CN106774154B - A kind of space curve interpolating method based on osculating plane theory - Google Patents
A kind of space curve interpolating method based on osculating plane theory Download PDFInfo
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- CN106774154B CN106774154B CN201611258996.1A CN201611258996A CN106774154B CN 106774154 B CN106774154 B CN 106774154B CN 201611258996 A CN201611258996 A CN 201611258996A CN 106774154 B CN106774154 B CN 106774154B
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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
- G05B19/404—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 control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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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
- G05B2219/35408—Calculate new position data from actual data to compensate for contour error
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Abstract
The invention belongs to Computerized Numerical Control processing technology fields, it is proposed that a kind of space curve interpolating method based on osculating plane theory is mainly used for tool-path planning operation in Multi-axis Machining.According to the local geometric shape on space curve at interpolated point, the interpolated point of the high error of the bow such as equidistant surface construction satisfaction is utilized on the principal normal direction from section of each interpolated point.But the high error of bow of the high error of bow that this side up not necessarily truly, establishes apart from meaning followed by analytic geometry midpoint to straight line and bends high error functionThe high error of most longbow calculated between two adjacent discrete points is verified.Cutting step can adaptively be adjusted using new method, realize the high error of bow truly, be evenly distributed respectively approaching the high error of the bow in straightway, high precision machining, surface quality is good.
Description
Technical field：
The invention belongs to Computerized Numerical Control processing technology field more particularly to a kind of space curve interpolation sides based on osculating plane theory
Method is mainly used for tool-path planning operation in Machining of Curved Surface.
Background technology：
In the process industries such as aviation, aerospace industry, automobile and mold, there is largely have complex-curved part,
These parts not only complex geometry, and the accuracy of manufacture and surface quality requirements are very high.With computer technology and certainly
The development of dynamic control technology, has application of the complex-curved part in industrial products more and more extensive.Currently, complex-curved
The processing of part is mostly realized by numerically-controlled machine tool.Tool-path planning is the important composition of design for NC
Part, designing quality directly affect the machining accuracy and processing efficiency of part.The cutter path of Machining of Curved Surface is by one
Cutter-contact point trace curve composition, from geometrically saying, each cutter-contact point trace curve is essentially all a space curve, because
This tool-path planning is converted to the interpolated point computational problem of a rule space curve.Different interpolation point calculating methods are with regard to shape
At different interpolating methods.
Currently, the wider interpolation point calculating method of application range mainly has equal parameter step lengths method, equidistant step length, step-length
Screening method etc..
Equal parameter step lengths method and equidistant step length are divided to parameter and curve equidistant, although both methods is simple,
However in order to enable the approximate error of every section of straight line is met the requirements, step-length or parameter increase can only be selected using adverse conditions the most
It takes, to cause remaining processing sequences huge, the actual high error of bow is unevenly distributed.
Based on step-length screening method uses equal steps, smaller equidistance or parameter discrete cutter rail are used before this
Then mark checks the practical approximate error of every section of straight line, finally need to delete extra discrete point, so that remaining trajectory error
More uniformly.The shortcomings that parameter step lengths methods such as although step-length screening method overcomes and equidistant step length, but checking every section directly
All it is approximately to bend high error when the high error of bow in line, to influence the surface quality of curved surface, reduces the processing essence of workpiece
Degree.
Invention content：
In order to solve the problems, such as that conventional method exists in terms of Multi-axis Machining tool-path planning step size computation, the present invention carries
A kind of space curve interpolating method of the satisfaction bow high franchise theoretical based on osculating plane is gone out.It can be according to P on space curve0Point
The local geometric shape at place, is adaptively adjusted cutting step, and the practical bow in every section of straight line is calculated using high error function is bent
High error so that be evenly distributed respectively approaching the high error of the bow in straightway, high precision machining, surface quality is good.
According to the relevant knowledge of Differential Geometry, at any on space curve, three orthogonal tangent lines, principal normals
The fundamental three-vector form that curve is constituted with binormal, is generated the osculating plane of this point by them, normal plane and from section.?
In these three planes, the plane that osculating plane is " most close to curve " was tangent line and perpendicular to osculating plane from section.It is based on
This conclusion, the high error requirements of the bow such as satisfaction obtain discrete interpolated point on the principal normal direction from section, due at each point
Bent curvature of a curve and torsion difference, the high error of the bow of error not necessarily truly at this time, so also needing to utilize
Bend the high error of most longbow that high error function calculates between two-phase neighbor interpolation point to be verified.
According to being described above, it includes following step to bend the space curve interpolating method of high franchise based on the theoretical satisfaction of osculating plane
Suddenly：
Step (1) assumes parametric equation r=r (t)={ x (t), y (t), z (t) } t ∈ [a, b] of a space curve Γ,
When interpolation starts, the 0th interpolated point P0Parameter be t0=a, bends high franchise ε, and the high franchise size of bow influences free curve
Surface quality and machining accuracy, it is better to bend the smaller surface quality of high franchise, and the high franchise of bow is by manufacturer according to being processed
Surface set, be known quantity；
Step (2) is in P0At point, r (t are calculated0),r′(t0),r″(t0), acquire equation the r " (t from section π0)·[ρ-r
(t0)]=0, ρ be from section any point vector, on principal normal direction with bend high franchise ε be distance construction from section π's
Equidistant surface π1；
Step (3) simultaneous equidistant surface π1The equation of equation and space curve Γ solves equidistant surface π1With the friendship of space curve Γ
The parameter t of point1；
Step (4) calculates t0And t1Two corresponding interpolated point P0And P1Between the high error max δ of most longbow.Solve most longbow
High error has mid-point method, dichotomy and Fibonacci method, but is not the high error of most longbow truly, error degree ratio
Higher, the present invention establishes P by using the knowledge of the distance at analytic geometry midpoint to straight line0And P1Any point between 2 points
The high error function of bowThe method being most worth is asked to acquire max δ using function；
Step (5) is if max δ<ε, then P1As next interpolated point, satisfaction bow Gao Yun is otherwise found using line search method
The point that difference requires is as next interpolated point；
Step (6) return to step (2)；Until the operation of a space curve terminates.
Description of the drawings
Fig. 1 is equidistant surface schematic diagram.
Fig. 2 is flow chart of the method for the present invention.
Fig. 3 is the interpolated point schematic diagram of space curve Γ.
Fig. 4 is the high error curve diagram of most longbow between space curve Γ interpolated points.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, below in conjunction with attached drawing 1-4 and embodiment
The present invention is further described in detail in son.Specific embodiment described herein is only used for explaining the present invention, not
For limiting the present invention.
1. assuming that the parametric equation of a space curve Γ is r=r (t)={ t, t2,t3T ∈ [0,100], the 0th interpolation
Point P0Parameter be t0=0, bend high franchise ε=0.001.
2. in P0At point, r (t are calculated0),r′(t0),r″(t0),
Then r (t0)={ t0,t0 2,t0 3, r, ' (t0)={ 1,2t0,3t0 2, r " (t0)={ 0,2,6t0,
It obtains from section π equations and is：r″(t0)·[ρ-r(t0)]=0, i.e. y+3t0z-t0 2-3t0 4=0, ρ are to take up an official post from section
The vector of a bit.
To bend equidistant surface πs of the high franchise ε for distance construction from section π on the principal normal direction from section π1：
3. simultaneous equidistant surface π1The equation of equation and space curve Γ obtains intersection point P1Parameter t1It is equationRoot, utilize matlab softwares solve.
4. calculating P0And P1The high error max δ of most longbow between two-phase neighbor interpolation.Utilize distance between beeline and dot in analytic geometry
Meaning, establish P0And P1The high error function of bow of any point between 2 pointsProfit
The method being most worth is asked to acquire max δ with function；
5. if max δ<ε, then P1As next interpolated point, section is gradually otherwise reduced using line search method and is found completely
The point of the high tolerance requirements of arch of foot is as next interpolated point；
6. return to step (2)；Until all interpolated points on a space curve have determined.
Space curve Γ interpolated points schematic diagram and the high error curve diagram of most longbow are as shown in figs. 34.
Claims (2)
1. a kind of space curve interpolating method based on osculating plane theory, which is characterized in that be as follows：
Step (1) assumes that the parametric equation of a space curve Γ is r=r (t) t ∈ [a, b], when interpolation starts, the 0th interpolation
Point P0Parameter be t0=a bends high franchise ε；
Step (2) is in P0At point, r (t are calculated0),r′(t0),r″(t0), acquire equation the r " (t from section π0)·[ρ-r(t0)]
=0, ρ are the vector of any point from section, are constructed from the equidistant of section π for distance on principal normal direction with bending high franchise ε
Face π1；
Step (3) simultaneous equidistant surface π1The equation of equation and space curve Γ solves equidistant surface π1With the intersection point of space curve Γ
Parameter t1；
Step (4) calculates t0And t1Two corresponding interpolated point P0And P1Between the high error max δ of most longbow；
Step (5) is if max δ < ε, P1As next interpolated point, [t is gradually otherwise reduced using line search method0,t1] area
Between find and meet the point for bending high tolerance requirements as next interpolated point；
Step (6) return to step (2)；Until the operation of a space curve terminates.
2. the space curve interpolating method according to claim 1 based on osculating plane theory, which is characterized in that
Step (4) establishes P0And P1The high error function of bow of any point between 2 points
The method being most worth is asked to acquire max δ using function.
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| CN107145126B (en) * | 2017-06-29 | 2018-01-16 | 南京航空航天大学 | Consider the numerical control machining knife rail subregion mapping method of error band distribution |
| CN110116353B (en) * | 2019-06-03 | 2021-01-15 | 武汉理工大学 | Abrasive belt grinding and polishing step length optimization method for blade front and rear edge robot |
| CN111983975B (en) * | 2020-07-23 | 2023-04-18 | 江苏威泽智能科技股份有限公司 | Spline curve interpolation method for parameter increment compensation |
| CN112987647B (en) * | 2021-01-04 | 2022-03-29 | 苏州科技大学 | Equal-error tool path generation method for five-axis machining of parametric curved surface flat-bottom tool |
| CN114563979B (en) * | 2022-02-25 | 2023-10-13 | 苏州谷夫道自动化科技有限公司 | Compensation method and system for single-channel semi-closed-loop multi-spindle multi-station processing |
| CN114879606B (en) * | 2022-04-29 | 2024-08-06 | 燕山大学 | Adaptive control interpolation method for micromachining precision of arbitrary parameter curve |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6225771B1 (en) * | 1999-12-01 | 2001-05-01 | General Electric Company | Probe chord error compensation |
| CN105045211A (en) * | 2015-07-13 | 2015-11-11 | 太原科技大学 | Equal-chord-error variable-step tangent interpolation method |
| CN105676787A (en) * | 2015-12-28 | 2016-06-15 | 龙兵 | Elliptic arc interpolation algorithm |
| CN105759725A (en) * | 2016-03-22 | 2016-07-13 | 大连理工大学 | Speed-sensitive section constant-speed curve interpolation speed planning method |
-
2016
- 2016-12-30 CN CN201611258996.1A patent/CN106774154B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6225771B1 (en) * | 1999-12-01 | 2001-05-01 | General Electric Company | Probe chord error compensation |
| CN105045211A (en) * | 2015-07-13 | 2015-11-11 | 太原科技大学 | Equal-chord-error variable-step tangent interpolation method |
| CN105676787A (en) * | 2015-12-28 | 2016-06-15 | 龙兵 | Elliptic arc interpolation algorithm |
| CN105759725A (en) * | 2016-03-22 | 2016-07-13 | 大连理工大学 | Speed-sensitive section constant-speed curve interpolation speed planning method |
Non-Patent Citations (1)
| Title |
|---|
| 等弓高误差变步长的插补点求取方法优化;杨振玲，等;《工具技术》;20160831;42-46 * |
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