CN106126930A - A kind of machine tooling boundary of stability's fast solution method based on two way classification - Google Patents
A kind of machine tooling boundary of stability's fast solution method based on two way classification Download PDFInfo
- Publication number
- CN106126930A CN106126930A CN201610472814.4A CN201610472814A CN106126930A CN 106126930 A CN106126930 A CN 106126930A CN 201610472814 A CN201610472814 A CN 201610472814A CN 106126930 A CN106126930 A CN 106126930A
- Authority
- CN
- China
- Prior art keywords
- grid
- boundary
- stability
- sub
- way classification
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16Z—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS, NOT OTHERWISE PROVIDED FOR
- G16Z99/00—Subject matter not provided for in other main groups of this subclass
Landscapes
- Numerical Control (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a kind of machine tooling boundary of stability's fast solution method based on two way classification, comprise the steps: parameter preset plane, sentence steady function and iterations, parameter plane is carried out Preliminary division；Utilize two dimension two way classification that each grid is again divided into less sub-grid；Numerical integrating is utilized to solve the functional value sentencing steady function on the summit of each sub-grid, it is judged that whether sub-grid is for comprising grid；The non-grid that comprises again being divided and judges, if being still the non-grid that comprises, then terminating, otherwise, it is thus achieved that newly comprise grid；Utilizing two dimension two way classification is less sub-grid by all stress and strain model that comprise obtained；Repeat to judge and divide, Step wise approximation f (x) curve, until it reaches preset iterations；The all grids that comprise finally obtained are carried out linear interpolation, obtains approximation and sentence steady zero of a function, draw scatterplot and obtain boundary of stability.The present invention can effectively reduce the calculating time, reaches the purpose of rapid solving boundary of stability.
Description
Technical field
The present invention relates to Machine-settings optimization and milling stability analysis field, particularly relate to asking of boundary of stability
Solve, more particularly, to a kind of machine tooling boundary of stability's fast solution method based on two way classification.
Background technology
Complex free curved surface class part (such as impeller, blade, propeller etc.) is tied due to thin-walled, cantilever etc. in the course of processing
Structure feature, stiffness by itself is weak, if machined parameters selection is improper in the course of processing, can frequently result in course of processing unstability, sends out
The phenomenons such as raw tremor, and then cause manufacturing deficiency, cause the problems such as equipment fault, and the abrasion of cutter can be accelerated.Wherein, add
Work unstability refers to due to the interaction generation judder between cutter and workpiece in the course of processing, its mainly by resonance and
Tremor causes, and relative to processing resonance, processing tremor is difficult to avoid that.Therefore, in order to reduce the impact of processing tremor, need to select
Reasonably machined parameters, and carry out processing stability analysis, solve processing stability border (also known as flap figure).
At present, solving processing stability has multiple method, and the coefficient of zero order proposed such as Altintas, Budak et al. is average
Method (ZOA), the timing departure method (TFEA) that Bayly et al. proposes, the semi-discrete method that Insperger, Stepan et al. propose
(SDM) and firelight or sunlight et al. the approximate shceme method (FDM) proposed of fourth and numerical integrating (NIM) (YeDing, LiMinZhu,
XiaoJianZhangandHanDing,
NumericalIntegrationMethodforPredictionofMillingStabilit y,
JournalofManufacturingScienceandEngineering, 133 (3), 031005, Jun08,2011) etc..On an equal basis
Under the conditions of, the computational efficiency of numerical integrating is better than additive method, and precision is higher, is the most outstanding to solve processing stability
One of method.It is contemplated that solving of stable region needs discrete parameter territory plane, the calculating speed of numerical integrating is the most not
Enough fast, especially parameter field discrete point is more when, calculate the longest, it is difficult to meet engineering actual demand.
Summary of the invention
For disadvantages described above or the Improvement requirement of prior art, the invention provides a kind of machine tooling based on two way classification
Boundary of stability's fast solution method, it participates in the interstitial content calculated, and utilizes in using two dimension two way classification parameters optimization territory
Numerical integrating solves the characteristic root of kinetics equation transfer matrix at parameter field discrete grid block node, can significantly reduce parameter field
The number of interior nodes, reduces the calculating time, reaches the purpose of rapid solving boundary of stability.
For achieving the above object, the present invention proposes a kind of machine tooling boundary of stability's rapid solving based on two way classification
Method, comprises the steps:
(1) parameter plane on preset need Numerical solution border boundary condition, sentence steady function f (x) and iterations, root
Parameter plane needed for obtaining according to described boundary condition, carries out Preliminary division to described parameter plane, is divided into P × Q
Grid；
Wherein: described in sentence steady function f (x) and be specially at given grid node and sentence steady bar according to what Floquet theorem provided
Part, its functional value uses equation below to calculate:
F (x)=ρ (Φ)-1；
In formula: ρ (Φ)=max{ | λi| it is the spectral radius of Φ, Φ is for being tried to achieve by numerical integrating at given grid node
Floquet transfer matrix, λiEigenvalue for transfer matrix Φ；
(2) utilize two dimension two way classification that described each grid is divided again, be divided into less sub-grid；
(3) apex at each sub-grid utilize numerical integrating solve described in sentence the functional value of steady function f (x), right
In each sub-grid, if the functional value of f (x) has contrary sign in four summits, then this sub-grid is for comprising grid, otherwise, then and this son
Grid is non-to comprise grid；
(4) the described non-grid that comprises is performed step (2)～(3) to twice, non-comprise grid if remained as, then tie
Bundle；Otherwise, it is thus achieved that new comprises grid, and turns to step (5)；
(5) all of acquisition in step (3) and (4) are comprised grid repeated execution of steps (2)～(4), Step wise approximation f
(x) curve, until it reaches described default iterations；
(6) all grids that comprise finally obtained are carried out linear interpolation, obtain the zero point sentencing steady function f (x) of approximation,
Scatterplot is drawn, it is thus achieved that required boundary of stability according to described zero point.
As it is further preferred that described parameter plane is two dimensional surface, this two dimensional surface with cutting speed as transverse axis, with
Cutting depth is the longitudinal axis.
As it is further preferred that described P and Q is respectively less than 5, described two dimension two way classification refers specifically to that each plane is had battery limit (BL)
Territory is divided into four less bounded subregions similar to former region.
As it is further preferred that described utilize numerical integrating to solve to sentence the functional value of steady function f (x) and refer specifically to: profit
Try to achieve work in-process with numerical integrating and give the Floquet transfer matrix at grid node, the spectral radius of transfer matrix is subtracted
1 is gone to obtain functional value.
As it is further preferred that in described four summits the functional value of f (x) have contrary sign to refer specifically to each grid four top
It is positive sign during functional value symbol difference at Dian or is asynchronously negative sign.
As it is further preferred that described all grids that comprise finally obtained are carried out linear interpolation, obtain approximation
The zero point sentencing steady function f (x) specifically includes following steps: set the two contrary sign apex coordinates comprising grid and functional value is respectively
(x1,y1,f1), (x2,y2,f2), due to functional value f1With f2Contrary sign, then between this two summit, existence function value is the zero point of 0, if
The coordinate of this zero point and functional value are (x0,y0, 0), then utilize following formula to calculate the coordinate figure of zero point, it is thus achieved that to sentence steady function f (x)
Zero point:
x0=x1-f1·(x2-x1)/(f2-f1)=(x1·f2-x2·f1)/(f2-f1)；
y0=y1-f1·(y2-y1)/(f2-f1)=(y1·f2-y2·f1)/(f2-f1)。
As it is further preferred that described step (3) also includes sub-step (3.1): by the coordinate on each sub-grid summit
And the functional value of correspondence stores, and set up look-up table.
In general, by the contemplated above technical scheme of the present invention compared with prior art, mainly possess following
Technological merit:
1. the present invention uses two dimension two way classification to divide whole parameter plane, is obtained by iteration and comprises stability limit
The part on boundary, to participate in the interstitial content calculated in parameters optimization territory, thus reduces the calculating time, can be significantly during calculating
The number of reduction parameter field interior nodes, thus the boundary of stability in quick obtaining milling, for selecting suitably processing in processing
Technological parameter provides foundation, it is achieved efficient, Precision Machining in processing.
2. the two-dimentional two way classification used in the present invention has strong robustness, and speed is fast, and the feature of moderate accuracy can be applicable to
The rapid solving of the boundary of stability under multiple processing environment, by being analyzed processing stability, can be effectively ensured and add
Working medium amount, thus reach part is carried out the target of process parameter optimizing and high speed and high precision processing.
Accompanying drawing explanation
Fig. 1 (a) is all grid node schematic diagrams used in two dimension two way classification；
Fig. 1 (b) is the functional image schematic diagram using two dimension two way classification to obtain；
Fig. 1 (c) is directly to draw the functional image schematic diagram obtained；
Fig. 2 be the inventive method be embodied as flow chart；
Fig. 3 is two-dimentional two way classification and the numerical integrating comparison diagram of single-degree-of-freedom milling example；
Fig. 4 is two-dimentional two way classification and the numerical integrating comparison diagram of two degrees of freedom milling example.
Detailed description of the invention
In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, right
The present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, and
It is not used in the restriction present invention.If additionally, technical characteristic involved in each embodiment of invention described below
The conflict of not constituting each other just can be mutually combined.
The ultimate principle of the present invention be use two dimension two way classification parameters optimization territory in participate in the interstitial content of calculating, and utilize
Numerical integrating (NIM) solves the characteristic root of kinetics equation transfer matrix at parameter field discrete grid block node, it is possible to significantly contract
Subtract the number of parameter field interior nodes, reduce the calculating time, reach the purpose of rapid solving boundary of stability, for processing selecting close
Suitable working process parameter provides theoretical foundation, it is achieved processing efficient, accurate in processing.
A kind of based on two way classification machine tooling boundary of stability's fast solution method of the present invention, specifically includes following step
Rapid:
(1) boundary condition of the parameter plane on preset need Numerical solution border and sentence steady function f (x), according to described limit
Parameter plane needed for boundary's condition acquisition, carries out Preliminary division to described parameter plane, is divided into P × Q grid.
In step (1), parameter plane is to be cutting speed by transverse axis, and the longitudinal axis is the two dimensional surface of cutting depth, function f (x)
Be based on that Floquet theorem provides sentences steady condition, and f (x) is (special for Floquet transfer matrix spectral radius at given grid node
Levy the maximum of root absolute value) deduct 1, i.e. set matrix Φ as the Floquet tried to achieve by numerical integrating at given grid node
Transfer matrix, λiFor its eigenvalue, ρ (Φ)=max{ | λi| be the spectral radius of Φ, then f (x)=ρ (Φ)-1, according to Floquet
Theorem, correspond to the boundary of stability of system when f (x) is equal to 0.
Wherein, parameter plane is carried out the Preliminary division complexity mainly in view of boundary of stability and (there may be prominent
Become, spike and isolated island etc.), if directly using two dimension two way classification to be likely to result in erroneous judgement, cause partial trace section lose (such as:
Very difficult search determines the existence of little isolated island, unless through successive ignition), so, the present invention in advance parameter plane is divided into P ×
Q grid (P is horizontal decile number, and Q is longitudinally to wait point number), wherein P and Q is respectively less than 5, is equivalent to whole parameter plane
It is finely divided, the most each grid is analyzed.
(2) utilize two dimension two way classification that described each grid is divided again, be divided into less sub-grid.
Above-mentioned two dimension two way classification is the method that one-dimensional two way classification is extended to two dimensional surface.In one-dimensional two way classification, each
Interval is divided into two subintervals, similar, and in two dimension two way classification, each plane bounded domain is divided into four with former
The less bounded subregion that region is similar, when the method is applied to Calculation of Stability Region, is also constantly to have parameter plane
Boundary region divides, with iterations increase, the grid of division tapers into, its area be inversely proportional to iterations square.
Therefore, by the continuous division of two dimension two way classification so that comprise grid the finest, can obtain when finally carrying out linear interpolation
The boundary of stability that precision is higher.
(3) summit (node) place at each sub-grid utilize numerical integrating solve described in sentence steady function f (x), obtain
Its functional value, for each sub-grid, if the functional value of f (x) has contrary sign (four apex of the most each grid in four summits
Functional value symbol difference time be positive sign or be asynchronously negative sign, at least there are two summit contrary signs), then it is assumed that this sub-grid is
Comprise grid, i.e. including at least a part for f (x) curve in this sub-grid；Otherwise, then it is assumed that this sub-grid is non-to comprise net
Lattice.
Apex at each sub-grid utilize numerical integrating solve sentence steady function f (x) functional value particularly as follows:
The transfer matrix at given node is solved, at the summit (bag of certain sub-grid given first with numerical integrating
Containing cutting rotational speeds Ω=60 T N and cutting depth information apAfter), the Floquet transfer matrix at this node can be obtained, its
Expression formula is:
Wherein Φ is transfer matrix, matrix I1For unit matrix, Matrix C1, D1Can be obtained by three below equation with E
:
Wherein: τ=(T-tf)/n, represents cutter incision section time interval [t0+tf,t0+ T] it is divided into n part.
Wherein M, C, K represent mass of system, damping and rigidity respectively；KcT () is Cutting Force Coefficient period matrix function, i.e.
Kc(t)=Kc(t+T)；
After the conditions such as given processing conditions and time interval centrifugal pump, apCan obtain according to mesh point coordinate with τ: ap
Equal to grid node ordinate of orthogonal axes, i.e. cutting depth；τ can be calculated by grid node transverse axis coordinate；Calculate after obtaining Φ, root
The functional value of f (x) can be drawn according to f (x)=ρ (Φ)-1.
Concrete, assess the functional value at each sub-grid summit (grid node) place, by analyzing each grid four top
The positive negativity of the functional value of point can tentatively judge whether this grid comprises grid.In one-dimensional two way classification, for continuous function,
If the functional value contrary sign of interval two-end-point, then it is assumed that this interval is with the presence of function zero-point.It is similar to, in two dimension two way classification,
If the four of a grid summits existing the situation of the functional value contrary sign of its f (x), then it is assumed that this grid includes f (x) letter
A part for number curve, is defined as comprising grid；Otherwise, then it is assumed that this grid does not comprise curved section, it is defined as non-comprising net
Lattice.
Further, since there is adjacent mesh to be the situation comprising grid, its public vertex (grid node) can be repeated
Calculate.For solving the problems referred to above, the present invention proposes the method reducing grid node number to be calculated: to each net obtained
Coordinate and the functional value thereof of lattice node store, and set up look-up table, carry out tabling look-up to reduce further by look-up routine
The calculating time, if the functional value of grid node is calculated, then can inquire about from look-up table and obtain, otherwise this node be counted
Calculate and store this point coordinates and functional value.
(4) comprise grid for non-, then repeated execution of steps (2)～(3) to twice, be i.e. right with the non-grid that comprises
As, again with two dimension two way classification, the non-grid that comprises is divided again, be divided into less sub-grid, then at each subnet
The apex of lattice utilizes numerical integrating to solve the functional value sentencing steady function f (x), it may be judged whether for the non-network that comprises, if obtained
Sub-grid remain as and non-comprise grid, then terminate；Otherwise, it is thus achieved that new comprises grid, and turns to step (5).
Owing to erroneous judgement can be caused when determination methods searching times is few, it is judged as non-comprising grid if grid will be comprised, then can
The integrity of f (x) function curve that impact approaches, therefore, the present invention reuses two dimension two way classification iteration to the non-grid that comprises
One to twice, if sub-grid is non-to comprise grid the most entirely, then it is assumed that this grid is really for the non-grid that comprises, and terminates this sub-process；
Otherwise, can obtain and new comprise grid, f (x) the function curve integrity approached with guarantee.
(5) all of acquisition in step (3) and (4) are comprised grid repeated execution of steps (2)～(4), Step wise approximation f
(x) curve, until it reaches described default iterations.I.e. again with two dimension two way classification by acquisition in step (3) and (4)
All stress and strain model that comprise are less sub-grid, then with these less sub-networks as object, again at each sub-grid
Apex utilize numerical integrating to solve the functional value sentencing steady function f (x), it may be judged whether for the non-network that comprises, for non-packet
Repeat to divide and calculate containing grid, it is thus achieved that newly comprise grid, with Step wise approximation f (x) curve, until it reaches default iterations
(i.e. repeating step (2)～the number of times of (4)) or required computational accuracy, say, that acquisition is comprised grid Reusability
Two dimension two way classification, continuous tessellated mesh, continuous iteration is until meeting iterations, it is thus achieved that approach f (x) function with higher precision bent
Line comprise grid.
(6) by finally obtain all comprise grid (i.e. after default iterations final obtain all comprise
Grid) carry out linear interpolation, obtain the zero point (i.e. boundary of stability's point) sentencing steady function f (x) of approximation.I.e. change to last
The grid that comprises that generation obtains is analyzed, each comprise grid must at least two summit contrary signs, at two of mutual contrary sign
Carry out linear interpolation between summit, the zero point sentencing steady function f (x) of approximation can be obtained, linearly insert all comprising grid
After value, just can draw the scatterplot of f (x) function zero-point, i.e. form boundary of stability.After obtaining stable type border, work in-process
Suitable machined parameters can be chosen according to stability diagram, not only be avoided that tremor generation but also working (machining) efficiency can be improved, to optimize
Working process parameter.
Linear interpolation is particularly as follows: set the two contrary sign apex coordinates comprising grid and functional value respectively (x thereof1,y1,f1),
(x2,y2,f2), due to functional value f1With f2Contrary sign, then between this two summit, existence function value is the point of 0, if its coordinate and function
Value is (x0,y0, 0), by linear interpolation:
x0=x1-f1·(x2-x1)/(f2-f1)=(x1·f2-x2·f1)/(f2-f1)；
y0=y1-f1·(y2-y1)/(f2-f1)=(y1·f2-y2·f1)/(f2-f1)；
Scatterplot is drawn, it is thus achieved that required boundary of stability according to described zero point coordinate.
It it is below the specific embodiment of the present invention.
Embodiment 1
This embodiment is a single-mode system, carries out milling stability according to the method for the present invention and solves, its step
For:
(1) setup parameter plane, parameter plane is: x-axis is Milling Speed Ω (rpm), up-and-down boundary be 5000rpm～
25000rpm, y-axis is milling depth apM (), up-and-down boundary is 0～0.008m；Function f (x) is the characteristic root sentencing steady matrix
The maximum of absolute value deducts 1；Set radially cutting-in a/D=0.50；Set iterations i=5.Other relevant parameters: milling cutter
Number N of teeth=2；Cutting force COEFFICIENT Kt=6 × 108(N/m2)；Normal direction Cutting Force Coefficient Kn=2 × 108(N/m2)；System is intrinsic
Frequency fn=922 (Hz)；Relative damping ζ=0.011；Model quality mt=0.03993 (kg)；Initial discrete in numerical integrating
Number n=20；Then, the whole parameter plane of Preliminary division, it is divided into 4 × 1 grids, i.e. at the upper decile of x-axis (Milling Speed)
Being 4 sections, divide one section every 5000rpm, keep constant y-axis (milling depth) is upper, grid now is thought to be and is comprised net
Lattice；
(2) all grids that comprise being used two dimension two way classification respectively, each grid is divided into 4 less sub-grids；
(3) four summit (grid node) places at each sub-grid solve and sentence steady function f (x), obtain four nodes
Functional value；All-ones subnet lattice are analyzed, if the functional value at the four of a grid nodes has contrary sign, then it is assumed that this grid
It is to comprise grid, stores coordinate and the functional value of these four nodes of grid, set up look-up routine to carry out calculating next time；
(4) non-comprise grid if having in step (3), then all non-grids that comprise are analyzed, and store this subflow
The new coordinate comprising grid obtained in journey and functional value, for EQUILIBRIUM CALCULATION FOR PROCESS efficiency and computational accuracy, in this example, the most right
The non-grid that comprises that iteration obtains for the first time carries out the computing of this sub-process.
(5) for all grids that comprise obtained in step (3) and (4), repeated execution of steps (2)～(4), Step wise approximation
The curve of f (x), i.e. Step wise approximation milling stability border, until reaching the iterations i=5 set；
(6) the last all grids that comprise obtained are carried out linear interpolation, obtain boundary of stability's point of approximation, and store
Boundary point coordinate, processes border point and draws, it is thus achieved that boundary of stability.After obtaining stable type border, work in-process can
To choose suitable machined parameters according to stability diagram, not only it is avoided that tremor generation but also working (machining) efficiency can be improved, add to optimize
Work technological parameter.Tremor can be caused to produce if choosing machined parameters above stability scatterplot, the surface after impact processing
Quality, and below stability scatterplot, choose machined parameters tremor can be avoided to produce, but in the feelings of unknown stability diagram
Under condition, the machined parameters chosen is less than normal, causes working (machining) efficiency low, and therefore the method according to the invention is obtaining stability diagram
After, suitable machined parameters can be selected, process with high-speed and high-efficiency, can guarantee that crudy simultaneously.
The boundary of stability's result utilizing the present invention to obtain is obtained result with utilizing existing numerical integrating (NIM)
Comparing, the boundary of stability using the method for the present invention to obtain schemes comparison diagram such as Fig. 3 of (lobes figure) and numerical integrating
Shown in, wherein, Fig. 3 (a) is the result figure of the present invention, and Fig. 3 (b) is the result figure of numerical integrating, compared with numerical integrating,
The computational efficiency of the present invention is higher (time is greatly shortened), and calculated result is basically identical, although use two dimension two
The figure that point-score obtains can lose some details (such as spike, little isolated island), but to the choosing of working process parameter in reality processing
Take and do not affect.
Example 2
This embodiment is a coupled system, carries out milling stability according to the method for the present invention and solves, its step
For:
(1) setup parameter plane, parameter plane is: x-axis is Milling Speed Ω (rpm), up-and-down boundary be 5000rpm～
25000rpm；Y-axis is milling depth apM (), up-and-down boundary is 0～0.008m；Function f (x) is the characteristic root sentencing steady matrix
The maximum of absolute value deducts 1；Set radially cutting-in a/D=0.50；Set iterations i=4.Other parameters: cutter tooth number N
=2；Cutting force COEFFICIENT Kt=6 × 108 (N/m2)；Normal direction Cutting Force Coefficient Kn=2 × 108 (N/m2)；System frequency
ωx=ωy=922 (Hz)；Relative damping ζx=ζy=0.011；Model quality mx=my=0.03993 (kg)；Numerical integrating
Middle initial discrete number n=15；Then the whole parameter plane of Preliminary division, is divided into 4 × 1 grids, i.e. in x-axis (milling speed
Degree) on be divided into 4 sections, divide one section every 5000rpm, keep constant y-axis (milling depth) is upper, grid now thinks equal
For comprising grid；
(2) all grids that comprise being used two dimension two way classification respectively, each grid is divided into 4 less sub-grids；
(3) four summit (grid node) places at each sub-grid solve and sentence steady function f (x), obtain four nodes
Functional value；All-ones subnet lattice are analyzed, if the functional value at the four of a grid nodes has contrary sign, then it is assumed that this grid
It is to comprise grid, stores coordinate and the functional value of these four nodes of grid, set up look-up routine to carry out calculating next time；
(4) non-comprise grid if having in step (3), then all non-grids that comprise are analyzed, and store this subflow
The new coordinate comprising grid obtained in journey and functional value thereof, for EQUILIBRIUM CALCULATION FOR PROCESS efficiency and computational accuracy, in this example, only
The non-grid that comprises obtaining first time iteration carries out the computing of this sub-process；
(5) for all grids that comprise obtained in step (3) and (4), step (2)～(4), Step wise approximation f (x) are repeated
Curve, i.e. Step wise approximation milling stability border, until reach set iterations i=4.
(6) the last all grids that comprise obtained are carried out linear interpolation, obtain boundary of stability's point of approximation, and store
Boundary point coordinate, processes border point and draws.
The boundary of stability's result utilizing the present invention to obtain is entered with utilizing existing numerical integrating (NIM) acquisition result
Row compares, and uses boundary of stability's figure (lobes figure) and comparison diagram such as Fig. 4 institute of numerical integrating that the method for the present invention obtains
Showing, wherein, Fig. 4 (a) is the result figure of the present invention, and Fig. 4 (b) is the result figure of numerical integrating, compared with numerical integrating, this
The computational efficiency higher (time is greatly shortened) of invention, and calculated result is basically identical, although use two dimension two points
The figure that method obtains can lose some details (such as spike, little isolated island), but in processing reality, working process parameter is chosen
Not impact.
As it will be easily appreciated by one skilled in the art that and the foregoing is only presently preferred embodiments of the present invention, not in order to
Limit the present invention, all any amendment, equivalent and improvement etc. made within the spirit and principles in the present invention, all should comprise
Within protection scope of the present invention.
Claims (7)
1. machine tooling boundary of stability's fast solution method based on two way classification, it is characterised in that comprise the steps:
(1) parameter plane on preset need Numerical solution border boundary condition, sentence steady function f (x) and iterations, according to institute
State the parameter plane needed for boundary condition obtains, described parameter plane is carried out Preliminary division, is divided into P × Q grid；
Wherein: described in sentence steady function f (x) and be specially at given grid node and sentence steady condition according to what Floquet theorem provided, its
Functional value uses equation below to calculate:
F (x)=ρ (Φ)-1；
In formula: ρ (Φ)=max{ | λi| it is the spectral radius of Φ, Φ is to be tried to achieve by numerical integrating at given grid node
Floquet transfer matrix, λiEigenvalue for transfer matrix Φ；
(2) utilize two dimension two way classification that described each grid is divided again, be divided into less sub-grid；
(3) apex at each sub-grid utilize numerical integrating solve described in sentence the functional value of steady function f (x), for often
Individual sub-grid, if the functional value of f (x) has contrary sign in four summits, then this sub-grid is for comprising grid, otherwise, then this sub-grid
Grid is comprised for non-；
(4) the described non-grid that comprises is performed step (2)～(3) to twice, non-comprise grid if remained as, then terminate；
Otherwise, it is thus achieved that new comprises grid, and turns to step (5)；
(5) all grid repeated execution of steps (2)～(4) of comprising that will obtain in step (3) and (4), Step wise approximation f (x) is bent
Line, until it reaches described default iterations；
(6) all grids that comprise finally obtained are carried out linear interpolation, obtain the zero point sentencing steady function f (x) of approximation, according to
Described zero point draws scatterplot, it is thus achieved that required boundary of stability.
2. machine tooling boundary of stability's fast solution method based on two way classification as claimed in claim 1, it is characterised in that
Described parameter plane is two dimensional surface, and this two dimensional surface is with cutting speed as transverse axis, with cutting depth as the longitudinal axis.
3. machine tooling boundary of stability's fast solution method based on two way classification as claimed in claim 1 or 2, its feature exists
Be respectively less than 5 in, described P and Q, described two dimension two way classification refer specifically to be divided into each plane bounded domain four with former region phase
As less bounded subregion.
4. machine tooling boundary of stability's fast solution method based on two way classification as claimed in claim 3, it is characterised in that
Described utilize numerical integrating to solve to sentence the functional value of steady function f (x) and refer specifically to: utilize numerical integrating try to achieve work in-process to
Determine the Floquet transfer matrix at grid node, the spectral radius of transfer matrix is deducted 1 and obtains functional value.
5. machine tooling boundary of stability's fast solution method based on two way classification as claimed in claim 4, it is characterised in that
In described four summits, the functional value of f (x) has contrary sign to refer specifically to during the functional value symbol difference of each four apex of grid to be
Positive sign or be asynchronously negative sign.
6. machine tooling boundary of stability's fast solution method based on two way classification as claimed in claim 5, it is characterised in that
Described all grids that comprise finally obtained being carried out linear interpolation, the zero point sentencing steady function f (x) obtaining approximation specifically includes
Following steps: set the two contrary sign apex coordinates comprising grid and functional value is respectively (x1,y1,f1), (x2,y2,f2), due to letter
Numerical value f1With f2Contrary sign, then between this two summit, existence function value is the zero point of 0, if the coordinate of this zero point and functional value are (x0,
y0, 0), then utilize following formula to calculate the coordinate figure of zero point, it is thus achieved that to sentence the zero point of steady function f (x):
x0=x1-f1·(x2-x1)/(f2-f1)=(x1·f2-x2·f1)/(f2-f1)；
y0=y1-f1·(y2-y1)/(f2-f1)=(y1·f2-y2·f1)/(f2-f1)。
7. the machine tooling boundary of stability's fast solution method based on two way classification as described in any one of claim 1-6, its
Being characterised by, described step (3) also includes sub-step (3.1): by coordinate and the functional value of correspondence thereof on each sub-grid summit
Store, and set up look-up table.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610472814.4A CN106126930B (en) | 2016-06-24 | 2016-06-24 | A kind of machine tooling boundary of stability's fast solution method based on dichotomy |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610472814.4A CN106126930B (en) | 2016-06-24 | 2016-06-24 | A kind of machine tooling boundary of stability's fast solution method based on dichotomy |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106126930A true CN106126930A (en) | 2016-11-16 |
| CN106126930B CN106126930B (en) | 2018-11-30 |
Family
ID=57265536
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610472814.4A Active CN106126930B (en) | 2016-06-24 | 2016-06-24 | A kind of machine tooling boundary of stability's fast solution method based on dichotomy |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106126930B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107679288A (en) * | 2017-09-11 | 2018-02-09 | 宝鸡石油机械有限责任公司 | Determine the method and assembly method of sealing ring assembling radius bend |
| CN108520117A (en) * | 2018-03-26 | 2018-09-11 | 华中科技大学 | A method of obtaining the stability lobes diagram using approximate shceme method |
| CN113779840A (en) * | 2021-09-14 | 2021-12-10 | 内蒙古工业大学 | Method for determining rolling process parameters of snake-shaped rolled plate |
| CN114352469A (en) * | 2021-12-08 | 2022-04-15 | 国网江西省电力有限公司电力科学研究院 | High-order water turbine regulating system stability region calculation method and system |
-
2016
- 2016-06-24 CN CN201610472814.4A patent/CN106126930B/en active Active
Non-Patent Citations (5)
| Title |
|---|
| DÁNIEL BACHRATHY等: "Bisection method in higher dimensions and the efficiency number", 《PERIODICA POLYTECHNICA MECHANICAL ENGINEERING》 * |
| YE DING等: "Numerical Integration Method for Prediction of Milling Stability", 《JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING》 * |
| 丁汉等: "铣削过程稳定性分析的时域法研究进展等", 《科学通报》 * |
| 丁烨: "铣削动力学—稳定性分析方法与应用", 《中国博士学位论文全文数据库-工程科技I辑》 * |
| 卢晓红等: "铣削过程颤振稳定性分析的研究进展", 《振动与冲击》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107679288A (en) * | 2017-09-11 | 2018-02-09 | 宝鸡石油机械有限责任公司 | Determine the method and assembly method of sealing ring assembling radius bend |
| CN107679288B (en) * | 2017-09-11 | 2021-01-26 | 宝鸡石油机械有限责任公司 | Method for determining assembling bending radius of sealing ring and assembling method |
| CN108520117A (en) * | 2018-03-26 | 2018-09-11 | 华中科技大学 | A method of obtaining the stability lobes diagram using approximate shceme method |
| CN108520117B (en) * | 2018-03-26 | 2020-07-10 | 华中科技大学 | Method for acquiring stability lobe graph by using full-discrete method |
| CN113779840A (en) * | 2021-09-14 | 2021-12-10 | 内蒙古工业大学 | Method for determining rolling process parameters of snake-shaped rolled plate |
| CN114352469A (en) * | 2021-12-08 | 2022-04-15 | 国网江西省电力有限公司电力科学研究院 | High-order water turbine regulating system stability region calculation method and system |
| CN114352469B (en) * | 2021-12-08 | 2024-02-09 | 国网江西省电力有限公司电力科学研究院 | Stability domain calculation method and system for high-order water turbine regulating system |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106126930B (en) | 2018-11-30 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106126930A (en) | A kind of machine tooling boundary of stability's fast solution method based on two way classification | |
| Caretto et al. | Two numerical methods for three-dimensional boundary layers | |
| CN101599104B (en) | Method for simulating blade flutter boundary of aviation turbine engine | |
| CN102945019B (en) | Generation method of planar spiral and annular milling tracks | |
| CN106802630A (en) | The Parallel frequency domain method of the milling parameter stability prediction based on thin-wall part | |
| CN103632006B (en) | Method for determining critical rotating speed of wet rotor of multistage centrifugal pump | |
| CN102262692A (en) | Method for optimizing skins of airplane airfoil by subsonic flutter | |
| CN104007696B (en) | Aircraft structural component cavity complex corner residual region tool path generation method | |
| CN115774903B (en) | Helicopter rotor disk load real-time generation method, device, equipment and medium | |
| CN106940746A (en) | The parallel time domain method of milling parameter stability prediction based on thin-wall part | |
| CN106682262A (en) | Numerical simulation method for obtaining aircraft flow fields | |
| Huo et al. | CNC tool path generation for freeform surface machining based on preferred feed direction field | |
| CN107918957A (en) | A kind of three-dimensional building model simplifying method of holding structure and textural characteristics | |
| CN101114379A (en) | Method for judging point whether or not situated in polygon | |
| CN104361625A (en) | Ray principle based cloud data compaction algorithm with boundary reservation | |
| CN104143214A (en) | Electronic map polygon triangulation method and device | |
| Zatarain et al. | Implicit subspace iteration as an efficient method to compute milling stability lobe diagrams | |
| CN110955934B (en) | Cutting simulation implementation method for real-time processing monitoring | |
| CN101387506A (en) | Point cloud optimum alignment method | |
| Lin et al. | Global uncut regions removal for efficient contour-parallel milling | |
| CN108520117A (en) | A method of obtaining the stability lobes diagram using approximate shceme method | |
| CN103984794A (en) | Fixed-outline integrated circuit floorplanning method for soft module | |
| CN104794747A (en) | Three-dimensional point cloud data simplification algorithm based on ray theory | |
| CN111400969A (en) | Method for accelerating generation of unstructured right-angle grid | |
| CN114036773B (en) | Quick retrieval method for outline geometry of block discrete element numerical model |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |