CN106873529A - The algorithm that cutter rings body is projected to the side of triangular plate in a kind of five-axis robot track - Google Patents
The algorithm that cutter rings body is projected to the side of triangular plate in a kind of five-axis robot track Download PDFInfo
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- CN106873529A CN106873529A CN201710158712.XA CN201710158712A CN106873529A CN 106873529 A CN106873529 A CN 106873529A CN 201710158712 A CN201710158712 A CN 201710158712A CN 106873529 A CN106873529 A CN 106873529A
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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
- G05B19/408—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 data handling or data format, e.g. reading, buffering or conversion of data
- G05B19/4086—Coordinate conversions; Other special calculations
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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
- G05B2219/35356—Data handling
Abstract
The invention belongs to Milling Process correlative technology field, it discloses the algorithm that cutter rings body in a kind of five-axis robot track is projected to the side of triangular plate, it is comprised the following steps：(1) judge the special circumstances that cutter rings body is projected to the side of triangular plate, if there are special circumstances, go to step (5), otherwise go to step (2)；(2) primary iteration angle is determined according to the first geometry constraint conditions；(3) calculated and discrete primary iteration angular regions based on the second geometry constraint conditions and the 3rd geometry constraint conditions, to determine more excellent primary iteration angle；(4) based on the second geometry constraint conditions and the 3rd geometry constraint conditions, optimal angle is searched for using secant method, step (5) is gone to if success, otherwise terminated；(5) cutter-contact point is calculated according to the optimal angle for searching.The algorithm that the present invention is provided calculates preferably primary iteration point and accurate search gradient using three geometry constraint conditions, improves cutter-contact point computational efficiency.
Description
Technical field
The invention belongs to Milling Process correlative technology field, justify more particularly, to cutter in a kind of five-axis robot track
The algorithm that ring body is projected to the side of triangular plate.
Background technology
Five-shaft numerical control processing can ensure that the geometry cutting profile of cutter is more fitted workpiece geometric jacquard patterning unit surface, can set more
Big cuts the number to reduce track wide, and then improves processing efficiency.But, complicated calculating, cross that the interference such as to cut or owe to cut existing
As limiting application of the five-shaft numerical control processing in actual industrial.
By taking projection algorithm as an example, it is first determined drive surface and planning drive track, then by cutter by driving point along projection
Direction projects towards curve surface of workpiece, and holding cutter-orientation is constant, and until cutter is tangent with workpiece surface first, the point of contact is cutter
To the subpoint of curve surface of workpiece.When planning drives track, generally consider and cut the wide, smooth degree of track and mismachining tolerance.Throw
The machining locus of shadow algorithm generation have similar regularity and continuity with track is driven, and projection algorithm is that cutter and workpiece is bent
Face contact highest point of contact is used as cutter-contact point, it is ensured that the machining locus of generation are cut without mistake.Additionally, calculating complicated to reduce
Degree, cutter and curve surface of workpiece generally asked friendship to be reduced to cutter to ask friendship with the discrete triangular plate of curve surface of workpiece.
At present, relevant technical staff in the field has done some researchs, but big both for along fixed cutter axis orientation
Projection, only minority relate to the concept that cutter is projected along any direction towards triangular plate, such as document《Fixed-axis tool
positioning with built-in global interference checking for NC path
generation》The concept that cutter is projected along any direction towards triangular plate is proposed first, but does not provide specific reality
Existing scheme.Although three axis machining, in five-axis robot, each cutter-contact point can be met along fixed cutter axis orientation projection
Cutter axis orientation is all different, if still projected along cutter axis orientation, the regular and company of the machining locus of projection algorithm generation
Continuous property will be inconsistent with driving track, therefore, cutter urgently to be resolved hurrily is along any direction towards asking that triangular plate is projected in five-axis robot
Topic, wherein cutter rings body are more complicated to the side projection of triangular plate, and time-consuming more long, and especially projecting direction is any direction
When.And for example document《A multipoint method for 5-axis machining of triangulated surface
models》、《Numeric implementation of drop and tilt method of 5-axis tool
positioning for machining of triangulated surfaces》Derive cutter rings body to triangular plate
The equation of higher degree of side projection, and equation root is asked using iterative numerical approach, but the method calculates complicated, takes more long, precision
It is limited, and the method address only the situation consistent with cutter axis orientation of projecting direction in three axis machining.Correspondingly, this area is present
A kind of cutter rings body suitable for five-axis robot Track Pick-up that can improve computational efficiency of development to be thrown to the side of triangular plate
The technical need of the algorithm of shadow.
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, justify the invention provides cutter in a kind of five-axis robot track
The algorithm that ring body is projected to the side of triangular plate, the characteristics of it is based on cutter rings body in five-axis robot track and is projected to triangular plate,
Designed to the algorithm that the side of triangular plate projects for cutter rings body.The algorithm passes through three geometry constraint conditions,
It is determined that preferably primary iteration angle, and accurate search gradient is calculated, justify by the cutter vertical with the side of triangular plate
Optimum point is searched on the curve of ring body, it is to avoid calculate the root of the equation of higher degree, it is ensured that the computational accuracy of subpoint, improve knife
The computational efficiency of contact, and machining locus can be quickly generated, it is simple and practical.
To achieve the above object, thrown to the side of triangular plate the invention provides cutter rings body in a kind of five-axis robot track
The algorithm of shadow, it is comprised the following steps：
(1) judge the special circumstances that cutter rings body is projected to the side of triangular plate, if there are special circumstances, go to step
(5) step (2), is otherwise gone to；
(2) primary iteration angle is determined according to the first geometry constraint conditions；
(3) primary iteration angular regions are calculated based on the second geometry constraint conditions and the 3rd geometry constraint conditions and is given
It is discrete, to determine more excellent primary iteration angle, θ0Or α0；
(4) based on the second geometry constraint conditions, the 3rd geometry constraint conditions and more excellent primary iteration angle, θ0Or α0, use
Secant method searches for optimal angle on the curve of the cutter rings body vertical with the side of triangular plateopOr αop, gone to if success
Step (5), otherwise terminates；
(5) the corresponding cutter-contact point P of the optimal angle is calculated according to the optimal angle for searchingop。
Further, first constraints is：Point of contact corresponding method misorientation amount on cutter rings bodyWith the edge-vector V=(V of triangular platex, Vy, Vz) vertical, i.e. f (α, θ)=Vxcos(α)cos
(θ)+Vycos(α)sin(θ)-Vz(α, θ are the search curve for determining, the search curve is in cutter rings for sin (α)=0, wherein f
On body；α and θ represent the longitude and latitude of cutter rings body.
Further, second constraints is：If cutter rings body is projected successfully to the side of triangular plate, point of contact
The opposite direction of corresponding method arrow on cutter rings bodyPositioned at shared corresponding triangular plate
Side two adjacent triangular plates method arrowWith
Between, wherein α1And θ1For representation swears NF1Parameter, α2And θ2For representation swears NF2Parameter.
Further, the 3rd geometry constraint conditions are：By cutter rings body and the point of contact Q on the side of triangular platei(αi, θi)
Along projecting direction PV(Ux, Uy, Uz) projection straight line to the side of triangular plate apart from liIt is 0.
Further, V is worked aszWhen=0, f (α, θ)=Vxcos(α)cos(θ)+VyCos (α) sin (θ)=0, and as cos (θ)
When ≠ 0, tan (θ)=- Vx/Vy, θ has two values, now determines that search primary iteration angle is α.
Further, V is worked aszWhen ≠ 0, search curve f (α, θ)=Vxcos(α)cos(θ)+Vycos(α)sin(θ)-Vzsin
(α)=0 and angle, θ are mapping relations one by one, that is, give an angle, θ, have unique point to correspond to therewith on cutter rings body, are given
A fixed angle [alpha], has two points to correspond to therewith on cutter rings body, now determine that primary iteration angle is θ.
Further, optimal angle is searched on the curve of the cutter rings body vertical with the side of triangular plate includes following step
Suddenly：
(41) i-th search angle [alpha] to givingiOr θi, projection straight line is calculated with side apart from liWith precise search gradient Any point Q of the search curve wherein on torusT(QTx, QTx, QTx)；
(42) l is worked asi≠ 0, step (43) is carried out, otherwise go to step (45)；
(43) if iterations i=0, step-size in search s is madei=| gi|, iteration angle, θi+1=θi-sigiOr αi+1=αi-
sigi), make θi=θi+1Or αi=αi+1, go to step (41)；
(44) if gi=gi+1≠ 0, then make step-size in search si+1=| gi+1|, otherwise make step-size in search
OrCalculate next iteration point θi+2=θi+1-si+1gi+1Or αi+2=αi+1-si+1gi+1, make θi=θi+2Or
αi=αi+2, go to step (41)；
(45) optimal iteration angle, θ is exportedopOr αop。
Further, cutter-contact point PopCalculating comprise the following steps：
(51) according to optimal angleopOr αopAnd formula Vxcos(α)cos(θ)+VyCos (α) sin (θ)=0, tries to achieve corresponding
Angle [alpha]opOr θop；
(52) by (αop, θop) calculate optimum point Pop, and as cutter-contact point.
Wherein (d, h) is the coordinate value of the center of circle in tool coordinate system of cutter rings body portion, and R is the circle of cutter rings body
The radius of arc portion point.
Further, the special circumstances include edge-vector V (Vx, Vy, Vz) and projecting direction PV(Ux, Uy, Uz) it is parallel and
Subpoint is outside the sideline section of triangular plate.
In general, by the contemplated above technical scheme of the present invention compared with prior art, the five of present invention offer
The algorithm that cutter rings body is projected to the side of triangular plate in axle machining locus, it is based on three geometry constraint conditions, it is determined that more excellent
Primary iteration angle, and calculate accurate search gradient, give simplified secant iteration search, by with triangle
On the curve of the vertical torus in the side of piece search for optimum point, it is to avoid calculate the root of the equation of higher degree, it is ensured that the meter of subpoint
Precision is calculated, the computational efficiency of cutter-contact point is improve, and machining locus can be quickly generated, it is adaptable to which commercial Application, practicality is preferable.
Brief description of the drawings
Fig. 1 is that cutter rings body is projected to the side of triangular plate in the five-axis robot track that better embodiment of the present invention is provided
Algorithm flow chart；
Fig. 2 is cutter rings body is related to the algorithm that the side of triangular plate projects in the five-axis robot track in Fig. 1 first
The schematic diagram of search angle is determined in geometry constraint conditions by the method arrowhead amount of two neighboring triangular plate；
Fig. 3 is the cutter that cutter rings body is related to the algorithm that the side of triangular plate projects in the five-axis robot track in Fig. 1
Side projection and the schematic diagram of second geometry constraint conditions of the torus to triangular plate；
Fig. 4 is cutter rings body is related to the algorithm that the side of triangular plate projects in the five-axis robot track in Fig. 1 the 3
Geometry constraint conditions and schematic diagram from cutter rings body to the side Projection Iteration search principle of triangular plate；
Fig. 5 is the determination that cutter rings body is related to the algorithm that the side of triangular plate projects in the five-axis robot track in Fig. 1
The schematic diagram of primary iteration angle；
Fig. 6 is the calculating that cutter rings body is related to the algorithm that the side of triangular plate projects in the five-axis robot track in Fig. 1
And the schematic diagram of discrete primary iteration angular regions；
Fig. 7 is the utilization that cutter rings body is related to the algorithm that the side of triangular plate projects in the five-axis robot track in Fig. 1
Secant method searches for the schematic diagram of optimal corner on the curve of cutter rings body.
Specific embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as additionally, technical characteristic involved in invention described below each implementation method
Not constituting conflict each other can just be mutually combined.
Fig. 1 to Fig. 4 is referred to, cutter rings body is to triangle in the five-axis robot track that better embodiment of the present invention is provided
The algorithm of the side projection of piece, it uses three geometry constraint conditions to determine preferably primary iteration angle, and calculates accurate
Search gradient, simplified secant iteration search is given, by the curve of the torus vertical with the side of triangular plate
Search optimum point, it is to avoid calculate the root of the equation of higher degree, it is ensured that the computational accuracy of subpoint, improves the calculating effect of cutter-contact point
Rate, and machining locus can be quickly generated, practicality is preferable.
In present embodiment, the first geometry constraint conditions are：Point of contact corresponding method arrowhead amount on cutter rings bodyWith the edge-vector V=(V of triangular platex, Vy, Vz) vertical, i.e. f (α, θ)=Vxcos(α)cos
(θ)+Vycos(α)sin(θ)-Vz(α, θ are the search curve for determining, the search curve is in cutter rings for sin (α)=0, wherein f
On body；As shown in (a) figure and (b) figure in Fig. 2, α and θ represents the longitude and latitude of cutter rings body；As shown in figure 3, second
Geometry constraint conditions are：If cutter rings body is projected successfully to the side of triangular plate, point of contact is corresponding on cutter rings body
The opposite direction of method arrowTwo of one side for being positioned at shared corresponding triangular plate are adjacent
The method arrow of triangular plateWithBetween, wherein α1With
θ1For representation swears NF1Parameter, α2And θ2For representation swears NF2Parameter；As shown in (a) figure in Fig. 4, the 3rd geometrical constraint
Condition is：By cutter rings body and the point of contact Q on the side of triangular platei(αi, θi) along projecting direction PV(Ux, Uy, Uz) projection it is straight
Line is to the side of triangular plate apart from liIt is 0, works as liWhen=0, the optimum point Q on cutter rings body curve can be obtainedopAnd its correspondence exists
Optimum point P on the side of triangular plateop.；As shown in (b) figure in Fig. 4, parameter ξ is usediRepresent any point on search curve
Qi, projection straight line is by point QiWith projecting direction PVDetermine, the side of triangular plate is by summit P1Determined with edge-vector V.Define projection straight line
It is l with the distance between the side of triangular platei, parameterRepresent apart from liOpposing curves parameter ξiDifferential.
In present embodiment, cutter rings body is main to the algorithm that the side of triangular plate projects in described five-axis robot track
Comprise the following steps：
Step one, judges the special circumstances that cutter rings body is projected to the side of triangular plate, if there are special circumstances, goes to
Step 5, otherwise goes to step 2.Specifically, the special circumstances include edge-vector V (Vx, Vy, Vz) and projecting direction PV(Ux,
Uy, Uz) parallel and subpoint triangular plate sideline section outside, i.e. projecting direction PV(Ux, Uy, Uz) with the edge-vector V of triangular plate
(Vx, Vy, Vz) parallel；Subpoint is in line segment P1P2Outside.
Fig. 5 is referred to, step 2, according to the first geometry constraint conditions, determines primary iteration angle.It is specific as follows：
(21) V is worked aszWhen=0, f (α, θ)=Vxcos(α)cos(θ)+VyCos (α) sin (θ)=0, as cos (θ) ≠ 0,
Tan (θ)=- Vx/Vy, θ only two is worth, that is, such case lower curve f (α, θ) is discontinuous for angle, θ, the situation
It is lower to determine that search primary iteration angle is α；
(22) V is worked aszWhen ≠ 0, search curve f (α, θ)=Vxcos(α)cos(θ)+Vycos(α)sin(θ)-VzSin (α)=
0 is mapping relations one by one with angle, θ, that is, give an angle, θ, has unique point to correspond to therewith on cutter rings body, gives one
Individual angle [alpha], has two points to correspond to therewith on cutter rings body, in this case determine that primary iteration angle is θ.
Step 3, based on the second geometry constraint conditions and the 3rd geometry constraint conditions, calculates and discrete primary iteration angle
Region, to determine more excellent primary iteration angle.Specifically, comprise the following steps：
(31) by the second geometry constraint conditions, NF1≤-NT≤NF2, wherein
NF1And NF2Can be tried to achieve by sharing two adjacent triangular plates on the side of triangular plate, and then try to achieve primary iteration angle
Region：α1≤α≤α2And θ1≤θ≤θ2；
(32) discrete primary iteration angular regions [θ1, θ2] or [α1, α2], gathered { θiOr { αi, wherein walk-off angle
Degree is utilizedOrCalculate, wherein the numerical value of n is by primary iteration angular regions segment length
Degree and the decision of arc section radius, and n ∈ (0,1].As shown in fig. 6, can be in cutter rings body after primary iteration angular regions are discrete
Search curve on obtain discrete point set { Qi(αi, θi), to specific discrete point Qi(αi, θi) and projecting direction PV(Ux, Uy,
Uz) projection straight line is may make up, projection straight line is l apart from the distance of straight line where the side of triangular platei, distance set { l can be obtainedi}。
From the 3rd geometry constraint conditions, the corresponding projection straight line of discrete point is shorter with the distance between the side of triangular plate, the iteration
Angle from optimal angle more close to, be more conducive to Accelerated iteration process.From distance set { liIn to select most short distance corresponding
Discrete point on search curve, the discrete point correspondence that will be selected is in set { θiOr { αiIn iteration angle as preferably
Primary iteration angle, θ0Or α0。
Step 4, based on the second geometry constraint conditions and the 3rd geometry constraint conditions, using secant method with triangular plate
Optimal angle is searched on the curve of the vertical cutter rings body in side, step 5 is gone to if success, otherwise terminated.Specifically, according to
According to preferably primary iteration angle, θ0Or α0, projecting direction PV(Ux, Uy, Uz), the edge-vector V=(V of triangular platex, Vy, Vz) and its
Summit P1And P2And cutter rings body obtains optimal angle αopOr θop, as shown in fig. 7, specifically including following steps：
(41) i-th search angle [alpha] to givingiOr θi, calculate the distance between the side of projection straight line and triangular plate liWith
Precise search gradient Any point Q of correspondence search curve wherein on cutter rings bodyT(QTx, QTx, QTx)。
Precision differential li' specific derivation it is as follows：
Search curve is f (α, θ)=Vxcos(α)cos(θ)+Vycos(α)sin(θ)-VzSin (α)=0, using parameter ξ
F (α, θ) is represented, then be can obtain：
DifferentialWithIt is independent, ignores constant and can obtain：
To (α, the θ) of any on given cutter rings body, accurate search gradient can be defined asIt is available
Such as following formula：
In formula,
WillWithSubstitute into above formula,Based on the 3rd geometry constraint conditions, definition is searched
Any point and the link vector at any point on the side of triangular plate are V on funicular curvec, then the side institute of projection straight line and triangular plate
It is in the distance of straight lineWherein NP=PV× V, can obtain：
For the point Q arbitrarily on search curvei(αi, θi), the precision differential of its search gradient is
(42) l is worked asi≠ 0, step (43) is carried out, otherwise go to step (45)；
(43) if iterations i=0, step-size in search s is madei=| gi|, iteration angle, θi+1=θi-sigiOr αi+1=αi-
sigi, make θi=θi+1Or αi=αi+1, go to step (41)；
(44) if gi=gi+1≠ 0, then make step-size in search si+1=| gi+1|, otherwise make step-size in search
OrCalculate next iteration point θi+2=θi+1-si+1gi+1Or αi+2=αi+1-si+1gi+1, make θi=θi+2Or
αi=αi+2, go to step (41)；
(45) optimal iteration angle, θ is exportedopOr αop。
Step 5, the corresponding cutter-contact point of output optimum point.Specifically, mainly include the following steps that：
(51) by optimal iteration angle, θopOr αopCalculate corresponding αopOr θop,
Using the Formula Vxcos(α)cos(θ)+Vycos(α)sin(θ)-VzSin (α)=0, tries to achieve corresponding angle, θopOr
αop。
(52) by (αop, θ op) and calculate optimum point Pop, and as cutter-contact point.
Wherein (d, h) is the coordinate value of the center of circle in tool coordinate system of cutter rings body portion, and R is the circle of cutter rings body
The radius of arc portion point.
Cross point QopAlong projecting direction PVThe intersection point of edge-vector of straight line and triangular plate be point Pop, and will point PopAs knife
Contact exports.
The algorithm that cutter rings body is projected to the side of triangular plate in the five-axis robot track that the present invention is provided, it uses three
Geometry constraint conditions, it is determined that preferably primary iteration angle, and accurate search gradient is calculated, give simplified secant method
Iterative search, optimum point is searched for by the curve of the torus vertical with the side of triangular plate, it is to avoid the calculating equation of higher degree
Root, it is ensured that the computational accuracy of subpoint, improve the computational efficiency of cutter-contact point, and machining locus can be quickly generated, be applicable
In commercial Application.
As it will be easily appreciated by one skilled in the art that the foregoing is only presently preferred embodiments of the present invention, it is not used to
The limitation present invention, all any modification, equivalent and improvement made within the spirit and principles in the present invention etc., all should include
Within protection scope of the present invention.
Claims (9)
1. the algorithm that cutter rings body is projected to the side of triangular plate in a kind of five-axis robot track, it is comprised the following steps：
(1) judge the special circumstances that cutter rings body is projected to the side of triangular plate, if special circumstances, then go to step (5), it is no
Then go to step (2)；
(2) primary iteration angle is determined according to the first geometry constraint conditions；
(3) calculated based on the second geometry constraint conditions and the 3rd geometry constraint conditions primary iteration angular regions and give from
Dissipate, to determine more excellent primary iteration angle, θ0Or α0；
(4) based on the second geometry constraint conditions, the 3rd geometry constraint conditions and more excellent primary iteration point θ0Or α0, using secant method
Optimal angle is searched on the curve of the cutter rings body vertical with the side of triangular plateopOr αop, step is gone to if success
(5), otherwise terminate；
(5) the corresponding cutter-contact point P of the optimal angle is calculated according to the optimal angle for searchingop。
2. the algorithm that cutter rings body is projected to the side of triangular plate in five-axis robot track as claimed in claim 1, its feature exists
In：First constraints is：Point of contact corresponding method misorientation amount on cutter rings bodyWith
Edge-vector V=(the V of triangular platex, Vy, Vz) vertical, i.e. f (α, θ)=Vxcos(α)cos(θ)+Vycos(α)sin(θ)-Vzsin
(α)=0, wherein f (α, θ) are the search curve for determining, the search curve is on cutter rings body；α and θ represent cutter rings body
Longitude and latitude.
3. the algorithm that cutter rings body is projected to the side of triangular plate in five-axis robot track as claimed in claim 2, its feature
It is：Second constraints is：If cutter rings body is projected successfully to the side of triangular plate, point of contact is in cutter rings body
The opposite direction of upper corresponding method arrow Positioned at two phases on the side for sharing corresponding triangular plate
The method arrow of adjacent triangular plateWithBetween, wherein α1
And θ1For representation swears NF1Parameter, α2And θ2For representation swears NF2Parameter.
4. the algorithm that cutter rings body is projected to the side of triangular plate in five-axis robot track as claimed in claim 3, its feature
It is：3rd geometry constraint conditions are：By cutter rings body and the point of contact Q on the side of triangular platei(αi, θi) along projecting direction PV
(Ux, Uy, Uz) projection straight line to the side of triangular plate apart from liIt is 0.
5. the algorithm that cutter rings body is projected to the side of triangular plate in five-axis robot track as claimed in claim 4, its feature
It is：Work as VzWhen=0, f (α, θ)=Vxcos(α)cos(θ)+VyCos (α) sin (θ)=0, and as cos (θ) ≠ 0, tan (θ)
=-Vx/Vy, θ has two values, now determines that search primary iteration angle is α.
6. the algorithm that cutter rings body is projected to the side of triangular plate in five-axis robot track as claimed in claim 4, its feature
It is：Work as VzWhen ≠ 0, search curve f (α, θ)=Vxcos(α)cos(θ)+Vycos(α)sin(θ)-VzSin (α)=0 and angle
θ is mapping relations one by one, that is, give an angle, θ, has unique point to correspond to therewith on cutter rings body, gives an angle [alpha],
There are two points to correspond to therewith on cutter rings body, now determine that primary iteration angle is θ.
7. the algorithm that cutter rings body is projected to the side of triangular plate in five-axis robot track as claimed in claim 4, its feature
It is：Optimal angle is searched on the curve of the cutter rings body vertical with the side of triangular plate to comprise the following steps：
(41) i-th search angle [alpha] to givingiOr θi, projection straight line is calculated with side apart from liWith precise search gradient Any point Q of the search curve wherein on torusT(QTx, QTx, QTx)；
(42) l is worked asi≠ 0, step (43) is carried out, otherwise go to step (45)；
(43) if iterations i=0, step-size in search s is madei=| gi|, iteration angle, θi+1=θi-sigiOr αi+1=αi-sigi), order
θi=θi+1Or αi=αi+1, go to step (41)；
(44) if gi=gi+1≠ 0, then make step-size in search si+1=| gi+1|, otherwise make step-size in searchOrCalculate next iteration point θi+2=θi+1-si+1gi+1Or αi+2=αi+1-si+1gi+1, make θi=θi+2Or αi
=αi+2, go to step (41)；
(45) optimal iteration angle, θ is exportedopOr αop。
8. the algorithm that cutter rings body is projected to the side of triangular plate in five-axis robot track as claimed in claim 4, its feature
It is：Cutter-contact point PopCalculating comprise the following steps：
(51) according to optimal angleopOr αopAnd formula Vxcos(α)cos(θ)+VyCos (α) sin (θ)=0, tries to achieve corresponding angle
Degree αopOr θop；
(52) by (αop, θop) calculate optimum point Pop, and as cutter-contact point.
Wherein (d, h) is the coordinate value of the center of circle in tool coordinate system of cutter rings body portion, and R is the arc sections of cutter rings body
The radius for dividing.
9. the algorithm that cutter rings body is projected to the side of triangular plate in five-axis robot track as claimed in claim 1, its feature
It is：The special circumstances include edge-vector V (Vx, Vy, Vz) and projecting direction PV(Ux, Uy, Uz) parallel and subpoint is in triangle
Outside the sideline section of piece.
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| CN101271326A (en) * | 2008-03-21 | 2008-09-24 | 哈尔滨工业大学 | Ruled surface impeller tool path planning and processing method |
| CN101303583A (en) * | 2008-06-19 | 2008-11-12 | 上海交通大学 | Method for planning five-axis numerical control to process safety shortest cutting tool length |
| CN101829801A (en) * | 2010-03-08 | 2010-09-15 | 淮阴工学院 | Five-axis linkage simulation machining method of dental prosthesis |
| CN102866638A (en) * | 2012-10-22 | 2013-01-09 | 天津商业大学 | Double-turntable five-axis numerical control machine tool virtual assembling and numerical control machining simulation method |
| WO2015092228A1 (en) * | 2013-12-17 | 2015-06-25 | Fives Forest-Line | Mixed multiaxial pivoting head |
| CN105759717A (en) * | 2016-04-25 | 2016-07-13 | 华中科技大学 | Cutter path overcut prevention method used for five-axis numerical control processing |
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|---|---|---|---|---|
| CN101271326A (en) * | 2008-03-21 | 2008-09-24 | 哈尔滨工业大学 | Ruled surface impeller tool path planning and processing method |
| CN101303583A (en) * | 2008-06-19 | 2008-11-12 | 上海交通大学 | Method for planning five-axis numerical control to process safety shortest cutting tool length |
| CN101829801A (en) * | 2010-03-08 | 2010-09-15 | 淮阴工学院 | Five-axis linkage simulation machining method of dental prosthesis |
| CN102866638A (en) * | 2012-10-22 | 2013-01-09 | 天津商业大学 | Double-turntable five-axis numerical control machine tool virtual assembling and numerical control machining simulation method |
| WO2015092228A1 (en) * | 2013-12-17 | 2015-06-25 | Fives Forest-Line | Mixed multiaxial pivoting head |
| CN105759717A (en) * | 2016-04-25 | 2016-07-13 | 华中科技大学 | Cutter path overcut prevention method used for five-axis numerical control processing |
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