from
Directional curvature de-regulation according to adjacent path corresponding point position is needed by the path separation on curved surface.
Classified with the different process of manufacturing process, numerical control processing belongs to " subtracting material manufacture ".Corresponding 3 D-printing
Belong to " increasing material manufacturing ", the path planning of 3 D-printing equally exists above-mentioned similar constraint.Application No. is
A kind of patent " 3D printing paths planning method based on your helix of Fermat " of CN201610242579.1, proposes that one kind is based on
The 3D printing paths planning method of Fermat helix (Fermat Spiral) can generate arbitrary topological connected region
There is the printing head path of continuous and smooth two kinds of characteristics simultaneously, significantly improve print quality and reduce the print time.But it should
The path planning algorithm of patent is on two-dimensional surface, and path separation is identical, and the path cooked up, which exists, processes hard turning, is added
Working medium amount has to be hoisted, and is unfavorable for cutting-tool's used life.
Summary of the invention
To overcome above-mentioned the deficiencies in the prior art, the present invention provides a kind of free form surface bulbs based on Fermat helix
Tool-path planning method and system can be calculated one continuously not for the free form surface region of one piece of topology connection
Disconnected and smooth, zone boundary is related, the ball head knife finishing track that residual altitude is evenly distributed.
To achieve the above object, the present invention adopts the following technical scheme:
A kind of free form surface ball-end mill paths planning method based on Fermat helix, comprising the following steps:
The free form surface of connection is received, is calculated apart from scalar field, it is described to meet uniform residual altitude constraint apart from scalar field；
The isopleth in scalar field is extracted, connection Fermat helix is generated；
Under the constraint of maximum residual altitude, the connection Fermat helix of generation is smoothed.
Further, the calculating is specifically included apart from scalar field:
Generate initial distance field；
According to the relevant more new field of initial distance field computation residual altitude；
By more new field as heterogeneous description, distance field is recalculated；
Judge whether the variable quantity between the distance field and the preceding distance field once calculated that recalculate meets certain threshold value,
If not satisfied, calculating more new field and distance field again.
Further, the relevant more new field of the calculating residual altitude specifically includes:
Multiple sampled points are extracted from initial distance field, and its gradient direction and directional curvature are calculated for each sampled point；
According to the directional curvature, preset residual altitude and cutter parameters, the cutter path at each sampled point is calculated
Spacing obtains more new field.
Further, the cutter path distance equation calculated at each sampled point is as follows:
Wherein, h is the maximum residual altitude of input, RcutterFor ball head knife tip radius, G (p, Π) is vertical by point p
In the directional curvature of path Π, g (p, Π) is surface sampling point p under maximum residual altitude h constraint, passes through cutter path Π's
Path separation.
Further, it is described will more new field as heterogeneous description, recalculate distance field and specifically include:
Wherein, A is the diagonal matrix for describing tri patch area, A-1LcDefine Laplacian Matrix, LcDescribe three
The diagonal matrix of angle mesh point syntople, δγFor the boundary condition of initial heat distribution.H and LcEqually and triangulation network lattice point
The diagonal matrix of syntople, H are the diagonal matrix for having merged more new field information, each single item H of H-matrixI, jTriangle is described
Grid Sampling point piAnd pjCritical message.If piAnd pjThere is no critical relation, HI, jIt is set as infinitely great；If piAnd pjIn the presence of
Critical relation, HI, jIt is set as point piAnd pjRespective path spacing g (pi, Π) and g (pj, Π) average value.It indicates to angular moment
Battle array LcIt is multiplied with H respective items.
Further, described to extract the isopleth in scalar field, it generates connection Fermat helix and specifically includes:
Isopleth is extracted from the relevant distance field of residual altitude；
Adjacent isopleth is connected using oblique line and generates connection Fermat helix.
Further, the connection Fermat helix of described pair of generation, which is smoothed, specifically includes:
Uniform sampling is carried out on connection free form surface；
Curvature choice of dynamical path sampled point based on connection Fermat helix everywhere；
Each surface sampling point is calculated to path sampled point distance, distance is obtained and is less than ideal path at the surface sampling point
The surface sampling point of spacing, is denoted as center of attraction point；
Update is iterated to path sampled point using Laplce's exponential smoothing.
Further, Laplce's exponential smoothing is as follows:
Wherein, TSmoothCurrent point x is describediWith its front and back consecutive points xi-1And xi+1Difference, TAttractionCenter of attraction point is describedTo path sampled pointAttraction force；
TRepulsionSampled point in adjacent path is described to the repulsion force of path sampled point；λ1, λ2, λ3For every weight, λ1+λ2+
λ3=1.0.
Second purpose according to the present invention, the present invention also provides a kind of free form surface ball head knifes based on Fermat helix
Have path planning system, including memory, processor and stores the computer journey that can be run on a memory and on a processor
Sequence, which is characterized in that the processor realizes the paths planning method when executing described program.
Third purpose according to the present invention, the present invention also provides a kind of computer readable storage mediums, are stored thereon with
Computer program executes the free form surface tool-path planning based on Fermat helix when the program is executed by processor
Method.
Beneficial effects of the present invention
1, path planning algorithm of the invention is on three-dimensional free surface, it is contemplated that the residual altitude point in machining
Cloth uniformly constrains, path separation be not it is equidistant, obtained path effectively reduces the hard turning quantity of processing, conducive to mentioning
Processing efficiency and quality are risen, conducive to the load balancing of cutter cutting process, extends cutter life；
2, path residual altitude of the present invention is evenly distributed, and is conducive to promote milling efficiency；
3, the present invention proposes Fermat helix being applied to three-dimension curved surface, and in Art Design field, there are application potentials.
Detailed description of the invention
The accompanying drawings constituting a part of this application is used to provide further understanding of the present application, and the application's shows
Meaning property embodiment and its explanation are not constituted an undue limitation on the present application for explaining the application.
Fig. 1 is that the present invention is based on the flow charts of the free form surface tool-path planning method of Fermat helix；
Fig. 2 is distance field schematic diagram, wherein Fig. 2 (a) is initial distance field, and Fig. 2 (b) is to calculate after being superimposed more new field
The distance field arrived；
Fig. 3 is residual altitude distribution map, wherein Fig. 3 (a) is the corresponding residual altitude distribution of initial distance field isopleth
Figure, Fig. 3 (b) are the residual altitude distribution map being superimposed after more new field；
Fig. 4 is connection Fermat helix structural map, wherein Fig. 4 (a) is the communication path generated using the prior art, Fig. 4
(b) communication path generated for the method for the present invention；
5 (a) -5 (f) be smoothing process figure in Fig. 5.
Specific embodiment
It is noted that described further below be all exemplary, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
In the absence of conflict, the features in the embodiments and the embodiments of the present application can be combined with each other.
A job related to the present invention, which is Keenan et al., to be applied to geodesic distance for heat transfer theory and leaves the theatre in solution,
By the solution to system of linear equations, can fast and stable solution grid, the geodesic distance on the various definitions domain such as point cloud leaves the theatre
(Keenan Crane, Clarisse Weischedel, and Max Wardetzky.2013a.Geodesics in Heat:
ANew Approach to Computing Distance Based on Heat Flow.ACM Trans.on Graph32,5
(2013), 152:1-152:11.).Keenan et al. uses a kind of homogeneous (homogeneous) heat field, that is, thinks to define
The speed of the propagation of all-pair heat is consistent in domain.It is evenly distributed for the residual altitude in free form surface path planning
Constraint when, heterogeneous (homogeneous) the heat field computation of proposed adoption one kind of the present invention in view of residual distribution distance field.
Embodiment one
Present embodiment discloses a kind of free form surface ball-end mill paths planning method based on Fermat helix, such as Fig. 1
It is shown, comprising the following steps:
(1) for given connection free form surface S, calculate one meet uniform residual altitude constraint apart from scalar field；
(2) isopleth in extraction step 1 in calculated scalar field generates connection Fermat helix；
(3) under the constraint of maximum residual altitude, the connection Fermat helix of generation is smoothed.
In the step (1), specific steps include:
(1-1) generates initial distance field with the method for Keenan et al., as shown in Fig. 2 (a)；
The relevant more new field of residual altitude is calculated in (1-2) from distance field；
More new field is added in field computation by (1-3) as heterogeneous description, recalculates distance field；
(1-4) iteration step (1-2) and (1-3) reach certain threshold requirement until distance field variable quantity；
Wherein, in the step (1-2), specific steps include:
(1-2-1) calculates the gradient direction of each sampled point p in initial distance field, and calculates its corresponding directional curvature G
(p, Π).
(1-2-2) brings following formula into and calculates cutter path spacing g (p, Π) at point p, obtains more new field.
Wherein, h is the maximum residual altitude of input, RcutterFor ball head knife tip radius, G (p, Π) is vertical by point p
In the directional curvature of path Π, g (p, Π) is surface sampling point p under maximum residual altitude h constraint, passes through cutter path Π's
Path separation.
In the step (1-3), specific steps include:
More new field is added in step 1 of the Keenan et al. by calorie spread method calculating distance field by (1-3-1):
Wherein, A is the diagonal matrix for describing tri patch area, A-1LcDefine Laplacian Matrix, LcDescribe three
The diagonal matrix of angle mesh point syntople, δγFor the boundary condition of initial heat distribution.H and LcEqually and triangulation network lattice point
The diagonal matrix of syntople, H are the diagonal matrix for having merged more new field information, each single item H of H-matrixI, jTriangle is described
Grid Sampling point piAnd pjCritical message.If piAnd pjThere is no critical relation, HI, jIt is set as infinitely great；If piAnd pjIn the presence of
Critical relation, HI, jIt is set as point piAnd pjRespective path spacing g (pi, Π) and g (pj, Π) average value.It indicates to angular moment
Battle array LcIt is multiplied with H respective items.
(1-3-2) recalculates the distance field after superposition more new field, as shown in Fig. 2 (b).As shown in figure 3, Fig. 3 (a) is
The corresponding residual altitude distribution map of initial distance field isopleth, Fig. 3 (b) are the residual altitude distribution map being superimposed after more new field.
In the step (2), specific steps include:
(2-1) extracts isopleth from the relevant distance field of residual altitude；
(2-2) generates connection Fermat helix using oblique line connection isopleth；As shown in figure 4, generating Fermat helix
It is to connect adjacent isopleth with " oblique line ", hard turning number can be effectively reduced, Fig. 4 (a) is directly to use patent
The communication path that CN201610242579.1 method generates, Fig. 4 (b) are the communication path that the method for the present invention generates.
Specifically, referring to patent CN201610242579.1, the method that connection Fermat helix is generated according to isopleth are as follows:
(2-2-1) constructs the spiral connected graph of sideband weight according to uniform isopleth；
(2-2-2) is spiral connection tree by the minimum spanning tree that spiral connected graph generates；
Spiral connection tree is decomposed into multiple independent Fermat helix subtrees and trunk node by (2-2-3)；
(2-2-4) connects the corresponding uniform isopleth of Fermat helix subtree and generates sub- Fermat helix；
The corresponding uniform isopleth of (2-2-5) connexon Fermat helix trunk node associated with it；
(2-2-6) is using the corresponding uniform isopleth of oblique line connection trunk node.
In the step (3), the connection Fermat helix of generation is carried out smoothly, specific steps include:
(3-1) uniform sampling on connection free form surface S
The curvature choice of dynamical path sampled point of (3-2) based on connection Fermat helix everywhere
(3-3) calculates sampled pointIn each point pi to path sampled pointDistance, distance are less than g (pi, Π)
Definition be center of attraction point, obtained center of attraction point is denoted asWherein, g (p, Π) is piBetween the ideal path at place
Away from.Such as Fig. 5, the stain in smoothing process figure is center of attraction point.
(3-4) is iterated update to sampled point path using the smooth mode of Laplce；
Wherein, TSmooth, TAttraction, TRepulsionThe respectively smooth item of Laplce's operation, gravitation item and repulsion item.
λ1, λ2, λ3For every weight, λ1+λ2+λ3=1.0.TSmoothCurrent point x is describediWith its front and back consecutive points xi-1And xi+1Difference,TAttractionCenter of attraction point is describedTo path sampled pointAttraction make
Firmly；TRepulsionSampled point in adjacent path is described to the repulsion force of path sampled point.
It is bigger in curvature based on connection Fermat helix curvature choice of dynamical sampled point everywhere in the step (3-2)
Local sampled point choose number it is more.
Embodiment two
The purpose of the present embodiment is to provide a kind of computing system.
A kind of free form surface ball-end mill path planning system based on Fermat helix, including memory, processor and
The computer program that can be run on a memory and on a processor is stored, the processor is realized following when executing described program
Step, comprising:
The free form surface of connection is received, is calculated apart from scalar field, it is described to meet uniform residual altitude constraint apart from scalar field；
The isopleth in scalar field is extracted, connection Fermat helix is generated；
Under the constraint of maximum residual altitude, the connection Fermat helix of generation is smoothed.
Embodiment three
The purpose of the present embodiment is to provide a kind of computer readable storage medium.
A kind of computer readable storage medium, is stored thereon with computer program, execution when which is executed by processor
Following steps:
The free form surface of connection is received, is calculated apart from scalar field, it is described to meet uniform residual altitude constraint apart from scalar field；
The isopleth in scalar field is extracted, connection Fermat helix is generated；
Under the constraint of maximum residual altitude, the connection Fermat helix of generation is smoothed.
Each step involved in above embodiments two and three is corresponding with embodiment of the method one, and specific embodiment can be found in
The related description part of embodiment one.Term " computer readable storage medium " is construed as including one or more instruction set
Single medium or multiple media；It should also be understood as including any medium, any medium can be stored, encodes or be held
It carries instruction set for being executed by processor and processor is made either to execute in the present invention method.
Beneficial effects of the present invention
1, path planning algorithm of the invention is on three-dimensional free surface, it is contemplated that the residual altitude point in machining
Cloth uniformly constrains, path separation be not it is equidistant, obtained path effectively reduces the hard turning quantity of processing, conducive to mentioning
Processing efficiency and quality are risen, conducive to the load balancing of cutter cutting process, extends cutter life；
2, path residual altitude of the present invention is evenly distributed, and is conducive to promote milling efficiency；
3, the present invention proposes Fermat helix being applied to three-dimension curved surface, and in Art Design field, there are application potentials.
It will be understood by those skilled in the art that each module or each step of aforementioned present invention can be filled with general computer
It sets to realize, optionally, they can be realized with the program code that computing device can perform, it is thus possible to which they are stored
Be performed by computing device in the storage device, perhaps they are fabricated to each integrated circuit modules or by they
In multiple modules or step be fabricated to single integrated circuit module to realize.The present invention is not limited to any specific hardware and
The combination of software.
The foregoing is merely preferred embodiment of the present application, are not intended to limit this application, for the skill of this field
For art personnel, various changes and changes are possible in this application.Within the spirit and principles of this application, made any to repair
Change, equivalent replacement, improvement etc., should be included within the scope of protection of this application.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention
The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not
Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.
Claims (3)
1. a kind of free form surface ball-end mill paths planning method based on Fermat helix, which is characterized in that including following step
It is rapid:
The free form surface of connection is received, is calculated apart from scalar field, it is described to meet uniform residual altitude constraint apart from scalar field；
The isopleth in scalar field is extracted, connection Fermat helix is generated；
Under the constraint of maximum residual altitude, the connection Fermat helix of generation is smoothed；
The calculating is specifically included apart from scalar field:
Generate initial distance field；
According to the relevant more new field of initial distance field computation residual altitude；
By more new field as heterogeneous description, distance field is recalculated；
Judge whether the variable quantity between the distance field and the preceding distance field once calculated that recalculate meets certain threshold value, if not
Meet, calculates more new field and distance field again；
The relevant more new field of the calculating residual altitude specifically includes:
Multiple sampled points are extracted from initial distance field, and its gradient direction and directional curvature are calculated for each sampled point；
According to the directional curvature, preset residual altitude and cutter parameters, the cutter path spacing at each sampled point is calculated,
Obtain more new field；
The cutter path distance equation calculated at each sampled point is as follows:
Wherein, h is the maximum residual altitude of input, RcutterFor ball head knife tip radius, G (p, Π) is by point p perpendicular to road
The directional curvature of diameter Π, g (p, Π) are surface sampling point p under maximum residual altitude h constraint, pass through the path of cutter path Π
Spacing；
It is described will more new field as heterogeneous description, recalculate distance field and specifically include:
Wherein, A is the diagonal matrix for describing tri patch area, A-1LcDefine Laplacian Matrix, LcDescribe triangle gridding
The diagonal matrix of point syntople, δγFor initial heat distribution, H has merged more new field information, and specific method is for LcIt is every
The average value of one path separation g (p, Π) multiplied by Grid Edge vertex correspondence；
It is described to extract the isopleth in scalar field, it generates connection Fermat helix and specifically includes:
Isopleth is extracted from the relevant distance field of residual altitude；
Adjacent isopleth is connected using oblique line and generates connection Fermat helix；
The connection Fermat helix of described pair of generation, which is smoothed, to be specifically included:
Uniform sampling is carried out on connection free form surface；
Curvature choice of dynamical path sampled point based on connection Fermat helix everywhere；
Each surface sampling point is calculated to path sampled point distance, distance is obtained less than surface sampling point processing and thinks path separation
Surface sampling point, be denoted as center of attraction point；
Update is iterated to path sampled point using Laplce's exponential smoothing；
Laplce's exponential smoothing is as follows:
Wherein, TSmoothCurrent point x is describediWith its front and back consecutive points xi-1And xi+1Difference, TAttractionCenter of attraction point is describedTo path sampled pointAttraction force；
TRepulsionSampled point in adjacent path is described to the repulsion force of path sampled point；λ1, λ2, λ3For every weight, λ1+λ2+
λ3=1.0.
2. a kind of free form surface ball-end mill path planning system based on Fermat helix, including memory, processor and deposit
Store up the computer program that can be run on a memory and on a processor, which is characterized in that the processor executes described program
Shi Shixian paths planning method as described in claim 1.
3. a kind of computer readable storage medium, is stored thereon with computer program, which is characterized in that the program is held by processor
The free form surface ball-end mill paths planning method based on Fermat helix as described in claim 1 is executed when row.
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| CN112363455B (en) * | 2020-11-02 | 2021-09-24 | 中国科学院数学与系统科学研究院 | Tool path determination method and system based on dynamics constraint |
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| CN105711102A (en) * | 2016-04-19 | 2016-06-29 | 山东大学 | 3D printing path programming method based on Fermat spiral |
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| DE102009019443A1 (en) * | 2009-04-29 | 2010-12-16 | Siemens Aktiengesellschaft | Kinematic approximation algorithm with ruled surface |
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| CN101109944A (en) * | 2007-08-23 | 2008-01-23 | 上海交通大学 | Method for planning smooth and non-interference tool route of 5-axis numerical control machining |
| CN105711102A (en) * | 2016-04-19 | 2016-06-29 | 山东大学 | 3D printing path programming method based on Fermat spiral |
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