CN107065770A - High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone - Google Patents

High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone Download PDF

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CN107065770A
CN107065770A CN201710301544.5A CN201710301544A CN107065770A CN 107065770 A CN107065770 A CN 107065770A CN 201710301544 A CN201710301544 A CN 201710301544A CN 107065770 A CN107065770 A CN 107065770A
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point
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cutter
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CN107065770B (en
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冯毅雄
王琪瑞
王绪鹏
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Zhejiang University ZJU
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/45—Nc applications
    • G05B2219/45136—Turning, lathe

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  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
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Abstract

The invention discloses a kind of High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone.It is constant with top rake first to be20 0 Method generate initial cutter path, set up the boundary condition and object function of generating tool axis vector；Then the cutter shaft feasible zone of point of contact in cutter track is carried out to equidistant discrete, the composition feasible domain model of discretization；Secondly each euclidean distance between node pair on adjacent feasible arc is calculated, and penalty is applied to the length of side more than threshold value；Finally application digraph method finds most short cutter path, and fairing is carried out to cutter path.This method combination machine tool motion configuration carries out generating tool axis vector fairing, avoid lathe shaft rotary corner excessive, extruding cutting curved surface influences Forming Quality, corner total journey of the lathe rotating shaft in High-speed machining process is reduced, and largely reduces the amount of calculation of computer.

Description

High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone
Technical field
The invention belongs to Milling Process field, add more particularly, to a kind of high speed based on cutter shaft discretization feasible zone Work cutter shaft method for fairing.
Background technology
For five complicated shaft end Milling Machinings, cutter path planning is often confined to how to avoid interference with, obtains maximum processing Bandwidth, but when cutter shaft single corner is excessive, rotation non-continuous event can be produced, cause lathe to shake, molded surface is caused Excessive compression, easily causes workpiece functional form face to scrap and cutter interference.When cutter axis orientation vector is conllinear with workpiece law vector, The region that the processing stand is referred to as near singular point, singular point is referred to as singular regionses, when cutter shaft passes through singular regionses, cutter shaft corner It can increased dramatically, this phenomenon is referred to as Singular point, cutter shaft single corner described above is excessive including this phenomenon.
(the mechanical engineering journal, 2009,45 (9) such as Luo Ming:158-163) combine the mechanical feature of lathe, it is indicated that lathe turns Monotone Mappings relation between axle and cutter top rake, and generating tool axis vector on wall scroll track is optimized, realize lathe angle Generating tool axis vector fairing under speed, machining interference and the limitation of lathe angular acceleration.(the mechanical engineering journal, 2012,48 such as Zhang Yongnian (5)：180-186) consider the factors such as crudy, material removing rate, cutter shaft fairing, set up adjacent cutter shaft fairness measurement Index, and to normalize Measure Indexes weighting as the target component of optimal tool orientation, with generating tool axis vector to crudy Many-side influence is converted into many spring mechanical equilibrium points problem in Gaussian sphere.Cutting quality evaluating is equivalent to spring Potential energy, optimal solution is equivalent to by controlled particle coordinate, the optimal tool orientation scheme sought under multifactor impact.CN 102528554A substitutes the cutter shaft of singular regionses using the average value of the generating tool axis vector of the non-singularity zone before and after singular regionses Vector, the purpose of singular regionses cutter path double optimization is reached with this；But the cutter shaft of singular regionses that this method is obtained In the range of the cutter shaft feasible zone that vector might not be in this place.
Existing processing method, is all based on greatly the optimization for the generating tool axis vector sequence that Machine kinematics level is provided, and what is had is logical Cross polynomial interpolator to solve the problems, such as singular point, but so can directly increase amount of calculation, increase the calculating time；What is had passes through The method of double optimization solves the problems, such as singular point, but this considers other restrictive conditions such as cutter shaft feasible zone, So can might not well ensure crudy and efficiency.And existing optimal tool orientation method is mostly not attached Plus the optimization to continuous cutter path of condition, substantial amounts of calculating cost can be wasted.
The content of the invention
The problems such as to solve singular point and the big generating tool axis vector sequence calculating cost in Milling Process, the invention provides one Plant the High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone.
A kind of High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone, comprises the following steps：
1) constant with top rake is that 20 ° of method generates initial cutter path；
2) boundary condition and object function of generating tool axis vector are set up；
3) the cutter shaft feasible zone of each point of contact in cutter track is carried out to equidistant discrete, the composition feasible domain model of discretization；
4) distance on adjacent feasible arc between any two node is calculated, penalty then is applied to the side more than threshold value；
5) application digraph method finds most short cutter path.
The step 2) in set up generating tool axis vector boundary condition and object function it is specific as follows：
A) boundary condition is set up, to the cutter path that point of contact number is n, the feasible zone of a cutter point of contact in office is seen Make a circular arc, then the feasible zone of cutter shaft is described as [τmin,τmax], wherein τ is the angle of feasible arc and point of contact normal vector；
B) object function：Define between i-th and i+1 point of contact apart from DiFor lathe turns to from i-th of point of contact During i+1 point of contact, the angle R that A axles and C axles are rotatedAiAnd RCiIn maximum, wherein 1≤i≤n be any point of contact compile Number：
Di=max (RAi,RCi),
Wherein,
RCi=| Ai+1-Ai|,
CiAnd Ci+1Respectively cutter shaft at i-th and i+1 point of contact with the angles of lathe C axles,
AiAnd Ai+1Respectively cutter shaft in i-th and the angle of i+1 point of contact and lathe A axles,
Set object function be
The step 4) calculate on adjacent feasible arc, the distance between any two node, and the side application more than threshold value is punished Penalty function, it is specific as follows：
C) distance of k-th of node to j-th of node on i+1 point of contact on i-th of point of contact is calculatedAccording to Lathe parameter sets threshold value
If d)It is then rightApply penalty, use
SubstituteT is strength of punishment coefficient, t>1.
The step 5) in application digraph method find the specific as follows of most short cutter path：
E) assignment is carried out to each node in cutter path on the feasible arc of each point of contact, the implication of the value is from initial Point of contact to the node on the point of contact beeline, for j-th of node of i+1 point of contactFor setIn minimum value；
F) in the assignment procedure more than, the minimum corresponding rail of node of numerical value is obtained on the feasible arc of last point of contact Mark, i.e. most short cutter path.
On the one hand this method solves the problems, such as the singular point that cutter path is present by applying the method for penalty, it is ensured that The surface quality of workpiece, on the other hand finds most short cutter path, it is ensured that the processing efficiency of workpiece by digraph method.Together When, it is discrete by being carried out to feas ible space, the conversion of continuous tool path optimization problem for discrete tool path optimization Problem, largely reduces the calculating cost of cutter path, improves computational efficiency.
Brief description of the drawings
Fig. 1 is cutter shaft discretization feasible zone model schematic；
Fig. 2 is to find most short cutter path schematic diagram with digraph method；
Fig. 3 is to implement the cutter shaft corner figure that the method that constant top rake is 20 ° is calculated；
Fig. 4 is application this method but the optimal cutter shaft corner figure being not added with the conditions of penalty；
Fig. 5 is to set penalty parameter to be αmax=2 °, n=2 cutter shaft corner figure.
Embodiment
The inventive method is described in further detail below in conjunction with the accompanying drawings.
This method is used for the workpiece of processing one 40 × 40, the used a diameter of 8mm of corner rounding(milling) cutter, and chamfer radius are 1mm.Lathe model JDVT600, relevant parameter is as follows：
The maximum (top) speed of lathe C axles：NC=20r/min,
Interpolation cycle：tp=1.8ms,
Lathe allows feed speed：MC∈ [850mm/min, 10000mm/min],
Cutter path step-length：S=0.25mm,
Single interpolation maximum the anglec of rotation be：nc=NC·tp=0.216 °,
Single step maximum machining time be：T0=S/MCmin=0.01764s=17.64ms,
Single step maximum interpolation number of times：N=T0/tp=17.64ms/18ms=9.8, takes n=10,
The hard-over of admissible lathe single step feeding is φmax=nnc=2.16 °,
To simplify calculating and rotational angle is less than φmax, take
Constant with top rake is that 20 ° of method generates initial cutter path, and it is P to obtain numbering in Fig. 11P2P3P4... Cutter path, this cutter path has 160 point of contact, and corresponding cutter shaft corner figure is Fig. 3.As can be seen from the figure cutter rail Mark accumulation corner locally lies in the problem of cutter shaft corner is excessive close to 180 °.；
Cutter shaft feasible zone [the τ of each point of contact is determined using discrete point cloud methodmin,τmax], for each point of contact, its knife Axle feasible zone is exactly the boundary condition of the permission rotation space, i.e. cutter shaft of cutter shaft herein, and wherein τ is feasible arc and point of contact normal direction The angle of amount；.
Due to lathe single revolution time in the axle of A, C two the maximum side of rotational angle determine, therefore defined herein i-th Apart from D between i+1 point of contactiFor, lathe from i-th of point of contact turn to i+1 point of contact when, A axles and C axles are rotated Angle RAiAnd RCiIn maximum, wherein being 1≤i≤n any point of contact numbering：
Di=max (RAi,RCi),
Wherein：
RCi=| Ai+1-Ai|,
CiAnd Ci+1Respectively cutter shaft at i-th and i+1 point of contact with the angles of lathe C axles,
AiAnd Ai+1Respectively cutter shaft in i-th and the angle of i+1 point of contact and lathe A axles,
Object function is set to make the total journey of the corner of lathe minimum, i.e.,：
Cutter shaft feasible zone is carried out in equidistant discrete, the feasible domain model of composition, such as Fig. 1 P1Corresponding feasible arc is discrete to be 4 nodes；
Calculate distance of k-th of node to j-th of node on i+1 point of contact on i-th of point of contactAccording to machine Bed parameter setting threshold valueTake t=2；
IfIt is then rightApply penalty, setting penalty is
T is strength of punishment coefficient, t>1,
Substituted with E correspondingFairing is carried out to cutter path.
When cutter axis orientation vector is conllinear with workpiece law vector, the processing stand turns into the region near singular point, singular point Referred to as singular regionses.Because Singular point refers to, when cutter shaft passes through singular regionses, the phenomenon that cutter shaft corner can increased dramatically, because The present invention the problem of all single cutter shaft corners are excessive is can solve the problem that in implementation process, so the present invention solve it is unusual Point problem.
Assignment, the implication of the value are carried out to each node in cutter path on the feasible arc of each point of contact with digraph method For the beeline of the node from initial point of contact to the point of contact.Fig. 2 is to find most short cutter path with digraph method Schematic diagram, P0For the initial position of cutter, P1For first point of contact on workpiece.It can be found from point of contact using the above method P0To point of contact P2Shortest path beAnd now：
Understood in assignment procedure more than, the minimum node of numerical value is obtained on the feasible arc of last point of contact corresponding Track, i.e. most short cutter path.
As shown in figure 4, under initial tool track, to be still not added with penalty using this method, obtained accumulation knife Have corner and minimum cutter path corner figure.It can see in figure, the method can make the reduction of cutter accumulation corner a lot, The total journey of corner still has the problem of cutter shaft corner is excessive about 115 ° at some point of contact.
As shown in figure 5, being us using the optimized algorithm for adding penalty, maximum is limited by the method for weighting Cutting-tool angle changes, and big corner is not selected, and setsThe ultimate range quilt of i.e. adjacent generating tool axis vector Limitation is less than 2 °.Final accumulation corner is 128.10, although cutter accumulation corner is relative to the calculation for being above not added with penalty Method has increase, but singular point problem is solved.Therefore this method finally ensure that the crudy of workpiece, although sacrifice The total journey of corner of some cutters, but the final total journey of cutter corner, are obtained much smaller than with cutter shaft constant inclination angle for 20 ° of method The total journey of corner of the cutter path arrived, so this method is effective.

Claims (4)

1. a kind of High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone, it is characterised in that comprise the following steps：
1) constant with top rake is that 20 ° of method generates initial cutter path；
2) boundary condition and object function of generating tool axis vector are set up；
3) the cutter shaft feasible zone of each point of contact in cutter track is carried out to equidistant discrete, the composition feasible domain model of discretization；
4) distance on adjacent feasible arc between any two node is calculated, penalty then is applied to the side more than threshold value；
5) application digraph method finds most short cutter path.
2. set up according to the method described in claim 1, it is characterised in that the step 2) generating tool axis vector boundary condition and Object function it is specific as follows：
A) boundary condition is set up, to the cutter path that point of contact number is n, the feasible zone of a cutter point of contact in office regards one as Circular arc, then the feasible zone of cutter shaft be described as [τmin,τmax], wherein τ is the angle of feasible arc and point of contact normal vector；
B) object function：Define between i-th and i+1 point of contact apart from DiFor lathe turns to i+1 from i-th of point of contact During point of contact, the angle R that A axles and C axles are rotatedAiAnd RCiIn maximum, wherein 1≤i≤n be any point of contact numbering：
Di=max (RAi,RCi),
Wherein,
<mrow> <msub> <mi>R</mi> <mrow> <mi>A</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>|</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>|</mo> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>&amp;le;</mo> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mo>-</mo> <mo>|</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>|</mo> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>&gt;</mo> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>
RCi=| Ai+1-Ai|,
CiAnd Ci+1Respectively cutter shaft at i-th and i+1 point of contact with the angles of lathe C axles,
AiAnd Ai+1Respectively cutter shaft in i-th and the angle of i+1 point of contact and lathe A axles,
Set object function be
<mrow> <mi>min</mi> <mo>{</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>D</mi> <mi>i</mi> </msub> <mo>|</mo> <msub> <mi>&amp;tau;</mi> <mi>i</mi> </msub> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mi>min</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mi>max</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>,</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mi>min</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mi>max</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>}</mo> <mo>.</mo> </mrow>
3. calculate according to the method described in claim 1, it is characterised in that the step 4) on adjacent feasible arc, any two section Distance between point, and penalty is applied to the side more than threshold value, it is specific as follows：
C) distance of k-th of node to j-th of node on i+1 point of contact on i-th of point of contact is calculatedAccording to lathe Parameter setting threshold value
If d)It is then rightApply penalty, use
SubstituteT is strength of punishment coefficient, t>1.
4. application digraph method finds most short sword tool according to the method described in claim 1, it is characterised in that the step 5) Path it is specific as follows：
E) assignment is carried out to each node in cutter path on the feasible arc of each point of contact, the implication of the value is from initial contact The beeline to the node on the point of contact is put, for j-th of node of i+1 point of contactFor setIn minimum value；
F) in the assignment procedure more than, the minimum corresponding track of node of numerical value is obtained on the feasible arc of last point of contact, That is most short cutter path.
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CN110362039A (en) * 2018-04-11 2019-10-22 华中科技大学 A kind of five-axis robot workpiece placing attitude optimization method
CN110456731A (en) * 2019-08-13 2019-11-15 成都飞机工业（集团）有限责任公司 A kind of numerical control cutting geometry knife rail feature extracting method
CN110658783A (en) * 2019-09-24 2020-01-07 华中科技大学 Solving method and system for feasible region of five-axis machining cutter shaft
WO2020034277A1 (en) * 2018-08-14 2020-02-20 南京工大数控科技有限公司 Discrete measurement and control online execution method
CN112051803A (en) * 2020-09-17 2020-12-08 华南理工大学广州学院 Small line segment fairing method based on space plane normal vector

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CN112051803A (en) * 2020-09-17 2020-12-08 华南理工大学广州学院 Small line segment fairing method based on space plane normal vector
CN112051803B (en) * 2020-09-17 2022-02-08 华南理工大学广州学院 Small line segment fairing method based on space plane normal vector

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