CN108415374A - Generating tool axis vector method for fairing based on lathe swivel feeding axis kinematics characteristic - Google Patents
Generating tool axis vector method for fairing based on lathe swivel feeding axis kinematics characteristic Download PDFInfo
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Abstract
The present invention is based on the generating tool axis vector method for fairing of lathe swivel feeding axis kinematics characteristic to belong to complex curved surface parts high-precision high-efficiency Milling Process technical field, is related to a kind of generating tool axis vector method for fairing based on lathe swivel feeding axis kinematics characteristic.This method is that constraint generates processing knife rail with equal scallop-heights according to surface geometry feature.The corresponding generating tool axis vector sequence of cutter-contact point is converted to the corner sequence of lathe swivel feeding axis, and determines section to be optimized according to lathe swivel feeding axis angle change by the coordinate transformation relation for establishing workpiece coordinate system and lathe coordinate system.Based on quaternary counting method, the corresponding generating tool axis vector coordinate of cutter-contact point in section to be optimized is calculated, and by least-square fitting approach to the lathe swivel feeding Shaft angle curve smoothing after optimization, interference checking and adjustment are carried out to the generating tool axis vector after optimization.This method effectively reduces the movement mutation of lathe swivel feeding axis in process, realizes steady processing, improves suface processing quality.
Description
Technical field
The invention belongs to complex curved surface parts high-precision high-efficiency Milling Process technical fields, are related to one kind and are rotated into based on lathe
To the generating tool axis vector method for fairing of axis kinematics characteristic.
Background technology
Complex curved surface parts are widely used in the every field such as aerospace, automobile, ship, how to realize complex-curved
The processing of part high-quality and high-efficiency is the hot and difficult issue of current research.Five-shaft numerical control processing increases two rotations compared with three-axis numerical control processing
Shaft can control the contact condition of cutter and finished surface with respect to the angle of local coordinate system by adjusting cutter, ensure
Part processing quality and efficiency, while avoiding the part between cutter and workpiece and global interference.Cutter shaft in five-axis robot at present
Direction vector is determined according to complex-curved local geometric information, but with the needs of present industrial development, surface modeling is more
Complexity, there are sudden turn of events features for local geometric information.The generating tool axis vector determined according to curved surface local geometric information easily leads to larger
Generating tool axis vector changes, the serious raising for restricting Machining of Curved Surface quality, therefore the generating tool axis vector for obtaining fairing is to improve Machining of Curved Surface
The key link of quality.Domestic and foreign scholars have carried out a large amount of research work in terms of optimal tool orientation at present, mainly think
There are two types of roads：One is cutter spacing is generated with machining softwares such as UG, then it is adjusted；Another kind be calculate at cutter-contact point can
Row cutter shaft space, then optimizes under the conditions of particular constraints, and checks interference.
The document " complex curved surface parts five-axis machining tool shaft global optimization method " of Wang Jing et al., aviation journal, 2013,34
(06)：1452-1462 calculates feasible cutter shaft space at all point of contact first, and on the basis for obtaining critical generating tool axis vector
On, Planar Mapping is carried out to it, establishes the initial feasible zone of cutter shaft swing；Secondly, uniform by being carried out to initial feasible zone
It is discrete, swing feasible zone to construct new cutter shaft；Finally, it establishes in current cutting row without interference and the variation of adjacent cutter shaft most
Small optimal tool orientation model realizes smooth control of the free form surface five-axis robot without interference generating tool axis vector.However this method
It is computationally intensive, and do not consider lathe swivel feeding axis kinematics characteristic in optimization process, there is larger limitation.Cycle etc.
The document " complex-curved five-shaft numerical control processing optimal tool orientation technique study " of people, mechanical engineering journal, 2013,49 (7),
184-192 generates fairing in interference region by being inserted into cutter-contact point in noninterference region using improved C-space methods
Generating tool axis vector, the case where this method can handle global interference and part interference, but be inserted into point of contact reduce it is practical into
To rate, processing efficiency is influenced, is not suitable for high-precision high-efficiency processing.
Invention content
The present invention is directed to prior art defect, and it is bent to have invented a kind of complexity based on lathe swivel feeding axis kinematics characteristic
Face five-shaft numerical control processes generating tool axis vector method for fairing.The method proposed can effectively reduce lathe swivel feeding axis in process
Movement mutation, realize the steady of process, improve suface processing quality, processed for complex-curved high-precision high-efficiency and theory is provided
With technical support.
The technical scheme is that a kind of generating tool axis vector method for fairing based on lathe swivel feeding axis kinematics characteristic,
It is that constraint generates processing knife rail with equal scallop-heights it is characterized in that according to surface geometry feature；Establish workpiece coordinate system and machine
The corresponding generating tool axis vector of cutter-contact point, is converted to the corner of lathe swivel feeding axis, and root by the transformational relation between bed coordinate system
Section to be optimized is determined according to the relationship of lathe swivel feeding Shaft angle and the cumulative arc length of knife rail；It is about with interval border generating tool axis vector
Beam optimizes generating tool axis vector using the cutter shaft homogenizing method based on quaternary number, and to be revolved after least square fitting principle adjusting and optimizing
Rotate into the generating tool axis vector for the arc length curve mean curvature maximum that adds up to Shaft angle and knife rail；Finally carry out interference checking.Method
It is as follows：
The first step：Knife rail cutter-contact point position is generated based on Constant scallop-height
It is S (u, v) to take complex-curved, in CAM softwares, using ball head knife as process tool, using constant scallop-height method
Knife rail r (ξ) is generated, cutter location file { P, V } is obtained, wherein P is point of a knife point coordinates, and V is unit generating tool axis vector, according to cutter location file
In point of a knife point coordinates, cutter-contact point coordinate P can be obtainedCFor：
PC=P+RV-RN (1)
In formula, R indicates ball head knife tool radius；Ν indicates the corresponding curved surface per unit system arrow of cutter-contact point.
The geological informations such as per unit system arrow N, the unit tangent vector T on curved surface S (u, v) are calculated according to formula (2)：
In formula, Su(u,v)、Sv(u, v) is the first-order partial derivative of curved surface, and T is unit tangent vector of the curved surface along knife rail direction,
R ' (ξ) is the first derivative of the specific knife rail of curved surface, and K is the cross product of curved surface per unit system arrow and unit tangent vector.
With cutter-contact point PCFor origin, it is respectively three reference axis with T, K, N, establishes local coordinate system PCTKN is turned by coordinate
The relationship of changing obtains the relation equation between pilot angle under ball head knife generating tool axis vector and local coordinate system：
In formula,Indicate that the generating tool axis vector under local coordinate system, α indicate that ball head knife is before K axis under local coordinate system
Inclination angle, β indicate that for ball head knife around the angle of heel of axis N, Rot (K, α) and Rot (N, β) are respectively rotation with K and N under local coordinate system
Shaft, rotation angle are the spin matrix of α and β, are indicated as follows：
Second step：Swivel feeding axis angle calculation under lathe coordinate system
By taking the bis- turntable-type five-axle number control machine tools of AC as an example, the shaft of rotary table A and the X-axis of lathe coordinate system are flat
Row, the shaft of rotary table C are parallel with the Z axis of lathe coordinate system.According to the configuration of machine tool feed axis, from workpiece basis coordinates system
Transformation matrix E to tool coordinate system is：
In formula, Rot (X ,-θA), Rot (Z ,-θC) rotary table is indicated respectively using X, Z axis as rotary shaft, rotation angle is
θA、θCSpin matrix；Trans (x, y, z) indicates translation matrix.Specially：
Remember unit generating tool axis vector V=[i under workpiece coordinate system*,j*,k*, 0], take cutter shaft inceptive direction vector VbaseDirection machine
Bed coordinate system Z axis is positive, i.e. Vbase=[0,0,1,0], then have：
V=EVbase (5)
It is available by formula (4) and (5)：
In formula, i*, j*, k*Indicate three components of the unit generating tool axis vector under workpiece coordinate system.
Relationship between generating tool axis vector V under lathe swivel feeding Shaft angle and workpiece coordinate system can be obtained by formula (6)：
Lathe swivel feeding shaft rotation angle value in order to obtain, according to formula (7), by cutter-contact point P under workpiece coordinate systemCIt is corresponding
Generating tool axis vector V obtains lathe swivel feeding Shaft angle sequence S { SA,SC}。
Third walks：Lathe swivel feeding axis angular rate counts with angular accelerometer and learns model foundation
Note processing curve is S (u, v), swivel feeding axis angular rate ω and angular acceleration in complex-curved five-shaft numerical control processing
A is：
In formula, θ indicates the angular position of lathe swivel feeding axis, θξAnd θξξFive-axis robot lathe swivel feeding is indicated respectively
Single order of the shaft rotation angle variable to processing trace curve parameter ξ, second dervative,WithProcessing trace curve ginseng is indicated respectively
Single orders of the number ξ to process time t, second dervative.
Since in real process, cutter-contact point is discrete point, therefore discrete method is used to solve lathe swivel feeding axis angular rate
And angular acceleration.By taking the m articles knife rail as an example, calculate as follows：
It takes and shares n cutter-contact point on the m articles knife rail, then i-th of cutter-contact point PCiCorresponding lathe A, C swivel feeding shaft angle speed
Degree is：
In formula,WithCorresponding lathe A, C swivel feeding the shaft rotation angle value of i-th of cutter-contact point is indicated respectively,With
Corresponding lathe A, C the swivel feeding axis angular rate of i-th of cutter-contact point, L are indicated respectivelyiIndicate cutter-contact point P on curved surfaceCiTo adjacent knife
Contact PCi+1Distance, v indicate processing when Constant feeding rate.
This makes it possible to obtain lathe swivel feeding axis angular rate values to be：
In formula, ωiIndicate the corresponding lathe swivel feeding axis angular rate of i-th of cutter-contact point.
I-th of cutter-contact point PCiCorresponding lathe A, C swivel feeding shaft angle acceleration is：
In formula, aAiAnd aCiCorresponding lathe A, C swivel feeding the shaft angle acceleration of i-th of cutter-contact point is indicated respectively.
This makes it possible to obtain lathe swivel feeding shaft angle acceleration values to be：
In formula, aiIndicate the corresponding lathe swivel feeding shaft angle acceleration of i-th of cutter-contact point.
4th step：Interval selection and generating tool axis vector fairing to be optimized
According to the enough vectors of adjacent cutter-contact point in lathe swivel feeding Shaft angle and the cumulative arc length relation curve of knife rail
Angle selection optimization section.Corresponding lathe swivel feeding shaft rotation angle value sequence at each cutter-contact point is acquired by formula (7) first
Arrange S { SA,SC, with adjacent cutter-contact point distance LiIt indicates its arc length, it is cumulative about knife rail to obtain lathe swivel feeding axis A, C corner
The angle curve of arc length, with adjacent cutter-contact point P on curveCi-1、PCiAnd PCi+1The following vector of definition：
PCiPCi-1=(bi,ci),PCiPCi+1=(bi+1,ci+1)
In formula, bi=Li, indicate the arc length between adjacent two cutter-contact point；ci=θi-θi-1, indicate that adjacent two cutter-contact point corresponds to
To the corner difference of lathe swivel feeding axis.
The vector angle that i-th of cutter-contact point is constituted with adjacent discrete cutter-contact point on calculated curve is：
In formula,mθiIndicate the vector angle that the m articles knife rail, i-th of cutter-contact point is constituted with adjacent cutter-contact point.
In i=2 ..., when n-1, the vector angle that each cutter-contact point is constituted with adjacent cutter-contact point is obtained, is then calculated all
The average value of cutter-contact point position vector angleFor：
By comparing the size of vector angle value and average value that each cutter-contact point is constituted with adjacent cutter-contact point, selection optimization
Section：
In formula, e indicates that the initial cutter-contact point serial number in section to be optimized on knife rail, f indicate that knife is terminated in section to be optimized on knife rail
Contact serial number.
Remember that the section of meeting formula (15) is section R=[e, f] to be optimized, is changed uniformly for principle with generating tool axis vector, taken into account
Boundary generating tool axis vector constraint, optimizes the generating tool axis vector of the section cutter-contact point position with the cutter shaft homogenizing method based on quaternary number.Base
Initial generating tool axis vector V is selected according to interval border to be optimized first in the cutter shaft homogenizing method of quaternary number1With end generating tool axis vector
Vn, with V1And VnTwo generating tool axis vectors are boundary, optimize the knife of the interior cutter-contact point position of section [e, f] to be optimized according to formula (16)
Axial vector.
In formula, ViIndicate the generating tool axis vector after the optimization of section to be optimized [e, f], V1And VnIndicate respectively region to be optimized [e,
F] initial cutter-contact point PCeWith termination cutter-contact point PCfCorresponding generating tool axis vector, θQ=arccos (V1·Vn), indicate generating tool axis vector V1
And VnThe angle of composition.
Thus the generating tool axis vector after corresponding cutter-contact point position optimization in section to be optimized is obtained, and is obtained according to formula (7)
Lathe swivel feeding shaft angle angle value at corresponding cutter-contact point position, and then the swivel feeding Shaft angle sequence after being optimized is
In formula,WithThe corner sequence of lathe A axis and C axis after optimizing is indicated respectively.
For the curve of smooth lathe swivel feeding Shaft angle and the cumulative arc length relationship of knife rail, swivel feeding shaft angle is avoided to add
Velocity jump, lathe swivel feeding Shaft angle after analysis optimization and knife rail add up the curve of arc length relationship, bent in trade-off curve
The maximum cutter-contact point P of rateCε, i.e. tip point neighbouring position, with bent near the tip point on least square fitting principle adjustment curve
Wire shaped makes curve F meet following constraint equation：
In formula, ωiIndicate the weight coefficient of each data point, θ*(Li) indicate cutter-contact point P after adjustmentCiLathe swivel feeding
Shaft rotation angle value, Li、θiCurve cross, ordinate are indicated respectively.
Swivel feeding Shaft angle and the cumulative arc length curve of knife rail can be seamlessly transitted by formula (18), obtain the rotation after re-optimization
Turning feed shaft sequence is
In formula,WithRespectively indicate final optimization pass after lathe A axis and C axis corner sequence.
Swivel feeding Shaft angle sequence can be transformed by formula (6) by the generating tool axis vector sequence indicated under workpiece coordinate system
RowkV=kV1,…,kVn, coordinate value of the generating tool axis vector under workpiece coordinate system after being optimized.
Top rake and angle of heel that corresponding workpiece local coordinate system at this time cuts axial vector are calculated, it is feasible with generating tool axis vector
Domain is compared, and is compared according to effective radius of clean-up of the local radius of curvature of curved surface to be processed at cutter-contact point and cutter
Compared with judging whether to interfere, if interfering, carry out the adjustment of tool axis direction, so that it is avoided collision interference, thus may be used
Generating tool axis vector after being optimized.
The remarkable result and benefit of the present invention is to propose a kind of new optimal tool orientation section selection principle, Ke Yiman
Situations such as complex-curved geometric properties of foot are mutated；It proposes on this basis a kind of based on lathe swivel feeding axis kinematics characteristic
Generating tool axis vector method for fairing, solve existing method in the processing of complex-curved five-shaft numerical control and be difficult to ensure lathe swivel feeding
The problem of axis stable movement, improve suface processing quality；During optimal tool orientation, lathe is considered and has been rotated into
It is more comprehensive to the processing that axis kinematics characteristic and generating tool axis vector are interfered.This method is based on lathe swivel feeding axis kinematics
The generating tool axis vector method for fairing of characteristic strong applicability in the processing of complex-curved five-shaft numerical control, is suitable for various complex characteristic curved surfaces
Five axis precise high-efficiencies processing, for improve curved surface processing quality and efficiency, give full play to the kinematics performance of lathe, improve
Workpiece surface processing quality has important practical application meaning.
Description of the drawings
Fig. 1-optimal tool orientation method overall flow figure.
Direction schematic diagram of Fig. 2-generating tool axis vector under local coordinate system.
Fig. 3 a) indicate that swivel feeding axis angular rate and the cumulative arc length relationship simulation result diagram of knife rail, abscissa indicate knife rail
Cumulative arc length, ordinate indicate angular speed；Fig. 3 b) indicate that swivel feeding shaft angle acceleration is tied with the cumulative arc length relationship emulation of knife rail
Fruit is schemed, and abscissa indicates that the cumulative arc length of knife rail, ordinate indicate angular acceleration.
Fig. 4 a) indicate swivel feeding axis angular rate and the cumulative arc length relationship simulation result of knife rail before and after optimal tool orientation
Figure, wherein 1,2 indicate to optimize forward and backward angular speed and the cumulative arc length relationship of knife rail respectively；Fig. 4 b) it indicates to be rotated into before and after optimization
To shaft angle acceleration and the cumulative arc length relationship simulation result diagram of knife rail.Wherein, 1,2 indicate to optimize respectively forward and backward angular acceleration with
The cumulative arc length relationship of knife rail.
Fig. 5 a) indicate machined surface roughness before optimal tool orientation, Fig. 5 b) indicate optimal tool orientation post-processing surface
Roughness；Ra is machined surface roughness.
Fig. 6-optimizes front and back finished surface silhouette contrast fitted figure under three coordinate measuring engine measurement, and 1, which indicates that optimization is preceding, adds
Work surface profile, 2 indicate optimization post-processing surface profile.
Specific implementation mode
Combination technology scheme and the attached drawing specific implementation mode that the present invention will be described in detail
In complex-curved five-shaft numerical control process, the mutation of generating tool axis vector or not fairing easily cause lathe swivel feeding axis
Angular speed is mutated, and is generated processing oscillation mark, is seriously affected workpiece surface processing quality, to solve cutter shaft during complex surface machining
The problem of vector fairing, has invented a kind of complex-curved five-shaft numerical control processing knife based on lathe swivel feeding axis kinematics characteristic
Axial vector method for fairing, overall flow are as shown in Fig. 1.
Using the bis- turntable-type five-axle number control machine tools of AC, with different curvature feature and there are the bumps of curvature feature mutation
For table top, by UG softwares and MATLAB softwares, illustrate the implementation process of the present invention.
Concave-convex table top is modeled first with UG softwares, selects to lean forward 15 ° along direction of feed as cutter axis orientation, i.e. α=
15 °, β=0 ° are that constraint generates processing knife rail with equal scallop-heights 0.002, obtain cutter location file, and according to formula (1)-(3)
Generate knife rail curve upper slitter contact coordinate.Generating tool axis vector is shown in attached drawing 2 relative to the position relationship of workpiece surface, analyzes workpiece coordinate
The transformational relation of system and lathe coordinate system calculates the corresponding lathe of cutter-contact point on knife rail curve according to formula (4)-(7) and is rotated into
Give shaft rotation angle value.
Secondly MATLAB softwares are utilized, lathe swivel feeding axis angular rate is calculated according to formula (8)-(12) and angle accelerates
Degree, obtains result of calculation referring to attached drawing 3.By calculating, maximum angular speed is 24 °/s on this knife rail, and maximum angular acceleration is
127°/s2。
Then select section to be optimized according to formula (13)-(15), section correspond to cutter-contact point serial number 26-47,69-72,
116-122}.In section to be optimized, according to formula (16)-(19), the tool axis direction after optimization is calculated.With cutter-contact point
Illustrated for serial number 69-72, the tool axis direction before optimization be (- 0.828,0.358,0.432) (- 0.81,
0.398,0.430) (- 0.791,0.438,0.428) (- 0.786,0.447,0.427) }, optimized using the method for the invention
Tool axis direction afterwards be (- 0.799,0.418,0.432) (- 0.801,0.416,0.431) (- 0.802,0.414,
0.43)(-0.803,0.412,0.431)}.Before lathe swivel feeding shaft angle angle value corresponding to the section cutter-contact point is not optimised
Corner sequence is S { SA,SC}={ (64.407, -66.599) (64.504, -63.854) (64.689, -60.987) (64.735, -
60.385) } through method of the present invention optimization after optimized after corner sequence be
Finally according to formula (8)-(12) calculate optimal tool orientation after lathe swivel feeding axis angular rate and angular acceleration,
And result of calculation comparison is obtained with optimal tool orientation is not carried out, referring to attached drawing 4.By comparing, the knife after optimal tool orientation
On rail maximum angular speed be 12 °/s, when being not optimised compared with generating tool axis vector angular speed reduce by 50%, maximum angular acceleration be 89 °/
s2, angular acceleration reduces by 30% when being not optimised compared with generating tool axis vector.
Further to verify the validity of proposed method, the cutter shaft in optimal tool orientation processing and CAM softwares is carried out
Vector optimization method contrast experiment, the experimental results showed that, the machined surface quality after the optimal tool orientation of the present invention is apparent
Better than the processing quality after the optimal tool orientation in CAM softwares.Measure the surface roughness of workpiece after processing, shown result ginseng
Shown in attached drawing 5.Measurement result shows that processing quality of the present invention at curvature mutation is improved, and surface roughness is by Ra=
1.6143 μm are reduced to Ra=1.1868 μm, reduce by 26.4%.Simultaneously by three coordinate measuring engine measurement workpiece intermediate position coordinates
Data measured is fitted, the surface topography after analysis processing, work in-process is deposited before fitting result shows optimal tool orientation
Phenomena such as cutting and owing to cut is being crossed, this phenomenon can improved after optimization, shown result is with reference to shown in attached drawing 6.Measurement result and experiment
As a result it preferably coincide, illustrates the generating tool axis vector method for fairing based on lathe swivel feeding axis kinematics characteristic using the present invention,
It can make lathe swivel feeding axis even running, hence it is evident that improve the processing quality at curvature mutation, it is bent to variable curvature in Practical Project
The processing of surface parts high-quality and high-efficiency provides directive function.
Claims (1)
1. a kind of generating tool axis vector method for fairing based on lathe swivel feeding axis kinematics characteristic, which is characterized in that this method root
It is that constraint generates processing knife rail with equal scallop-heights according to surface geometry feature；It establishes between workpiece coordinate system and lathe coordinate system
Transformational relation, the corresponding generating tool axis vector of cutter-contact point is converted to the corner of lathe swivel feeding axis, and be rotated into according to lathe
Section to be optimized is determined to the relationship of Shaft angle and the cumulative arc length of knife rail；With interval border generating tool axis vector be constraint, using based on
The cutter shaft homogenizing method of quaternary number optimizes generating tool axis vector, and with swivel feeding Shaft angle after least square fitting principle adjusting and optimizing
With the generating tool axis vector of the cumulative arc length curve mean curvature maximum of knife rail；Finally carry out interference checking；Method is as follows：
The first step：Knife rail cutter-contact point position is generated based on Constant scallop-height
It is S (u, v) to take complex-curved, in CAM softwares, using ball head knife as process tool, is generated using constant scallop-height method
Knife rail r (ξ) obtains cutter location file { P, V }, and wherein P is point of a knife point coordinates, and V is unit generating tool axis vector, according in cutter location file
Point of a knife point coordinates can obtain cutter-contact point coordinate PCFor：
PC=P+RV-RN (1)
In formula, R indicates ball head knife tool radius；Ν indicates the corresponding curved surface per unit system arrow of cutter-contact point；
The geological informations such as per unit system arrow N, the unit tangent vector T on curved surface S (u, v) are calculated according to formula (2)：
In formula, Su(u,v)、Sv(u, v) is the first-order partial derivative of curved surface, and T is curved surface along the unit tangent vector in knife rail direction, r ' (ξ)
For the first derivative of the specific knife rail of curved surface, K is the cross product of curved surface per unit system arrow and unit tangent vector；
With cutter-contact point PCFor origin, it is respectively three reference axis with T, K, N, establishes local coordinate system PCTKN is converted by coordinate and is closed
System obtains the relation equation under ball head knife generating tool axis vector and local coordinate system between pilot angle：
In formula,Indicate that the generating tool axis vector under local coordinate system, α indicate ball head knife leaning forward around K axis under local coordinate system
Angle, β indicate that for ball head knife around the angle of heel of axis N, Rot (K, α) and Rot (N, β) are respectively rotation with K and N under local coordinate system
Axis, rotation angle are the spin matrix of α and β, are indicated as follows：
Second step：Swivel feeding axis angle calculation under lathe coordinate system
By taking the bis- turntable-type five-axle number control machine tools of AC as an example, the shaft of rotary table A is parallel with the X-axis of lathe coordinate system, rotation
The shaft of revolving worktable C is parallel with the Z axis of lathe coordinate system；According to the configuration of machine tool feed axis, from workpiece basis coordinates system to knife
Tool coordinate system transformation matrix E be：
In formula, Rot (X ,-θA), Rot (Z ,-θC) expression rotary table is using X, Z axis as rotary shaft respectively, rotation angle θA、θC
Spin matrix；Trans (x, y, z) indicates translation matrix；Specially：
Remember unit generating tool axis vector V=[i under workpiece coordinate system*,j*,k*, 0], take cutter shaft inceptive direction vector VbaseLathe is directed toward to sit
Mark system Z axis is positive, i.e. Vbase=[0,0,1,0], then have：
V=EVbase (5)
It is available by formula (4) and (5)：
In formula, i*, j*, k*Indicate three components of the unit generating tool axis vector under workpiece coordinate system；
Relationship between generating tool axis vector V under lathe swivel feeding Shaft angle and workpiece coordinate system can be obtained by formula (6)：
Lathe swivel feeding shaft rotation angle value in order to obtain, according to formula (7), by cutter-contact point P under workpiece coordinate systemCCorresponding cutter shaft
Vector V obtains lathe swivel feeding Shaft angle sequence S { SA,SC}；
Third walks：Lathe swivel feeding axis angular rate counts with angular accelerometer and learns model foundation
Note processing curve is S (u, v), and swivel feeding axis angular rate ω and angular acceleration a is in complex-curved five-shaft numerical control processing：
In formula, θ indicates the angular position of lathe swivel feeding axis, θξAnd θξξFive-axis robot lathe swivel feeding shaft rotation is indicated respectively
Single order of the angle variable to processing trace curve parameter ξ, second dervative,Withξ pairs of processing trace curve parameter is indicated respectively
The single order of process time t, second dervative；
Since in real process, cutter-contact point is discrete point, therefore discrete method is used to solve lathe swivel feeding axis angular rate and angle
Acceleration；By taking the m articles knife rail as an example, calculate as follows：
It takes and shares n cutter-contact point on the m articles knife rail, then i-th of cutter-contact point PCiCorresponding lathe A, C swivel feeding axis angular rate
For：
In formula,WithCorresponding lathe A, C swivel feeding the shaft rotation angle value of i-th of cutter-contact point is indicated respectively,WithRespectively
Indicate corresponding lathe A, C the swivel feeding axis angular rate of i-th of cutter-contact point, LiIndicate cutter-contact point P on curved surfaceCiTo adjacent cutter-contact point
PCi+1Distance, v indicate processing when Constant feeding rate；
This makes it possible to obtain lathe swivel feeding axis angular rate values to be：
In formula, ωiIndicate the corresponding lathe swivel feeding axis angular rate of i-th of cutter-contact point；
I-th of cutter-contact point PCiCorresponding lathe A, C swivel feeding shaft angle acceleration is：
In formula, aAiAnd aCiCorresponding lathe A, C swivel feeding the shaft angle acceleration of i-th of cutter-contact point is indicated respectively；
This makes it possible to obtain lathe swivel feeding shaft angle acceleration values to be：
In formula, aiIndicate the corresponding lathe swivel feeding shaft angle acceleration of i-th of cutter-contact point；
4th step：Interval selection and generating tool axis vector fairing to be optimized
According to the angle of the enough vectors of adjacent cutter-contact point in lathe swivel feeding Shaft angle and the cumulative arc length relation curve of knife rail
Selection optimization section；Corresponding lathe swivel feeding Shaft angle value sequence S at each cutter-contact point is acquired by formula (7) first
{SA,SC, with adjacent cutter-contact point distance LiIt indicates its arc length, obtains lathe swivel feeding axis A, C corner about the cumulative arc length of knife rail
Angle curve, with adjacent cutter-contact point P on curveCi-1、PCiAnd PCi+1The following vector of definition：
PCiPCi-1=(bi,ci),PCiPCi+1=(bi+1,ci+1)
In formula, bi=Li, indicate the arc length between adjacent two cutter-contact point；ci=θi-θi-1, indicate that adjacent two cutter-contact point corresponds to machine
The corner difference of bed swivel feeding axis；
The vector angle that i-th of cutter-contact point is constituted with adjacent discrete cutter-contact point on calculated curve is：
In formula,mθiIndicate the vector angle that the m articles knife rail, i-th of cutter-contact point is constituted with adjacent cutter-contact point；
In i=2 ..., when n-1, the vector angle that each cutter-contact point is constituted with adjacent cutter-contact point is obtained, all knives is then calculated and touches
The average value of point position vector angleFor：
By comparing the size of vector angle value and average value that each cutter-contact point is constituted with adjacent cutter-contact point, selection optimization area
Between：
In formula, e indicates that the initial cutter-contact point serial number in section to be optimized on knife rail, f indicate that cutter-contact point is terminated in section to be optimized on knife rail
Serial number；
Remember that the section of meeting formula (15) is section R=[e, f] to be optimized, is changed uniformly for principle with generating tool axis vector, take into account boundary
Generating tool axis vector constrains, and optimizes the generating tool axis vector of the section cutter-contact point position with the cutter shaft homogenizing method based on quaternary number；Based on four
The cutter shaft homogenizing method of first number selectes initial generating tool axis vector V according to interval border to be optimized first1With end generating tool axis vector Vn, with
V1And VnTwo generating tool axis vectors are boundary, and the cutter shaft for optimizing the interior cutter-contact point position of section [e, f] to be optimized according to formula (16) is sweared
Amount；
In formula, ViIndicate the generating tool axis vector after the optimization of section to be optimized [e, f], V1And VnRegion to be optimized [e, f] is indicated respectively
Initial cutter-contact point PCeWith termination cutter-contact point PCfCorresponding generating tool axis vector, θQ=arccos (V1·Vn), indicate generating tool axis vector V1And Vn
The angle of composition；
Thus the generating tool axis vector after corresponding cutter-contact point position optimization in section to be optimized is obtained, and is corresponded to according to formula (7)
Lathe swivel feeding shaft angle angle value at cutter-contact point position, and then the swivel feeding Shaft angle sequence after being optimized is
In formula,WithThe corner sequence of lathe A axis and C axis after optimizing is indicated respectively；
For the curve of smooth lathe swivel feeding Shaft angle and the cumulative arc length relationship of knife rail, swivel feeding shaft angle acceleration is avoided
It is mutated, the curve of the lathe swivel feeding Shaft angle after analysis optimization and the cumulative arc length relationship of knife rail, trade-off curve mean curvature is most
Big cutter-contact point PCε, i.e. tip point neighbouring position, with curved shape near the tip point on least square fitting principle adjustment curve
Shape makes curve F meet following constraint equation：
In formula, ωiIndicate the weight coefficient of each data point, θ*(Li) indicate cutter-contact point P after adjustmentCiLathe swivel feeding shaft rotation
Angle value, Li、θiCurve cross, ordinate are indicated respectively；
Swivel feeding Shaft angle and the cumulative arc length curve of knife rail can be seamlessly transitted by formula (18), obtain being rotated into after re-optimization
It is to axis sequence
In formula,WithRespectively indicate final optimization pass after lathe A axis and C axis corner sequence；
Swivel feeding Shaft angle sequence can be transformed by formula (6) by the generating tool axis vector sequence indicated under workpiece coordinate systemkV=
{kV1,…,kVn, coordinate value of the generating tool axis vector under workpiece coordinate system after being optimized；
Calculate corresponding workpiece local coordinate system at this time and cut the top rake and angle of heel of axial vector, with generating tool axis vector feasible zone into
Row compares, and is compared according to effective radius of clean-up of the local radius of curvature of curved surface to be processed at cutter-contact point and cutter, sentences
It is disconnected whether to interfere, if interfering, the adjustment of tool axis direction is carried out, it is made to avoid collision interference, this makes it possible to obtain
Generating tool axis vector after optimization.
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| CN109759627A (en) * | 2019-02-01 | 2019-05-17 | 淮阴工学院 | A kind of method that numerical control four-axis horizontal milling machine realizes vertical conversion |
| CN109947049A (en) * | 2019-04-08 | 2019-06-28 | 大连理工大学 | A kind of cutter appearance angle feasible zone method for solving based on stagger |
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| CN110221576A (en) * | 2019-05-20 | 2019-09-10 | 大连理工大学 | The five-axis machining tool shaft linear optimization method of interference and kinematical constraint |
| CN113031516A (en) * | 2021-03-01 | 2021-06-25 | 上海智能制造功能平台有限公司 | Plane compensation trajectory optimization method and device considering diameter of milling cutter |
| CN113618253A (en) * | 2020-05-08 | 2021-11-09 | 大族激光科技产业集团股份有限公司 | Laser processing method, laser processing system, laser processing controller and storage medium |
| CN114117777A (en) * | 2021-11-23 | 2022-03-01 | 广西科技大学 | Vector transformation calculation method of laser cladding vector |
| CN115328030A (en) * | 2022-09-02 | 2022-11-11 | 江南大学 | Blade five-axis machining numerical control program evaluation and optimization method |
| CN113031516B (en) * | 2021-03-01 | 2024-10-22 | 上海智能制造功能平台有限公司 | Plane compensation track optimization method and device considering milling cutter diameter |
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| CN109375579A (en) * | 2018-12-13 | 2019-02-22 | 武汉科技大学 | Five-axis numerical control machining cutter posture planning method based on kinematics |
| CN109759627A (en) * | 2019-02-01 | 2019-05-17 | 淮阴工学院 | A kind of method that numerical control four-axis horizontal milling machine realizes vertical conversion |
| CN109947049B (en) * | 2019-04-08 | 2020-05-19 | 大连理工大学 | Tool attitude angle feasible region solving method based on swing error |
| CN109947049A (en) * | 2019-04-08 | 2019-06-28 | 大连理工大学 | A kind of cutter appearance angle feasible zone method for solving based on stagger |
| CN110032140A (en) * | 2019-04-16 | 2019-07-19 | 南京工业大学 | Spherical cutter shaft vector planning method in five-axis machining |
| CN110221576B (en) * | 2019-05-20 | 2020-08-14 | 大连理工大学 | Interference and kinematic constraint five-axis machining cutter shaft linear optimization method |
| CN110221576A (en) * | 2019-05-20 | 2019-09-10 | 大连理工大学 | The five-axis machining tool shaft linear optimization method of interference and kinematical constraint |
| CN113618253A (en) * | 2020-05-08 | 2021-11-09 | 大族激光科技产业集团股份有限公司 | Laser processing method, laser processing system, laser processing controller and storage medium |
| CN113618253B (en) * | 2020-05-08 | 2023-06-23 | 大族激光科技产业集团股份有限公司 | Laser processing method, system, laser processing controller and storage medium |
| CN113031516A (en) * | 2021-03-01 | 2021-06-25 | 上海智能制造功能平台有限公司 | Plane compensation trajectory optimization method and device considering diameter of milling cutter |
| CN113031516B (en) * | 2021-03-01 | 2024-10-22 | 上海智能制造功能平台有限公司 | Plane compensation track optimization method and device considering milling cutter diameter |
| CN114117777A (en) * | 2021-11-23 | 2022-03-01 | 广西科技大学 | Vector transformation calculation method of laser cladding vector |
| CN115328030A (en) * | 2022-09-02 | 2022-11-11 | 江南大学 | Blade five-axis machining numerical control program evaluation and optimization method |
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