CN106933189A - Generating tool axis vector method for fairing is processed based on AC type five-axle number control machine tools endless knife - Google Patents
Generating tool axis vector method for fairing is processed based on AC type five-axle number control machine tools endless knife Download PDFInfo
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Abstract
Generating tool axis vector method for fairing is processed based on AC type five-axle number control machine tools endless knife the invention discloses one kind, is comprised the following steps：The relation equation set up between endless knife generating tool axis vector and cutter spacing design variable；The motion transform equation set up between endless knife generating tool axis vector and five-axle number control machine tool gyroaxis A and C；The relation equation set up between endless knife cutter spacing design variable and five-axle number control machine tool gyroaxis A and C；Determine design variable, object function and the constraints of endless knife generating tool axis vector fairing, set up and generating tool axis vector fairing Mathematical Modeling is processed based on AC type five-axle number control machine tools endless knife；Determine the method for solving of above-mentioned generating tool axis vector fairing Mathematical Modeling.The method can avoid the drastically change of machine tool rotary axle, move machine tool rotary axle more steady and smooth, and the angular speed and angular acceleration of machine tool rotary axle is greatly reduced, so that the crudy and processing efficiency of curved surface are improved, with stronger actual application value.
Description
Technical field
The present invention relates to a kind of five-axle number control machine tool generating tool axis vector method for fairing, more particularly to based on AC type five shafts numerical controlled machines
Bed endless knife processing generating tool axis vector method for fairing, belongs to five-shaft numerical control processing technique field.
Background technology
When complex-curved using endless knife five-axis robot, because surface geometry property is poor, such as the normal vector of curved surface,
Principal direction, curvature etc., are easily caused generated endless knife generating tool axis vector and undergo mutation and fluctuation.Even if using most simple
Cutter positioning method (such as Sturz methods) above-mentioned curved surface area of five-axis robot, can also cause the acute variation of generating tool axis vector, so that shadow
Ring the nonlinearity erron in stationarity, the servo ability beyond machine tool feed axle and the increase process of five-axis machine tool motion
Deng.Therefore important research direction of the smooth generating tool axis vector of endless knife as Machining of Curved Surface technology in five-shaft numerical control processing is obtained.For
Smooth generating tool axis vector is obtained, domestic and foreign scholars have carried out numerous studies work in terms of optimal tool orientation, and propose many
Five-axis robot optimal tool orientation method, focuses primarily upon two aspects：One is that geometrical constraint is only considered in workpiece coordinate system
Optimal tool orientation method；Two is the optimal tool orientation side that geometrical constraint and kinematical constraint are considered in workpiece coordinate system
Method.
Prior art one, (cycle, Zhao Jibin and Liu Weijun, complex-curved five-shaft numerical control process optimal tool orientation to document
Technique study mechanical engineering journals, 2013 (07):184-192) propose that a kind of complex-curved five-shaft numerical control processing generating tool axis vector is excellent
Change method.The processing stand position that effectively insertion is limited first in non-interfering domain, it is ensured that the global optimization of generating tool axis vector；Simultaneously dry
Relate to and improved C-Space methods are used in domain, generate generating tool axis vector fairing feasible zone.
Prior art two, document (Wang Jing etc., complex curved surface parts five-axis robot cutter shaft global optimization method aviation journals,
2013(06):1452-1462) propose a kind of five axle generating tool axis vector global optimization methods based on critical constraint.Construct first
All feasible pendulum knife planes at given point of contact, and critical generating tool axis vector is calculated according to critical constraint in pendulum knife plane,
Obtain on the basis of critical generating tool axis vector, Planar Mapping is carried out to it, establish the initial feasible zone of cutter shaft swing；Secondly, lead to
Cross carries out uniform discrete to initial feasible zone, according to relative position relation construction adjacency matrix between discrete point, and combines most short
Path search algorithm obtains initial reference cutter shaft, and feasible zone is swung so as to construct new cutter shaft；Finally, current cutting is set up
Without interference and the minimum optimal tool orientation model of adjacent cutter shaft change in row, realize free form surface five-axis robot without interference cutter shaft
The smooth control of vector.Above-mentioned prior art at least has the following disadvantages：
The above method is main not occur to cut between cutter and workpiece/lathe with global interference etc. as constraints,
It is minimum with generating tool axis vector change in workpiece coordinate system or smooth change is turned to object function and carries out optimal tool orientation, so as to obtain
Without interference and smooth generating tool axis vector in workpiece coordinate system.And five-axle number control machine tool is larger because of architectural difference, although workpiece coordinate
The smooth change of generating tool axis vector in system, but it is difficult to ensure that in lathe coordinate system each reference axis of five-axis machine tool especially gyroaxis can light
Sliding movement and without jumping phenomenon occur so that influence the stationarity of machine tool motion, beyond the servo ability of machine tool feed axle and increasing
Nonlinearity erron during big processing etc..Therefore, it is necessary to carry out needing to consider during optimal tool orientation in workpiece coordinate system
The situation of change of machine tool rotary axle in lathe coordinate system, or directly to machine tool rotary axle to carry out fairing in lathe coordinate system excellent
Change.
The content of the invention
It is the problem for overcoming the existing complex-curved generating tool axis vector of endless knife five-axis robot to undergo mutation with fluctuation, this hair
It is bright to provide a kind of based on AC type five-axle number control machine tools endless knife processing generating tool axis vector method for fairing.
To achieve these goals, the technical solution adopted by the present invention is such：One kind is based on AC type five shafts numerical controlled machines
Bed endless knife processing generating tool axis vector method for fairing, comprises the following steps：
A, the relation equation set up between endless knife generating tool axis vector and cutter spacing design variable；
B, the motion transform equation set up between endless knife generating tool axis vector and five-axle number control machine tool gyroaxis A and C；
C, the relation equation set up between endless knife cutter spacing design variable and five-axle number control machine tool gyroaxis A and C；
D, the design variable for determining endless knife generating tool axis vector fairing, object function and constraints, set up and are based on AC types five
Shaft and NC Machining Test lathe endless knife processes generating tool axis vector fairing Mathematical Modeling；
E, the method for solving for determining generating tool axis vector fairing Mathematical Modeling in step D.
As preferred：The step A is specially：
(1) cutter local coordinate system is set up at cutter-contact point, local coordinate system O is derivedLXLYLZLMiddle endless knife cutter shaft arrow
Relation equation between amount and cutter spacing design variable：
In formula, θ be local coordinate system in endless knife around YLAxle rotate top rake, φ be local coordinate system in annular cutter around ZL
The side drift angle that axle is rotated,
In local coordinate system OLXLYLZLEndless knife cutter location footpath arrow is at middle cutter-contact point：
In formula, r is the radius of circle that cuts of endless knife, and R is the ring heart radius of circle of endless knife.
(2) relation equation between endless knife generating tool axis vector and cutter spacing design variable in workpiece coordinate system is set up：
In formula, e1=(x1,y1,z1)T, e2=(x2,y2,z2)T, e3=(x3,y3,z3)TRespectively local coordinate system
OLXLYLZL
Each reference axis is in workpiece coordinate system OwXwYwZwIn unit vector；
In workpiece coordinate system OwXwYwZwEndless knife cutter location footpath arrow is at middle cutter-contact point：
As preferred：It is each according to AC type five-axle number control machine tools concrete structure, machine tool motion chain and lathe in the step B
Relation between coordinate system, sets up relation equation between endless knife generating tool axis vector and five-axle number control machine tool gyroaxis A and C：
As preferred：In the step C, endless knife cutter spacing design variable and lathe are then derived in simultaneous formula (3) and (5)
Relation equation between gyroaxis A and C：
As preferred：In the step D, the machine tool rotary axle A and C using in lathe coordinate system as design variable, with curved surface
Every all cutter-contact point { P of row knife raili, i=1 ..., N } the compound angular acceleration in place quadratic sum as object function, with machine tool rotary
The angle of axle A and C, angular speed and angular acceleration limitation scope are set up and are based on AC type five-axle number control machine tool rings as constraints
Shape knife processes generating tool axis vector fairing Mathematical Modeling：
In formula, N is given row knife rail upper slitter number of contacts, β1And β2Machine tool rotary axle A and C corner, ω are represented respectively1With
ω2Machine tool rotary axle A and C angular speed, α are represented respectively1And α2Machine tool rotary axle A and C acceleration is represented respectively,With
Machine tool rotary angle beta is represented respectively1And β2Range of movement,WithMachine tool rotary angle beta is represented respectively1And β2Angular speed limits model
Enclose,WithMachine tool rotary angle beta is represented respectively1And β2Angular acceleration limits scope, any cutter-contact point P on curved surfaceiPlace is answered
Angular acceleration is closed to be defined as：
In formula,It is cutter-contact point PiThe generating tool axis vector at place, t represents the time.
As preferred：The step E is specially：
(1) using the cutter spacing at the given surface sampling cutter-contact point of the existing axle tool position optimization method of endless knife five generation, then
Obtain the initial generating tool axis vector at above-mentioned sampling cutter-contact point；
(2) the corresponding machine tool rotary angle A and C in each sampling cutter-contact point place is calculated using formula (5), recycles cubic spline
Machine tool rotary angle A and C at each sampling cutter-contact point is carried out Cubic Spline Fitting by interpolating function respectively；
(3) calculate often row knife rail knife using the cubic spline interpolation fitting function obtained by step (2) and touch each knife on curve
Machine tool rotary angle A and C at contact；Endless knife cutter spacing design variable θ and ψ at each cutter-contact point are calculated using formula (6)；Each knife is solved to touch
Endless knife error of cutter position distribution at point, and calculate minimal orientation-distance δ between endless knife and curve surface of workpiece；If δ ＜ 0, i.e. ring
Interfered between shape knife and curve surface of workpiece, then make endless knife along the cutter-contact point direction of normal translation distance | δ |；Using formula (4)
(3) endless knife cutter location footpath resultant generating tool axis vector at each cutter-contact point is calculated, is touched on curve until solving the row knife rail knife
The cutter location footpath resultant generating tool axis vector of all cutter-contact points.The beneficial effects of the invention are as follows the method can avoid machine tool rotary axle
Mutation and not fairing, move machine tool rotary axle more steady and smooth, and the angular speed and angle that machine tool rotary axle is greatly decreased add
Speed, so as to improve the crudy and processing efficiency of curved surface.
Brief description of the drawings
Fig. 1 is to process generating tool axis vector method for fairing flow chart based on AC type five-axle number control machine tools endless knife
Fig. 2 is endless knife Primary Location；
Fig. 3 is AC ' type five-axle number control machine tool structural representations；
Fig. 4 is the coordinate system in AC ' type five-axle number control machine tools；
Fig. 5 is to solve flow chart based on AC type five-axle number control machine tools endless knife processing generating tool axis vector fairing Mathematical Modeling.
Specific embodiment
It is of the invention a kind of based on AC type five-axle number control machine tools endless knife processing generating tool axis vector method for fairing, its basic procedure
As shown in figure 1, preferably specific embodiment is, including：
Step A, the relation equation set up between endless knife generating tool axis vector and cutter spacing design variable.The step A is specially：
(1) relation equation in local coordinate system between endless knife generating tool axis vector and cutter spacing design variable
As shown in figure 1, setting endless knife machining curve surface of workpiece S, r (u, v), Pcc(ucc,vcc) it is any point, n on curved surfacecc
For the per unit system of the point is sweared.R is made to cut radius of circle, O for endless knifeLIt is the origin of local coordinate system, thenWhereinRespectively point OLAnd PccCorresponding footpath arrow.Meanwhile, respectively with point PccThe unit for locating direction of feed cuts resultant per unit system
Arrow nccAs e1And e3, and take e2=e3×e1.Then, with OLIt is the origin of coordinates, vector e1、e2And e3Place direction is respectively XL、
YLAnd ZLAxle sets up point PccThe local coordinate system O at placeLXLYLZL.And OTXTYTZTIt is the tool coordinate system being connected with cutter, its coordinate
Origin OTPositioned at the center of cutter ring heart circle.Make OTXTYTZTEach change in coordinate axis direction and O in original stateLXLYLZLUnanimously, and haveWherein R is the ring heart radius of circle of endless knife.Now, cutter is in surface points PccPlace by Primary Location, but
Coordinate system OLXLYLZLIn still suffer from two frees degree：One is around YLThe top rake θ of axle rotation, two is around ZLThe side drift angle of axle rotation
φ, two jiaos of the above is cutter spacing design variable.
Different cutter spacing can be obtained by adjusting above-mentioned two angle, local coordinate system O can be obtainedLXLYLZLMiddle knife
Contact PccThe generating tool axis vector at place and cutter location footpath are sweared
In formula,
Can be obtained by formula (1)
Can be obtained by formula (2)
(2) relation equation in workpiece coordinate system between annular cutter generating tool axis vector and cutter spacing design variable assumes local seat
Mark system OLXLYLZLEach reference axis is in workpiece coordinate system OwXwYwZwIn vector be respectively e1=(x1,y1,z1)T, e2=(x2,y2,
z2)T, e3=(x3,y3,z3)T, then in workpiece coordinate system OwXwYwZwMiddle generating tool axis vector and cutter location footpath arrow are
Endless knife cutter spacing design variable (i.e. top rake θ and angle of heel ψ) and generating tool axis vector can obtain by formula (5)Between
Relation equation
Step B, the motion transform equation set up between endless knife generating tool axis vector and five-axle number control machine tool gyroaxis A and C.Institute
Step B is stated to be specially：
Different according to gyroaxis position, AC types five-axle number control machine tool can be divided into three types again：1) AC types (A and C
Axle is all located at main shaft side), 2) AC ' types (A axle positions are in main shaft side and C axle positions in turntable side), 3) (A and C axles are all located at turning A ' C ' types
Platform side).For simplicity, will be hereafter illustrated as research object using AC ' type five-axle number control machine tools, its derivation formula is fitted
For all AC types five-axle number control machine tools, as shown in Figure 2.Fig. 3 show in AC ' type five-axle number control machine tools and is closed between each coordinate system
System, general acquiescence workpiece coordinate system OwXwYwZwWith lathe coordinate system OmXmYmZmChange in coordinate axis direction it is consistent, digital control system can be by
Both are associated.It can thus be concluded that, relation equation between endless knife generating tool axis vector and five-axle number control machine tool gyroaxis A and C：
In formula,
Rearrangement formula (8) can be obtained
Step C, the relation equation set up between endless knife cutter spacing design variable and five-axle number control machine tool gyroaxis A and C.Institute
Step C is stated to be specially：
Formula (9) is substituted into formula (7) just to obtain between endless knife cutter spacing design variable and five-axle number control machine tool gyroaxis A and C
Relation equation：
Step D, the design variable for determining endless knife generating tool axis vector fairing, object function and constraints, set up and are based on AC
Type five-axle number control machine tool endless knife processes generating tool axis vector fairing Mathematical Modeling.The step D is specially：
(1) definition of angular acceleration is combined in five-axis robot
The concept of compound angular acceleration is introduced in lathe coordinate system, any cutter-contact point P on design curved surfaceiPlace's compound angle
The definition of acceleration is
In formula, β1And β2Machine tool rotary axle A and C corner is represented respectively,It is cutter-contact point PiThe generating tool axis vector at place, t
Represent time, ω1And ω2Machine tool rotary axle A and C angular speed, α are represented respectively1And α2Machine tool rotary axle A and C acceleration are represented respectively
Degree.
(2) build and generating tool axis vector fairing Mathematical Modeling is processed based on AC type five-axle number control machine tools endless knife
The machine tool rotary axle A and C using in lathe coordinate system as design variable, with the every all cutter-contact point { P of row knife rail of curved surfacei,
I=1 ..., N } the compound angular acceleration in place quadratic sum as object function, with the angle of machine tool rotary axle A and C, angular speed and
Angular acceleration limits scope as constraints, sets up and processes generating tool axis vector fairing number based on AC type five-axle number control machine tools endless knife
Learn model：
In formula,WithMachine tool rotary angle beta is represented respectively1And β2Range of movement,WithLathe is represented respectively
Angle of revolution β1And β2Angular speed sets scope,WithMachine tool rotary angle beta is represented respectively1And β2Angular acceleration sets scope.
Step E, the method for solving for determining generating tool axis vector fairing Mathematical Modeling in step D.The step E is specially：Propose
The method of the Mathematical Modeling of generating tool axis vector fairing, solution procedure are as shown in figure 4, its detailed process is as follows in a kind of solution procedure D：
(1) using the cutter spacing at the given surface sampling cutter-contact point of the existing axle tool position optimization method of endless knife five generation, then
Obtain the initial generating tool axis vector at above-mentioned sampling cutter-contact point.
First, by analyzing processing curve the characteristics of, the numerical value of preliminary given endless knife cutter spacing design variable, i.e. top rake
θ and side drift angle φ, it is assumed that it is N to touch curve up-sampling cutter-contact point number to stationary knife rail knife, and actual cutter-contact point number is M, public to fixed step size
Difference is h.Then, parameter discrete method generation sampling cutter-contact point { CC is utilized etc. on curve being touched to stationary knife rail knifei, i=1 ..., N }；
Finally, all sampling cutter-contact point CC are calculated using Sturz methodsiLocate generating tool axis vector { Tai, i=1 ..., N } and cutter location footpath arrow { Tpi,
I=1 ..., N }.
(2) each sampling cutter-contact point CC is calculated using formula (10)iThe corresponding machine tool rotary angle A in placeiAnd Ci, recycle three
Secondary spline interpolation function is by each sampling cutter-contact point CCiThe machine tool rotary angle A at placeiAnd CiCubic Spline Fitting is carried out, so as to obtain machine
Bed angle of revolution AiAnd CiCubic spline interpolation fitting function F (u, A) and F (u, C), wherein u be sample cutter-contact point parameter become
Amount.
(3) for touching curve to stationary knife rail knife, by given M or h and the parameter discrete method such as utilize or wait action error variance
Method generates actual cutter-contact point { PCi, i=1 ..., M }, cubic spline interpolation fitting function F (u, A) and F in recycle step (2)
(u, C) calculates the row knife rail knife and touches actual cutter-contact point P on curveCiThe corresponding machine tool rotary angle A in placeiAnd Ci；Then formula is utilized
(10) actual cutter-contact point P is obtainedCiLocate machine tool rotary angle AiAnd CiCorresponding endless knife cutter spacing design variable θiAnd φi；Solve knife
Contact PCiPlace's endless knife error of cutter position distribution, and calculate minimal orientation-distance δ between endless knife and curve surface of workpiece；If δ ＜
Interfered between 0, i.e. endless knife and curve surface of workpiece, then make endless knife along the cutter-contact point direction of normal translation distance | δ |；By formula
And (7) obtain cutter-contact point P (6)CiSwear T in the cutter location footpath for locating endless knifepiWith generating tool axis vector Tai, until i=M solves the row
Knife touches the cutter location and generating tool axis vector of all cutter-contact points on curve.
The above, the only present invention preferably specific embodiment, but protection scope of the present invention is not limited thereto,
Any one skilled in the art the invention discloses technical scope in, the change or replacement that can be readily occurred in,
Should all be included within the scope of the present invention.
Claims (6)
1. it is a kind of that generating tool axis vector method for fairing is processed based on AC type five-axle number control machine tools endless knife, it is characterised in that including as follows
Step：
A, the relation equation set up between endless knife generating tool axis vector and cutter spacing design variable；
B, the motion transform equation set up between endless knife generating tool axis vector and five-axle number control machine tool gyroaxis A and C；
C, the relation equation set up between endless knife cutter spacing design variable and five-axle number control machine tool gyroaxis A and C；
D, the design variable for determining endless knife generating tool axis vector fairing, object function and constraints, set up and are based on the number of axle of AC types five
Control lathe endless knife processing generating tool axis vector fairing Mathematical Modeling；
E, the method for solving for determining generating tool axis vector fairing Mathematical Modeling in step D.
2. according to claim 1 to process generating tool axis vector method for fairing based on AC type five-axle number control machine tools endless knife, it is special
Levy and be, the step A is specially：
(1) cutter local coordinate system is set up at cutter-contact point, local coordinate system O is derivedLXLYLZLMiddle endless knife generating tool axis vector with
Relation equation between cutter spacing design variable：
In formula, θ be local coordinate system in endless knife around YLAxle rotate top rake, φ be local coordinate system in annular cutter around ZLAxle is rotated
Side drift angle,
In local coordinate system OLXLYLZLEndless knife cutter location footpath arrow is at middle cutter-contact point：
In formula, r is the radius of circle that cuts of endless knife, and R is the ring heart radius of circle of endless knife.
(2) relation equation between endless knife generating tool axis vector and cutter spacing design variable in workpiece coordinate system is set up：
In formula, e1=(x1,y1,z1)T, e2=(x2,y2,z2)T, e3=(x3,y3,z3)TRespectively local coordinate system OLXLYLZLIt is each to sit
Parameter is in workpiece coordinate system OwXwYwZwIn unit vector；
In workpiece coordinate system OwXwYwZwEndless knife cutter location footpath arrow is at middle cutter-contact point：
3. according to claim 1 to process generating tool axis vector method for fairing based on AC type five-axle number control machine tools endless knife, it is special
Levy and be, in the step B, according to AC type five-axle number control machine tools concrete structure, between machine tool motion chain and each coordinate system of lathe
Relation, sets up relation equation between endless knife generating tool axis vector and five-axle number control machine tool gyroaxis A and C：
4. according to claim 1 to process generating tool axis vector method for fairing based on AC type five-axle number control machine tools endless knife, it is special
Levy and be, in the step C, endless knife cutter spacing design variable and machine tool rotary axle A and C are then derived in simultaneous formula (3) and (5)
Between relation equation：
5. according to claim 1 to process generating tool axis vector method for fairing based on AC type five-axle number control machine tools endless knife, it is special
Levy and be, in the step D, the machine tool rotary axle A and C using in lathe coordinate system as design variable, with the every row knife rail institute of curved surface
There is cutter-contact point { Pi, i=1 ..., N } the compound angular acceleration in place quadratic sum as object function, with the angle of machine tool rotary axle A and C
Degree, angular speed and angular acceleration limitation scope are set up and process knife based on AC type five-axle number control machine tools endless knife as constraints
Axial vector fairing Mathematical Modeling：
In formula, N is given row knife rail upper slitter number of contacts, β1And β2Machine tool rotary axle A and C corner, ω are represented respectively1And ω2Point
Machine tool rotary axle A and C angular speed, α are not represented1And α2Machine tool rotary axle A and C acceleration is represented respectively,WithGeneration respectively
Table machine tool rotary angle beta1And β2Range of movement,WithMachine tool rotary angle beta is represented respectively1And β2Angular speed limits scope,WithMachine tool rotary angle beta is represented respectively1And β2Angular acceleration limits scope, any cutter-contact point P on curved surfaceiPlace is combined
Angular acceleration is defined as：
In formula,It is cutter-contact point PiThe generating tool axis vector at place, t represents the time.
6. according to claim 1 a kind of based on AC type five-axle number control machine tools endless knife processing generating tool axis vector method for fairing,
Characterized in that, the step E is specially：
(1) using the cutter spacing at the given surface sampling cutter-contact point of the existing axle tool position optimization method of endless knife five generation, then obtain
Initial generating tool axis vector at above-mentioned sampling cutter-contact point；
(2) the corresponding machine tool rotary angle A and C in each sampling cutter-contact point place is calculated using formula (5), recycles cubic spline interpolation
Machine tool rotary angle A and C at each sampling cutter-contact point is carried out Cubic Spline Fitting by function respectively；
(3) calculate often row knife rail knife using the cubic spline interpolation fitting function obtained by step (2) and touch each cutter-contact point on curve
Place machine tool rotary angle A and C；Endless knife cutter spacing design variable θ and ψ at each cutter-contact point are calculated using formula (6)；Solve at each cutter-contact point
Endless knife error of cutter position is distributed, and calculates minimal orientation-distance δ between endless knife and curve surface of workpiece；If δ<0, i.e. endless knife with
Interfered between curve surface of workpiece, then make endless knife along the cutter-contact point direction of normal translation distance | δ |；Counted using formula (4) and (3)
Endless knife cutter location footpath resultant generating tool axis vector at each cutter-contact point is calculated, is touched until solving all knives on the tactile curve of the row knife rail knife
The cutter location footpath resultant generating tool axis vector of point.
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| CN109765841A (en) * | 2019-01-09 | 2019-05-17 | 西北工业大学 | The space-time mapping method of online monitoring data and part Working position |
| CN110209123A (en) * | 2019-06-10 | 2019-09-06 | 哈尔滨工业大学 | A kind of five-shaft numerical control under lathe driving restraint processes generating tool axis vector local optimization methods |
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