CN106897501B - Towards the positioning and optimizing method based on blade parts deformation in adaptive machining - Google Patents
Towards the positioning and optimizing method based on blade parts deformation in adaptive machining Download PDFInfo
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Abstract
The present invention proposes a kind of positioning and optimizing method towards based on blade parts deformation in adaptive machining, and the design section line according to the n item in blade design model along long-pending folded axle direction parallelly distribute on first obtains detection sectional plane lineParameter expression, next establishes the multiple objective function of positioning and optimizing, and constraint when carrying out multiple-objection optimization solution is established, it finally optimizes, by the shape of mathematical optimization models section line to achieve the purpose that find target processing curve in preform.The present invention finds target processing curve using the non-uniform profile degree tolerance in blade type face as geometry constraint conditions, in constraint, to meet subsequent blade profile testing requirements, improves the qualification rate of product.And positioning and optimizing method proposed by the present invention allows design section line to deform in constraint, while guaranteeing that detection sectional plane wire shaped and design section line are closest, improves the ability for searching out processable curved surface.
Description
Technical field
It is specifically a kind of based on non-equal the present invention relates to the positioning and optimizing field of blade parts in adaptive machining
The blade profile line of even profile tolerance tolerance constraints deforms positioning and optimizing method.
Background technique
In recent years, near-net-shape+accurate digital control technique realizes that the adaptive machining of the preforming blade of small surplus becomes main
The measurement point that trend, i.e. preforming blade after finish forge/essence casting are obtained by on-machine measurement with design a model do optimization be registrated, according to
Nc program is compensated according to the positioning posture of optimization rear blade.But since blade space is complex-shaped, near-net-shape technique
Blade afterwards causes adaptive machining position fixing process to can not find target processing curve and becomes waste product there may be mass defect, leaf
Piece is a huge loss for enterprise as mass production and period longer expensive high precision part.Therefore close
The target processing curve as programming foundation, the conjunction to blade is improved are found in preform after net forming technology as far as possible
Lattice rate has very important meaning.
Document " blade processing surplus adaptive optimization method [J] computer technology and development based on on-line checking,
2014,24 (11): 226-229. " is directed to the problem of blade blank allowance balance unevenness, establishes machining allowance adaptive optimization
Uniform mathematical model realizes the accurate positioning of blade.This method thinks design basis and machining benchmark the conversion weight when blade
After conjunction, designs a model and do the European transformation in space in preform to meet allowance for finish, but finding best orientation
There is no the profile tolerance tolerance for considering blade profile line during posture, the blade after causing finishing exceeds when detecting blade profile
Form tolerance and become waste product；Furthermore current positioning and optimizing method thinks that workpiece is rigid, cutting for blade is not recognized
Upper thread can deform in its profile tolerance tolerance constraints region, and the blade of small surplus will cause and can not find target processing song
Face and be mistakenly considered " waste product ", therefore current positioning and optimizing method be not fully suitable for near-net-shape class blade adaptive plus
Work.
Summary of the invention
Machined surface profile degree tolerance is not considered about in order to solve existing method during blade adaptive machining positioning and optimizing
Beam and the low both of these problems of searching target processing curve ability.The invention proposes one kind towards in adaptive machining be based on leaf
The positioning and optimizing method of piece class part deformation can not only meet the form tolerance requirement of subsequent detection blade profile, but also
The blade that current localization method is considered " scrapping " can be saved.
Blade is by family's design section line traffic control, and design section line can be divided into leaf basin, blade back, preceding according to function difference
Four partial region of edge and rear, the present invention is using the non-uniform profile degree tolerance of design section line as geometry constraint conditions, by excellent
Change the shape for the section line that designs a model to achieve the purpose that find target processing curve in preform.
The technical solution adopted by the present invention to solve the technical problems are as follows:
A kind of positioning and optimizing method towards based on blade parts deformation in adaptive machining, it is characterised in that:
The following steps are included:
Step 1: according to the n item in blade design model along the design section line of long-pending folded axle direction parallelly distribute onThe l bars detection sectional plane line is obtained using following stepsParameter expression, l=1,2 ... n；
Step 1.1: design section line is indicated using cubic B-spline parametric equation:
Wherein Ni,3It (t) is the basic function of B-spline Curve, ViFor the coordinate of the control vertex of B-spline curves, m0It indicates
The quantity of control vertex；
Step 1.2: design section line is around reference axis x, the postrotational parameter expression of y, z are as follows:
Wherein Rl=Rx(αl)·Ry(θl)·Rz(βl) be the l bars design section line spin matrix, Rx(αl) it is the l articles
Design section line rotates around x axis αlThe spin matrix at angle, Ry(θl) it is that the l bars design section line around y-axis rotates θlThe spin moment at angle
Battle array, Rz(βl) it is the l bars design section line around z-axis rotation βlThe spin matrix at angle；
Step 1.3: the spin matrix according to design section line obtains postrotational design section line base vector；Then it adjusts
CurvePosition of the control vertex on base vector direction obtain deformed sections lineWherein the shift in position amount of i-th of control vertex of the l bars design section line is { Δ x 'i,l,Δ
y′i,l}；
Step 1.4: by deformed sections lineSetting-out generates target processing curve s (u, v)；Target adds
The parametric equation of work curved surface s (u, v) is
Wherein Ni,3(u),Nj,3It (v) is respectively basic function of the Bicubic B-Spline Surfaces on the direction u and v, n1For u direction
The number of upper control vertex, m1For the number of control vertex on the direction v, Vi,jFor the control vertex coordinate of target processing curve；
Step 1.5: for the l bars design section line, according to its height z in the direction zl, calculate s (u, v)=zlWhen friendship
Point parameterN0Indicate the number of intersection point parameter；It willSubstitute into mesh
Processing curve parametric equation is marked, the coordinate of discrete point is obtainedAccording to discrete point coordinate, utilize
Interpolation method obtains the l bars detection sectional plane lineParameter expression；
Step 2: the detection sectional plane line obtained according to step 1Parameter expression, establish positioning
The multiple objective function of optimization, optimization aim are that detection sectional plane line and corresponding design section wire shaped are closest；
Step 3: establish constraint when carrying out multiple-objection optimization solution: including
Constraint 1, detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back are within upper profile tolerance tolerance range
Constraint function
WhereinIndicate that the l articles detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back exist
Upper profile tolerance tolerance rangePoint；
Constraint 2, detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back are except bottom profiled degree tolerance range
Constraint function
WhereinIndicate that the l articles detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back exist
Bottom profiled degree tolerance rangePoint；Indicate in the l articles profile tolerance tolerance range o'clock the l articles detect
Corresponding closest approach on section line；It indicates on the l bars detection sectional plane line outside the unit of corresponding closest approach
Method arrow；I1=1,2 ... N1, i2=1,2 ... N2, i3=1,2 ... N3, i4=1,2 ... N4, N1,N2,N3,N4Respectively before section line
The quantity of edge, rear, leaf basin and the point in blade back region；
Constrain 3, constraint function F of the blade blank measurement point on the outside of target processing curve2:
F2=(pi-s(ui,vi))·ni>=0 i=1,2 ... N
Wherein piIndicate that on-machine measurement obtains the ith measurement point of the blade blank after near-net-shape technique, N is measurement point
Quantity；s(ui,vi) it is closest approach of the ith measurement point on target processing curve, niIndicate closest approach s (ui,vi) in target
The outer method arrow of unit on processing curve；
Constraint 4, the line segment of detection sectional plane line are interior without inflection point constraint；
Step 4: with design section lineAround x, y, z-axis rotates angle { αl,θl,βl, l=1,2 ... n
And variation { the Δ x ' of control vertexi,l,Δy′i,l, i=1,2 ... m0For optimized variable, the multiple target that step 2 is established
Function optimizes, the design section line after being optimized, and obtains target processing curve s (u, v).
Further preferred embodiment, a kind of positioning and optimizing towards based on blade parts deformation in adaptive machining
Method, it is characterised in that: the profile tolerance tolerance range of the l bars design section line is
N (t)=t (t) × ez
WhereinFor the upper profile tolerance band of the l bars design section line,For upper profile variation amount, n (t) is design
Section lineMethod is sweared outside the unit of parameter t,For the bottom profiled tolerance range of the l bars design section line,For bottom profiled
Departure；T (t) is design section lineArrow, e are cut in the unit of parameter tzIndicate the unit vector in the direction z；To set
Count section lineArrow is cut in the single order of parameter t.
Further preferred embodiment, a kind of positioning and optimizing towards based on blade parts deformation in adaptive machining
Method, it is characterised in that: constrained in the line segment of detection sectional plane line without inflection point are as follows: the controlling polygon convex-concave of detection sectional plane line line segment
Property is consistent.
Further preferred embodiment, a kind of positioning and optimizing towards based on blade parts deformation in adaptive machining
Method, it is characterised in that: multiple objective function are as follows:
WhereinIndicate that the single order of the l bars design section line cuts arrow,Indicate the single order of the l bars detection sectional plane line
Cut arrow；Indicate the l articles design section curvature of a curve,Indicate the l articles detection sectional plane curvature of a curve,Indicate the l articles
The second order of design section line cuts arrow,Indicate that the second order of the l bars detection sectional plane line cuts arrow.
Beneficial effect
The present invention compares traditional surplus optimization method and has the advantages that
1. the present invention finds target in constraint using the non-uniform profile degree tolerance in blade type face as geometry constraint conditions
Processing curve improves the qualification rate of product to meet subsequent blade profile testing requirements.
2. current positioning and optimizing method can not find target processing curve for the blade of small surplus after near-net-shape technique
And using blade as " waste product ", positioning and optimizing method proposed by the present invention allows design section line to deform in constraint,
Guarantee that detection sectional plane wire shaped and design section line are closest simultaneously, improves the ability for searching out processable curved surface.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Above-mentioned and/or additional aspect of the invention and advantage will become from the description of the embodiment in conjunction with the following figures
Obviously and it is readily appreciated that, in which:
Fig. 1 blade positioning and optimizing flow diagram.
Fig. 2 blade design a model and the design requirement schematic diagram of type face section line.
Section line setting-out after Fig. 3 rotational deformation is curved surface schematic diagram.
The detection sectional plane line schematic diagram of Fig. 4 blade.
Fig. 5 B-spline curves concavity and convexity judges schematic diagram.
Fig. 6 is certain section Line contour degree tolerance range schematic diagram.
The relation schematic diagram of preform and the blade that designs a model before Fig. 7 positioning and optimizing.
The relation schematic diagram of preform and the blade that designs a model after Fig. 8 positioning and optimizing.
The relation schematic diagram of detection sectional plane line and profile tolerance tolerance after Fig. 9 positioning and optimizing.
Specific embodiment
The embodiment of the present invention is described below in detail, the embodiment is exemplary, it is intended to it is used to explain the present invention, and
It is not considered as limiting the invention.
By taking blade shown in Fig. 2 as an example, according to the process in summary of the invention, the present invention is made into one referring to attached drawing 3-9
The explanation of step, the specific steps of which are as follows:
Step 1: according to 5 in blade design model along the design section line of long-pending folded axle direction parallelly distribute on(meaning of unified representation design in subscript d text), obtains detection sectional plane line using following stepsThe parameter expression of (meaning of unified representation detection in subscript m text), l=1,2 ... 5.
Step 1.1: design section line is indicated using cubic B-spline parametric equation:
Wherein Ni,3It (t) is the basic function of B-spline Curve, ViFor the coordinate of the control vertex of B-spline curves, m0It indicates
The quantity of control vertex.
Step 1.2: design section line is around reference axis x, the postrotational parameter expression of y, z are as follows:
Wherein Rl=Rx(αl)·Ry(θl)·Rz(βl) be the l bars design section line spin matrix, Rx(αl) it is the l articles
Design section line rotates around x axis αlThe spin matrix at angle, Ry(θl) it is that the l bars design section line around y-axis rotates θlThe spin moment at angle
Battle array, Rz(βl) it is the l bars design section line around z-axis rotation βlThe spin matrix at angle.
Step 1.3: the spin matrix according to design section line obtains postrotational design section line base vector；Then it adjusts
CurvePosition of the control vertex on base vector direction obtain deformed sections lineWherein the shift in position amount of i-th of control vertex of the l bars design section line is { Δ x 'i,l,Δ
y′i,l}。
Blade profile line is deformed by adjustment B-spline curvesControl vertex along base vector
Position realize, section lineNot parallel xoy plane, therefore the base vector of plane after rotation need to be found.
The base vector of design section line is { (el,x,el,y) | l=1,2 ... 5 }, the base vector of plane is { (e ' after rotationl,x,e′l,y)=
(el,x·Rl,el,y·Rl) | l=1,2 ... 5 }, wherein (el,x,el,y) it is basal orientation of the l bars design section line on x, the direction y
Amount, (e 'l,x,e′l,y) it is the base vector of the l articles postrotational section line planar.Therefore the expression formula of section line after deforming
Are as follows:
ΔViFor the variation of i-th of control vertex, above formula be may also indicate that are as follows:
WhereinRespectively deformed section line is in x, y, the coordinate components on the direction z, { Δ
x′i,l,Δy′i,lIt is respectively section line after the l articles rotationI-th of control vertex along base vector (e 'l,x,e′l,y)
The amount of movement in direction.
Step 1.4: by deformed sections lineSetting-out generates target processing curve s (u, v)；Target processing
The parametric equation of curved surface s (u, v) is
I.e.
Wherein sx(u,v),sy(u,v),sz(u, v) is respectively x of the target processing curve at parameter (u, v), y, z value,
Vx,Vy,VzThe respectively coordinate V of control vertexi,jIn x, the component of y, z, Ni,3(u),Nj,3It (v) is respectively bi-cubic B spine song
Basic function of the face on the direction u and v, n1For the number of control vertex on u direction, m1For the number of control vertex on the direction v, Vi,j
For the control vertex coordinate of target processing curve.
Step 1.5: solving detection sectional plane lineSubstantially solve target processing curve s (u, v) with
The intersection of the xoy plane of specified altitude assignment.The equation of the l articles plane are as follows: Z=zl, wherein zlWith the l bars design section lineIn z
The height in direction is the same.For the l bars design section line, according to its height z in the direction zl, calculate s (u, v)=zlWhen
Intersection point parameterN0Indicate the number of intersection point parameter.
It is solved using Newton iteration method, it is contemplated that design section line rotates angle very little, uses design section line's
ParameterDetection sectional plane line is calculated as Newton iteration methodParameterInitial value, and parameterFor
[0,1] it is discrete severalIt obtains.
It willTarget processing curve parametric equation is substituted into, the coordinate of discrete point is obtainedAccording to discrete point coordinate, the l bars detection sectional plane line is obtained using cubic spline interpolation methodParameter expression.
If the l bars detection sectional plane lineParametric equation are as follows:
WhereinFor the control vertex coordinate of detection sectional plane line, p (t) is discrete point coordinate, and parametric equation can be expressed as
It solves above-mentioned matrix equation and obtains the control vertex of curveIt is determined by the control vertex and knot vector of curve
Detection sectional plane lineParameter expression.
Step 2: the detection sectional plane line obtained according to step 1Parameter expression, establish positioning
The multiple objective function of optimization, optimization aim are that detection sectional plane line and corresponding design section wire shaped are closest.
Multiple objective function are as follows:
WhereinIndicate that the single order of the l bars design section line cuts arrow,Indicate the single order of the l bars detection sectional plane line
Cut arrow；Indicate the l articles design section curvature of a curve,Indicate the l articles detection sectional plane curvature of a curve,Indicate the l articles
The second order of design section line cuts arrow,Indicate that the second order of the l bars detection sectional plane line cuts arrow.
Step 3: establish constraint when carrying out multiple-objection optimization solution: including
Constraint 1, detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back are within upper profile tolerance tolerance range
Constraint function
WhereinIndicate the l articles detection sectional plane line leading edge, four partial region of rear, leaf basin and blade back
In upper profile tolerance tolerance rangePoint；
Constraint 2, detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back are except bottom profiled degree tolerance range
Constraint function
WhereinIndicate the l articles detection sectional plane line leading edge, four partial region of rear, leaf basin and blade back
In bottom profiled degree tolerance rangePoint；Indicate in the l articles profile tolerance tolerance range o'clock the l articles examine
Survey corresponding closest approach on section line；Indicate the list of corresponding closest approach on the l bars detection sectional plane line
The outer method arrow in position；I1=1,2 ... N1, i2=1,2 ... N2, i3=1,2 ... N3, i4=1,2 ... N4, N1,N2,N3,N4Respectively section line
The quantity of leading edge, rear, leaf basin and the point in blade back region；
Constraint 3 will guarantee that target processing curve has machining allowance, then must assure that each measurement point in target processing curve
Outside, so establishing constraint function F of the blade blank measurement point on the outside of target processing curve2:
F2=(pi-s(ui,vi))·ni>=0 i=1,2 ... N
Wherein piIndicate that on-machine measurement obtains the ith measurement point of the blade blank after near-net-shape technique, N is measurement point
Quantity；s(ui,vi) it is closest approach of the ith measurement point on target processing curve, niIndicate closest approach s (ui,vi) in target
The outer method arrow of unit on processing curve；
Constraint 4, the line segment of detection sectional plane line are interior without inflection point constraint；
Detection sectional plane lineMathematic(al) representation be B-spline Curve.By the convex of B-spline curves
Packet property is it is found that when its controlling polygon is convex polygon, then its curve is convex curve；When controlling polygon is concave polygon
When, then curve is concave curve.Guarantee in curved section that then the controlling polygon convex-concave property of substantially section inner curve is without inflection point
It is consistent,
Establish the constraint f without inflection point in convex detection sectional plane line segment1For
Establish the constraint f without inflection point in recessed detection sectional plane line segment2For
viFor i-th of control vertex of curve, vi,x,vi,yFor the x of i-th of control vertex, y-coordinate component, vkIt is recessed for curve
The boundary control vertex of convexity.
And it constrains profile tolerance tolerance range in 1 and constraint 2 and is established by following procedure:
.The profile tolerance tolerance of blade profile line is considered design section lineAlong the offset line of normal distance, blade
Section line can be divided into leaf basin, blade back, leading edge, four partial region of rear according to scope difference, and the profile tolerance of this four parts is public
Difference requires different, the mathematic(al) representation of the l articles design section line tolerance range are as follows:
N (t)=t (t) × ez
WhereinFor the upper profile tolerance band of the l bars design section line,For upper profile variation amount (subscript U Wen Zhongtong
One meaning indicated, the meaning in subscript L text under unified representation), n (t) is design section lineOutside the unit of parameter t
Method arrow,For the bottom profiled tolerance range of the l bars design section line,For bottom profiled departure；T (t) is design section lineArrow, e are cut in the unit of parameter tzIndicate the unit vector in the direction z；For design section lineThe one of parameter t
Rank cuts arrow.
Step 4: with design section lineAround x, y, z-axis rotates angle { αl,θl,βl, l=1,2 ... 5
And variation { the Δ x ' of control vertexi,l,Δy′i,l, i=1,2 ... m0For optimized variable, the multiple target that step 2 is established
Function optimizes, and obtains detection sectional plane line.
The design section line of solution is around x, and y, the results are shown in Table 1 for z-axis rotation and the translational movement along base vector, excellent
Preform before change is with the relationship that designs a model as shown in fig. 7, preform after optimization and the relationship to design a model
As shown in figure 8, the relationship of detection sectional plane line and profile tolerance tolerance after optimization is as shown in Figure 9.The present invention is seen from optimum results
Positioning and optimizing method preform do not have to have found target processing curve in the case where machining allowance, while meeting blade type
The requirement of face form tolerance.
1 optimized variable result of table
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art are not departing from the principle of the present invention and objective
In the case where can make changes, modifications, alterations, and variations to the above described embodiments within the scope of the invention.
Claims (4)
1. it is a kind of towards in adaptive machining based on blade parts deformation positioning and optimizing method, it is characterised in that: including with
Lower step:
Step 1: according to the n item in blade design model along the design section line of long-pending folded axle direction parallelly distribute onThe l bars detection sectional plane line is obtained using following stepsParameter expression, l=1,2 ... n；
Step 1.1: design section line is indicated using cubic B-spline parametric equation:
Wherein Ni,3It (t) is the basic function of B-spline Curve, ViFor the coordinate of the control vertex of B-spline curves, m0Indicate control
The quantity on vertex；
Step 1.2: design section line is around reference axis x, the postrotational parameter expression of y, z are as follows:
Wherein Rl=Rx(αl)·Ry(θl)·Rz(βl) be the l bars design section line spin matrix, Rx(αl) it is the l articles design
Section line rotates around x axis αlThe spin matrix at angle, Ry(θl) it is that the l bars design section line around y-axis rotates θlThe spin matrix at angle, Rz
(βl) it is the l bars design section line around z-axis rotation βlThe spin matrix at angle；
Step 1.3: the spin matrix according to design section line obtains postrotational design section line base vector；Then curve is adjustedPosition of the control vertex on base vector direction obtain deformed sections lineIts
In the l bars design section line i-th of control vertex shift in position amount be { Δ x 'i,l,Δy′i,l}；
Step 1.4: by deformed sections lineSetting-out generates target processing curve s (u, v)；Target processing curve
The parametric equation of s (u, v) is
Wherein Ni,3(u),Nj,3It (v) is respectively basic function of the Bicubic B-Spline Surfaces on the direction u and v, n1To be controlled on u direction
The number on vertex, m1For the number of control vertex on the direction v, Vi,jFor the control vertex coordinate of target processing curve；
Step 1.5: for the l bars design section line, according to its height z in the direction zl, calculate s (u, v)=zlWhen intersection point ginseng
NumberN0Indicate the number of intersection point parameter；It willTarget is substituted into add
Work surface parameter equation obtains the coordinate of discrete pointAccording to discrete point coordinate, interpolation is utilized
Method obtains the l bars detection sectional plane lineParameter expression；
Step 2: the detection sectional plane line obtained according to step 1Parameter expression, establish positioning and optimizing
Multiple objective function, optimization aim are that detection sectional plane line and corresponding design section wire shaped are closest；
Step 3: establish constraint when carrying out multiple-objection optimization solution: including
Constrain 1, the constraint of detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back within upper profile tolerance tolerance range
Function
WhereinIndicate the l articles detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back in upper wheel
Wide degree tolerance rangePoint；
Constrain 2, the constraint of detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back except bottom profiled degree tolerance range
Function
WhereinIndicate the l articles detection sectional plane line leading edge, rear, leaf basin and four partial region of blade back in lower whorl
Wide degree tolerance rangePoint；Indicate in the l articles profile tolerance tolerance range o'clock in the l articles detection sectional plane
Corresponding closest approach on line；Indicate the outer method of the unit of corresponding closest approach on the l bars detection sectional plane line
Arrow；I1=1,2 ... N1, i2=1,2 ... N2, i3=1,2 ... N3, i4=1,2 ... N4, N1,N2,N3,N4Respectively section line leading edge,
The quantity of rear, leaf basin and the point in blade back region；
Constrain 3, constraint function F of the blade blank measurement point on the outside of target processing curve2:
F2=(pi-s(ui,vi))·ni>=0 i=1,2 ... N
Wherein piIndicate that on-machine measurement obtains the ith measurement point of the blade blank after near-net-shape technique, N is the number of measurement point
Amount；s(ui,vi) it is closest approach of the ith measurement point on target processing curve, niIndicate closest approach s (ui,vi) processed in target
The outer method arrow of unit on curved surface；
Constraint 4, the line segment of detection sectional plane line are interior without inflection point constraint；
Step 4: with design section lineAround x, y, z-axis rotates angle { αl,θl,βl, l=1,2 ... n and
Variation { the Δ x ' of control vertexi,l,Δy′i,l, i=1,2 ... m0For optimized variable, the multiple objective function that step 2 is established
It optimizes, the design section line after being optimized, and obtains target processing curve s (u, v).
2. a kind of positioning and optimizing method towards based on blade parts deformation in adaptive machining according to claim 1,
It is characterized by: the profile tolerance tolerance range of the l bars design section line is
N (t)=t (t) × ez
WhereinFor the upper profile tolerance band of the l bars design section line,For upper profile variation amount, n (t) is design section
LineMethod is sweared outside the unit of parameter t,For the bottom profiled tolerance range of the l bars design section line,It is inclined for bottom profiled
Residual quantity；T (t) is design section lineArrow, e are cut in the unit of parameter tzIndicate the unit vector in the direction z；For design
Section lineArrow is cut in the single order of parameter t.
3. a kind of positioning and optimizing side towards based on blade parts deformation in adaptive machining according to claim 1 or claim 2
Method, it is characterised in that: constrained in the line segment of detection sectional plane line without inflection point are as follows: the controlling polygon concavity of detection sectional plane line line segment
Matter is consistent.
4. a kind of positioning and optimizing method towards based on blade parts deformation in adaptive machining according to claim 3,
It is characterized by: multiple objective function are as follows:
WhereinIndicate that the single order of the l bars design section line cuts arrow,Indicate that the single order of the l bars detection sectional plane line is cut
Arrow；Indicate the l articles design section curvature of a curve,Indicate the l articles detection sectional plane curvature of a curve,Indicate that the l articles sets
The second order of meter section line cuts arrow,Indicate that the second order of the l bars detection sectional plane line cuts arrow.
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| CN108536932B (en) * | 2018-03-26 | 2020-07-28 | 华中科技大学 | Aviation blade stacking axis verticality calculation method based on mutual torsion constraint condition |
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