CN108746795A - A method of flutter in prediction mold cavity numerical control milling - Google Patents
A method of flutter in prediction mold cavity numerical control milling Download PDFInfo
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Abstract
A method of flutter in prediction mold cavity numerical control milling, the present invention relates to the methods of flutter in prediction mold cavity numerical control milling.The problem of the purpose of the present invention is to solve the milling stability prediction technique applicability of existing single cutter path is low, causing milling parameter prediction accuracy low, accelerating tool failure, influence the processing quality of mold cavity.It is a kind of to predict that the method detailed process of flutter in mold cavity numerical control milling is：Step 1 establishes the relative transfer function of tool-workpiece system；The relative transfer function for the tool-workpiece system that step 1 obtains is introduced into three-dimensional milling stability model by step 2, obtains the critical axial cutting depth at milling tool flutter frequency；Step 3: judging whether mold cavity numerical control milling occurs flutter based on the critical axial cutting depth that step 2 obtains.The present invention is used for mold cavity numerical control milling field.
Description
Technical field
The present invention relates to the methods of flutter in prediction mold cavity numerical control milling.
Background technology
Complex-shaped surface mould mold is widely used in the industries such as automobile, aerospace, ship and household electrical appliances, and general requirement has higher
Machining accuracy and surface quality.Usually shape feature is changeable in mold cavity, has irregular wedge angle, fillet or obtuse angle
The transition connection different etc. big low-angle and complicated variable curvature cavity structure, computer numerical control (CNC) Milling Process technology is this
One of important processing method of class workpiece.Computer numerical control at present (CNC) Milling Process technology has obtained good development, has
The advantages that metal-cutting waste is high, workpiece surface quality is good and efficient, but new product or component processing system are still needed
It is prolonged to test to obtain best processing technology.According to the processing conditions of production phase, however it remains to processing result not
The risk known.In addition, adaptive machining control errors and compensation system are not yet included in Universal CNC System completely, for numerical control plus
The operation at work center still relies on the experience and technology of engineer.Some common business software (examples of NC milling at present
Such as UG, MasterCAM, Power Mill) numerical control programming can be carried out, the emulation of process is provided, but be limited primarily to several
What is emulated.And mold cavity is due to diversified shape feature, when application different cutters and different milling parameters, milling
Process cutter and workpiece contact performance real-time change are cut, Milling Force changes greatly, flutter easily occurs, workpiece processing quality is caused to be disliked
Change.Flutter is always a problem in NC Machining Process, the especially mold zero of Low rigidity milling tool processing high-hardness
Part, many times still relies on Test-cut met to determine best milling condition and suitable cutter in digital control processing enterprise, this
Cause enterprise to increase production cost, reduces production efficiency.
Milling stability research is carried out in spite of a large amount of scholars, proposes a variety of milling stability models, but main research collection
In generated in the milling stable region of single cutter path, practical application is confined to single Simulation for tooling path.Bent is become for complexity
For the workpiece of this kind of milling condition consecutive variations of rate type cavity mould, the milling stability prediction technique of single cutter path is applicable in
Property it is low, cause milling parameter prediction accuracy low, accelerate tool failure, influence the processing quality of mold cavity.
Invention content
The purpose of the present invention is to solve the milling stability prediction technique applicability of existing single cutter path is low, lead
The problem of causing milling parameter prediction accuracy low, accelerating tool failure, influence the processing quality of mold cavity, and propose a kind of pre-
The method for surveying flutter in mold cavity numerical control milling.
It is a kind of to predict that the method detailed process of flutter in mold cavity numerical control milling is：
Step 1 establishes the relative transfer function of tool-workpiece system；
The transmission function of cutter subsystem and workpiece subsystem is obtained respectively
Gci(j ω)=Xci(jω)/[Fci(jω)] (1)
Gwi(j ω)=Xwi(jω)/[Fwi(jω)] (2)
In formula：Fci(j ω) and Fwi(j ω) is respectively cutter subsystem point of a knife point and workpiece subsystem workpiece surface milling
The suffered power of point, since the amount of force between cutter and workpiece is equal, direction is on the contrary, i.e. Fci(j ω)=- Fwi(jω)；
Xci(j ω) and Xwi(j ω) is respectively in Fci(j ω) and FwiThe lower displacement generated of (j ω) effect；I=1,2,3 indicate to abide by respectively
Follow X-direction, Y-direction, the Z-direction of the rectangular coordinate system of right-handed Cartesian rectangular coordinate system foundation；
By formula (1) and (2), the relative transfer function of tool-workpiece system is derived：
The relative transfer function for the tool-workpiece system that step 2 obtains step 1 introduces three-dimensional milling stability mould
In type, the critical axial cutting depth at milling tool flutter frequency is obtained；
Step 3: judging whether mold cavity numerical control milling quivers based on the critical axial cutting depth that step 2 obtains
It shakes.
Beneficial effects of the present invention are：
The present invention proposes a kind of method predicted for flutter in complicated variable curvature mold cavity NC milling, can
It is as follows with the effect reached：
1. the present invention can carry out complicated variable curvature mold cavity Milling Processes flutter prediction, become for different curvature
The mold cavity of change selects different milling parameter (radial cutting-in, the speed of mainshaft, axial directions using the cutter of unlike material and diameter
Cutting-in etc.) situations such as can carry out flutter prediction.
2. the present invention is based on the kinetic characteristics that relative transfer function considers cutter subsystem and workpiece subsystem, together
When consider the influence of oscillation crosswise and axial vibration to dynamic cuttings thickness, make flutter prediction it is more accurate.
3. the present invention in the numerical control geometric simulation of different curvature shape feature mold cavity, is avoided when milling condition becomes
The necessity of milling stability flap is repeatedly generated when change, prediction process is convenient and efficient, and milling parameter fast prediction may be implemented,
Efficiency is improved, it is to use the service life to extend cutter, ensure that the processing quality of mold cavity.
The milling stability prediction technique applicability for solving existing single cutter path is low, causes milling parameter prediction accurate
Exactness is low, the problem of accelerating tool failure, influence the processing quality of mold cavity.
In common milling engineering, judges whether that flutter occurs, need by computer, by the editing run to formula,
Result of calculation is obtained, whole process takes around consuming 30 seconds, can just obtain a result, and make corresponding adjustment.And it uses
The method of milling stability flap array is prejudged in milling process, is compared it is only necessary to 1 second time, is shortened 30 times
Time, and milling stability flap array obtain after can permanently use, time saving facility greatly improves milling
The efficiency of journey.
Description of the drawings
Tool-workpiece contact situation schematic diagram when Fig. 1 is mold cavity milling different curvature；
Tool-workpiece contact situation schematic diagram when Fig. 2 is different-diameter Tool in Milling；
Tool-workpiece contact situation schematic diagram when Fig. 3 is milling under different radial cutting-ins, ae1、ae2、ae3For different diameters
To cutting-in；
Fig. 4 is that flow diagram is predicted in flutter in mold cavity numerical control milling；
Fig. 5 is the cutter path schematic diagram of mold cavity Milling Process；
Fig. 6 is the transmission function schematic diagram that embodiment obtains；
Fig. 7 is the cutter path schematic diagram of embodiment mold cavity Milling Process；
Fig. 8 is that cutter is worked into the entrance angle of position 2 by position 1 and cuts out angle change schematic diagram；
Fig. 9 critical axial cutting-in a when being the different speeds of mainshaft and entrance angleplimChange schematic diagram.
Specific implementation mode
Specific implementation mode one：The specific mistake of method of flutter in a kind of prediction mold cavity numerical control milling of present embodiment
Cheng Wei：
Step 1 establishes the relative transfer function of tool-workpiece system；
The kinetic characteristics of tool-workpiece system, i.e. transfer function matrix are obtained, are to carry out Stability of Milling Processes
The important prerequisite of prediction.Previous research only considers the kinetic characteristics of tooling system mostly, and has ignored workpiece system to whole
The influence of body system of processing kinetic characteristics, the present invention has considered cutter subsystem and the dynamics of workpiece subsystem is special
Property, tool-workpiece system integral power model is established based on relative transfer function.
The transmission function of cutter subsystem and workpiece subsystem is obtained respectively
Gci(j ω)=Xci(jω)/[Fci(jω)] (1)
Gwi(j ω)=Xwi(jω)/[Fwi(jω)] (2)
In formula：Fci(j ω) and Fwi(j ω) is respectively cutter subsystem point of a knife point and workpiece subsystem workpiece surface milling
The suffered power of point, since the amount of force between cutter and workpiece is equal, direction is on the contrary, i.e. Fci(j ω)=- Fwi(jω)；
Xci(j ω) and Xwi(j ω) is respectively in Fci(j ω) and FwiThe lower displacement generated of (j ω) effect；I=1,2,3 indicate to abide by respectively
Follow X-direction, Y-direction, the Z-direction of the rectangular coordinate system of right-handed Cartesian rectangular coordinate system foundation；By formula (1) and (2), derive
The relative transfer function of tool-workpiece system：
The relative transfer function for the tool-workpiece system that step 2 obtains step 1 introduces three-dimensional milling stability mould
In type,
Obtain the critical axial cutting depth at milling tool flutter frequency；
Step 3: judging whether mold cavity numerical control milling quivers based on the critical axial cutting depth that step 2 obtains
It shakes.
Specific implementation mode two：The present embodiment is different from the first embodiment in that：By step in the step 2
The relative transfer function of the one tool-workpiece system obtained is introduced into three-dimensional milling stability model, obtains milling tool flutter
Critical axial cutting depth at frequency；Detailed process is：
During three-dimensional milling stability model milling tool mold groove cavity side based on frequency domain method, tangential force
FtAlong milling tool sword Milling Speed directional spreding, radial load FrIt is the radial direction of milling cutter feeding, axial force FaAlong milling cutter axial direction
Effect；In order to consider ordinary circumstance, in milling edge line, milling edge is divided into the small differentiation element of limited quantity.To each
Three direction chiploads of edge cells and corresponding differential loads are assessed, and digital integration is used in combination to predict respectively
The total power in three directions.
In milling edge line, milling edge is divided into M differentiation element, and M values are positive integer；To each edge differentiation element
Three direction chiploads and corresponding differential loads assessed, be used in combination digital integration to predict three directions respectively
Total power；Three directions, that is, tangential force Ft, radial load FrAnd axial force Fa；
If the corner amount of k-th of differentiation element on j-th of milling edgeExpression formula is：
Wherein：Corner amountFor the corner amount of k-th of differentiation element on j-th of milling edge, θr(k, t) is milling
The rotation angle that k-th of differentiation element of sword is measured in cartesian coordinate Y direction, 0≤k≤M；NfIt indicates contained by rose cutter
Cutter tooth quantity, n indicate cutter rotating speed, t is the time；J values are positive integer；
Differentiation element region transient state milling level productIt is transient state depth of cut, Δ a is one
The length of differentiation element；
Tangential force Ft, radial load Fr, axial force FaDifferentiation element on milling cutter milling sword is
dFt=KtcdAc dFr=KrcdAc dFa=KacdAc (5)
K in formulatcFor the Milling force parameter of tangential force, KrcFor the Milling force parameter of radial load, KacFor the Milling Force of axial force
Coefficient；
Tangential force Ft, radial load FrAnd axial force FaIt is converted into the dynamic milling in three directions under cutter cartesian coordinate
Power：
In formulaFor the dynamic milling force of cartesian coordinate X-direction,For cartesian coordinate Y direction
Dynamic milling force,For the dynamic milling force of cartesian coordinate Z-direction, apFor cutter axial direction cutting depth,To turn
Angular amount, KrFor the Milling force parameter of radial load and the ratio between the Milling force parameter of tangential force, Kr=Krc/Ktc；KaFor the milling of axial force
Cut the ratio between force coefficient and the Milling force parameter of tangential force, Ka=Kac/Ktc；Δxj=(xc(t)-xc(t-T))-(xw(t)-xw(t-
T)), Δ yj=(yc(t)-yc(t-T))-(yw(t)-yw(t-T)), Δ zj=(zc(t)-zc(t-T))-(zw(t)-zw(t-T)),
Δxj、Δyj、ΔzjIt is regeneration efficity vibration；
Wherein xc(t) it is X-direction (cartesian coordinate) dynamic displacement of the current cutter tooth of milling cutter, xc(t-T) it is that milling cutter is previous
X-direction (cartesian coordinate) dynamic displacement in cutter tooth period, xw(t) it is X-direction (Descartes of the workpiece under current cutter tooth milling
Coordinate) dynamic displacement, xw(t-T) it is X-direction (cartesian coordinate) dynamic displacement of workpiece under previous cutter tooth period milling；
yc(t) it is Y-direction (cartesian coordinate) dynamic displacement of the current cutter tooth of milling cutter, yc(t-T) it is the previous cutter tooth of milling cutter
Y-direction (cartesian coordinate) dynamic displacement in period, yw(t) it is that (Descartes sits Y-direction of the workpiece under current cutter tooth milling
Mark) dynamic displacement, yw(t-T) it is Y-direction (cartesian coordinate) dynamic displacement of workpiece under previous cutter tooth period milling；
zc(t) it is Z-direction (cartesian coordinate) dynamic displacement of the current cutter tooth of milling cutter, zc(t-T) it is the previous cutter tooth of milling cutter
Z-direction (cartesian coordinate) dynamic displacement in period, zw(t) it is that (Descartes sits Z-direction of the workpiece under current cutter tooth milling
Mark) dynamic displacement, zw(t-T) it is Z-direction (cartesian coordinate) dynamic displacement of workpiece under previous cutter tooth period milling；
T is the period；
[F (t)]=apKtc[A(t)]{Δr} (7)
Wherein：F (t) be withFor the column vector of element, { Δ r } is with Δ xj、Δyj、
ΔzjFor the column vector of element, dynamic milling force direction coefficient matrix [A (t)] is that angular frequency is ω, and the period is the period letter of T
Number；ω=NfΩ, T=2 π/ω；Ω is cutter spindle rotational angular velocity, unit rad/s；
[A (t)] is subjected to Fourier expansion, the Fourier transformation of high-order can obtain more accurately solving, but put into practice
Middle iterative characteristic value search is simultaneously undesirable, obtains mean direction coefficient matrix：
In formula, NfIndicate the cutter tooth quantity contained by rose cutter,For the entrance angle of cutter cutter tooth,For cutter cutter tooth
Cut out angle,For coefficient matrix,For corner amount；
The direction coefficient of dynamic milling process equation is changed according to the contact conditions of cutter and workpiece, by formula (8), by when
Become dynamic milling equation [F (t)] (formula 7) be converted to do not change over time but with the relevant form of tool-workpiece contact state：
[F (t)]=apKtc[A(0)]{Δr} (9)
Wherein,
{ Δ r }={ rc(t)}-{rc(t-T)}-({rw(t)}-{rw(t-T)})
In formula, rc(t) be the X-direction of the current cutter tooth of milling cutter, Y-direction, Z-direction (cartesian coordinate) dynamic displacement arrange to
Amount, rc(t-T) be the X-direction in milling cutter previous cutter tooth period, Y-direction, Z-direction (cartesian coordinate) dynamic displacement arrange to
Amount；
rw(t) it is X-direction, Y-direction, the dynamic displacement column vector of Z-direction of the workpiece under current cutter tooth milling, rw(t-T)
The X-direction, Y-direction, the dynamic displacement column vector of Z-direction that are workpiece under previous cutter tooth period milling；
In the case of single cutter path milling, in the case where milling parameter determines, cutter entrance angle and angle is cut out
Constant, the contact condition of tool-workpiece is fixed.And in complicated variable curvature mold cavity Milling Processes, with cavity song
When line curvature changes, the contact condition of tool-workpiece changes therewith, and cutter entrance angle is different with angle is cut out, such as Fig. 1 institutes
Show.In addition, when using different tool radius with different radial cutting-in, the contact condition of tool-workpiece equally changes, and cutter is cut
It is different with angle is cut out to enter angle, as shown in Figure 2 and Figure 3.Therefore, mold cavity variable curvature curve milling cutter-workpiece contact should be determined
Relationship between state and curvature, tool radius, radial cutting-in；
The curvature expression formula of variable curvature mold cavity curve (x (u), y (u)) is
In formula, u is the parametric variable in variable curvature mold cavity curve parametric equation, and ρ (u) is the song of parameter u corresponding points
Rate, the bending direction of variable curvature curve indicate that negative curvature represented is concave curve, positive number is bent by the positive and negative of curvature of curve
What rate represented is convex curve；X (u), y (u) are the parametric curve under cartesian coordinate, and x ' (u), y ' (u) are to be sat in Descartes
The differential of parametric curve x (u), y (u) under mark system；X " (u), y " (u) is the parametric curve x under cartesian coordinate system
(u), the second-order differential of y (u)；Parameter u is the independent variable of parametric curve；
When cutter climb cutting, the horizontal entrance angle of cutter tooth and cuts out angle and be respectivelyWith
When cutter upmilling, the horizontal entrance angle of cutter tooth and cuts out angle and be respectivelyWith
If the frequency response function of cutter subsystem is Gc(jω)；
The frequency response function of workpiece subsystem is Gw(jω)；
The vibration displacement vector of Tool in Milling is transformed to frequency domain by time domain, the coupling regeneration displacement of milling point is
{ Δ (j ω) }={ rc(jω)}-{roc(jω)}-({rw(jω)}-{row(j ω) })=(1-ejωT)[Gc(jω)
+Gw(jω)]{Fc}ejωT
In formula, rc(j ω) is the frequency domain vibration position of the X-direction of the current cutter tooth of milling cutter, Y-direction, Z-direction (cartesian coordinate)
Move vector, roc(j ω) is the time domain vibration displacement arrow of the X-direction of the current cutter tooth of milling cutter, Y-direction, Z-direction (cartesian coordinate)
Amount, rw(j ω) is the frequency domain vibration displacement of X-direction of the workpiece under current cutter tooth milling, Y-direction, Z-direction (cartesian coordinate)
Vector, row(j ω) is that workpiece is sweared in the time domain vibration displacement of the X-direction, Y-direction, Z-direction (cartesian coordinate) of current cutter tooth
Amount, FcFor the frequency domain of Milling Force；
ω T are the delayed phase between cutter tooth cycle T after generating vibration, are obtained：
{Fc}ejωT=ap[A(0)](1-ejωT)[Gc(jω)+Gw(jω)]{Fc}ejωT (13)
Enable ap[A(0)](1-ejωT)[Gc(jω)+Gw(j ω)] determinant be 0, obtain ap[A(0)](1-ejωT)[Gc(j
ω)+Gw(j ω)] particular solution：
det{[I]-ap[A(0)](1-ejωT)[Gc(jω)+Gw(j ω)] }=0 (14)
The characteristic value of formula (14) is：
A is obtained according to (14) and (15)p[A(0)](1-ejωT)[Gc(jω)+Gw(j ω)] characteristic equation be：
det{[I]+Λ[A(0)][Gc(jω)+Gw(j ω)] }=0 (16)
In formula, det { } is square formation function；
According to given milling tool flutter frequency (known), entrance angle cuts out angle (formula 11 or 12) and cutter-work
Part system transter (formula 3), acquires the characteristic value of formula (16), it is assumed that only considers the direct transmission of tool-workpiece system
Function, ignores the intersection transmission function of tool-workpiece system, and characteristic equation (16) is just reduced to a cubic function：
a3Λ3+a2Λ2+a1Λ+1=0 (17)
The characteristic value Λ of characteristic equation is acquired, because transmission function is plural number, a3Λ3+a2Λ2+a1The characteristic value of Λ+1=0
There are real and imaginary parts, therefore characteristic value Λ=ΛR+iΛI；
In formula, ΛRIt is characterized the real part of value, ΛIIt is characterized the imaginary part of value, i2=-1 is plural number；a1、a2、a3For coefficient；
Acquiring the critical axial cutting depth at milling tool flutter frequency is：
Speed of cutter spindle is converted to obtain by delay period：
In formula：K is the integer for the oscillation mark that milling tool circular arc leaves, that is, the number of stable region curve flap；n
For speed of cutter spindle.
Other steps and parameter are same as the specific embodiment one.
Specific implementation mode three：The present embodiment is different from the first and the second embodiment in that：It is described to work as cutter climb cutting
When, it the horizontal entrance angle of cutter tooth and cuts out angle and is respectivelyWithFormula is：
In formula, RcFor tool radius, aeFor radial cutting depth；
When cutter upmilling, the horizontal entrance angle of cutter tooth and cuts out angle and be respectivelyWithFormula is：
Other steps and parameter are the same as one or two specific embodiments.
Specific implementation mode four：Unlike one of present embodiment and specific implementation mode one to three：Cutter
The frequency response function of system
In formula, Gxxc(j ω) is that cutter subsystem is rung in X-direction (cartesian coordinate) excitation, X-direction (cartesian coordinate)
The direct frequency response function answered, Gxyc(j ω) is that in X-direction (cartesian coordinate) excitation, Y-direction, (Descartes sits cutter subsystem
Mark) response direct frequency response function, Gxzc(j ω) is cutter subsystem in X-direction (cartesian coordinate) excitation, Z-direction (flute card
Your coordinate) response direct frequency response function, Gyxc(j ω) is cutter subsystem (cartesian coordinate) excitation, X-direction in the Y direction
The direct frequency response function of (cartesian coordinate) response, Gyyc(j ω) is cutter subsystem (cartesian coordinate) excitation, Y in the Y direction
The direct frequency response function of direction (cartesian coordinate) response, Gyzc(j ω) is that (cartesian coordinate) swashs cutter subsystem in the Y direction
It encourages, the direct frequency response function of Z-direction (cartesian coordinate) response, Gzxc(j ω) is that in Z-direction, (Descartes sits cutter subsystem
Mark) it encourages, the direct frequency response function of X-direction (cartesian coordinate) response, Gzyc(j ω) is cutter subsystem in Z-direction (flute card
That coordinate) it encourages, the direct frequency response function of Y-direction (cartesian coordinate) response, Gzzc(j ω) is cutter subsystem in Z-direction
The direct frequency response function of (cartesian coordinate) excitation, Z-direction (cartesian coordinate) response；
The frequency response function of workpiece subsystem
In formula, Gxxw(j ω) is that workpiece subsystem is rung in X-direction (cartesian coordinate) excitation, X-direction (cartesian coordinate)
The direct frequency response function answered, Gxyw(j ω) is that in X-direction (cartesian coordinate) excitation, Y-direction, (Descartes sits workpiece subsystem
Mark) response direct frequency response function, Gxzw(j ω) is workpiece subsystem in X-direction (cartesian coordinate) excitation, Z-direction (flute card
Your coordinate) response direct frequency response function, Gyxw(j ω) is workpiece subsystem (cartesian coordinate) excitation, X-direction in the Y direction
The direct frequency response function of (cartesian coordinate) response, Gyyw(j ω) is workpiece subsystem (cartesian coordinate) excitation, Y in the Y direction
The direct frequency response function of direction (cartesian coordinate) response, Gyzw(j ω) is that (cartesian coordinate) swashs workpiece subsystem in the Y direction
It encourages, the direct frequency response function of Z-direction (cartesian coordinate) response, Gzxw(j ω) is that in Z-direction, (Descartes sits workpiece subsystem
Mark) it encourages, the direct frequency response function of X-direction (cartesian coordinate) response, Gzyw(j ω) is workpiece subsystem in Z-direction (flute card
That coordinate) it encourages, the direct frequency response function of Y-direction (cartesian coordinate) response, Gzzw(j ω) is workpiece subsystem in Z-direction
The direct frequency response function of (cartesian coordinate) excitation, Z-direction (cartesian coordinate) response.
Other steps and parameter are identical as one of specific implementation mode one to three.
Specific implementation mode five：Unlike one of present embodiment and specific implementation mode one to four：The step 3
In the critical axial cutting depth that is obtained based on step 2 judge whether mold cavity numerical control milling occurs flutter；Detailed process
For：
From mold cavity geometrical model milling numerical control code and Frequency-domain Stability flap construction algorithm, flutter has been derived
Stability prediction algorithm.The method specific implementation process of the prediction mold cavity milling parameter is as shown in Figure 4.
The kinetic characteristics for obtaining cutter subsystem and workpiece subsystem, obtain its transmission function.Cutter subsystem transmits
Function is obtained by the methods of mode experiment, RCSA or theoretical modeling, and workpiece subsystem transmission function passes through mode experiment, limited
The methods of member emulation obtains；The transmission function of two subsystems is imported in formula (3) again, it is opposite to obtain tool-workpiece system
Transmission function；Step 1 has obtained；
Cutter entrance angle is determined according to the information of Common Use Tools, common workpiece information, radial cutting depth bounds etc. and is cut
The variation range of angle of departure, which covers the common situations of mold cavity milling as possible, in conjunction with range of spindle speeds and upper one
The acquired tool-workpiece system relative transfer function of step generates stability flap array；
For a certain given mold cavity Milling Process condition, angle-determining is cut out according to the speed of mainshaft and milling cutter
Milling stability, the axial cutting depth a for the neutrality that step 2 is obtainedplimIt is defined as array, i.e., in speed of mainshaft model
It encloses and is cut out in angular region with entrance angle, any speed of mainshaft and entrance angle cut out angle all corresponding there are one the axial directions of neutrality
Cutting depth aplim.Step 2 has obtained；
For the NC milling of given die workpiece cavity, according to the initial number that usual processing experience is given
Milling condition is controlled, that is, selects cutter, selected milling parameter, selected Processing Strategies and planning cutter path.Fig. 5 show carry out mould
Have the cutter path of pocketing processing, formula (11) and formula (12) is utilized to calculate between cutter and workpiece with this condition
Situation is contacted, cutter cutter tooth entrance angle is obtained and cuts out angle, in conjunction with known cutter speed of mainshaft information in milling stability leaf
The axial cutting depth a of corresponding neutrality is found in valve arrayplim；
The milling that flutter prediction algorithm refers to the speed of mainshaft in NC geometric simulation models and incision is cut out under angle is steady
Critical Stability axial direction cutting depth (a in qualitative arrayplim) and practical axial cutting depth (ap) strictly compared；
It repeats step 2 and obtains the critical axial cutting depth under all rotating speeds, obtained all critical axial directions are cut
Cut depth aplimIt is defined as array, cutter cutter tooth entrance angle is calculated using formula (11) and formula (12) and cuts out angle, in conjunction with
Speed of cutter spindle forms milling stability flap array, according to cutter cutter tooth entrance angle, cuts out angle and speed of cutter spindle
Find the axial cutting depth a of corresponding neutrality in milling stability flap arrayplim, aplimIt is deep with practical axial cutting
Spend apIt compares；
If apLess than aplim, predict that milling is stablized, chatter phenomenon do not occur；If apMore than or equal to aplim, prediction generation
Chatter phenomenon.
Beneficial effects of the present invention are verified using following embodiment：
Embodiment one：
The method of flutter is specifically prepared according to the following steps in a kind of prediction mold cavity numerical control milling of the present embodiment：
This method is applied to mold cavity Milling Process, cutter subsystem transmission function, workpiece are obtained according to step 1
Subsystem transmission function obtains the relative transfer function of tool-workpiece system, as shown in Figure 6 on this basis.
Using CAM softwares by the tool paths generation numerical control code of planning, Fig. 7 indicates the cutter path generated, primary election
Axial milling depth is 0.7mm, and radial milling depth is 1mm, and cutter diameter is 20mm, calculates cutter and workpiece contact performance,
Fig. 8 shows cutter entrance angles when being worked into position 2 by position 1 and the situation of change for cutting out angle.
With the reduction of entrance angle, the critical axial cutting depth of stability curve, as shown in Figure 9.For given mould
Have cavity workpiece and cutter, flutter stability array can be generated before Numerical Control SimulationSide of the present invention
Method is calculated according to tool-workpiece contact situationVariation, and in flutter stability arrayIn extract pair
The a answeredplim, with actual apIt is compared.
When the pocketing speed of mainshaft is 5500rpm, different entrance angles and critical axial direction cutting-in a when angle is cut outplimSuch as Fig. 9
It is shown, it can obtain entrance angle (1.9rad) in given Working position and cut out the critical axial cutting-in at angle (3.14rad)
aplimIt is 0.56mm, and primary election axial direction cutting-in apIt is 0.7mm, is higher than aplim, predicted in this way in speed of mainshaft 5500rpm
Cutting out processing under angle (1.9rad, 3.14rad) with entrance angle becomes unstable, and flutter occurs.
When the pocketing speed of mainshaft is 7500rpm, entrance angle (1.9rad) can be obtained in fig.9 and cuts out angle
The critical axial cutting-in a of (3.14rad)plimIt is 0.89mm, is higher than the axial cutting-in a of primary electionp.This method is predicted in the speed of mainshaft
7500rpm and entrance angle cut out processing under angle (1.9rad, 3.14rad) and keep stablizing.
Claims (5)
1. a kind of method of flutter in prediction mold cavity numerical control milling, it is characterised in that：The method detailed process is：
Step 1 establishes the relative transfer function of tool-workpiece system；Detailed process is：
The transmission function of cutter subsystem and workpiece subsystem is obtained respectively
Gci(j ω)=Xci(jω)/[Fci(jω)] (1)
Gwi(j ω)=Xwi(jω)/[Fwi(jω)] (2)
In formula：Fci(j ω) and Fwi(j ω) is respectively suffered by cutter subsystem point of a knife point and workpiece subsystem workpiece surface milling point
Power, since the amount of force between cutter and workpiece is equal, direction is on the contrary, i.e. Fci(j ω)=- Fwi(jω)；Xci(jω)
And Xwi(j ω) is respectively in Fci(j ω) and FwiThe lower displacement generated of (j ω) effect；I=1,2,3 indicate to follow right hand flute respectively
X-direction, Y-direction, the Z-direction for the rectangular coordinate system that karr rectangular coordinate system is established；
By formula (1) and (2), the relative transfer function of tool-workpiece system is derived：
The relative transfer function for the tool-workpiece system that step 1 obtains is introduced into three-dimensional milling stability model by step 2,
Obtain the critical axial cutting depth at milling tool flutter frequency；
Step 3: judging whether mold cavity numerical control milling occurs flutter based on the critical axial cutting depth that step 2 obtains.
2. a kind of method for predicting flutter in mold cavity numerical control milling according to claim 1, it is characterised in that：The step
The relative transfer function for the tool-workpiece system that step 1 obtains is introduced into three-dimensional milling stability model in rapid two, is obtained
Critical axial cutting depth at milling tool flutter frequency；Detailed process is：
During three-dimensional milling stability model milling tool mold groove cavity side based on frequency domain method, tangential force FtEdge
Milling tool sword Milling Speed directional spreding, radial load FrIt is the radial direction of milling cutter feeding, axial force FaAxially make along milling cutter
With；
In milling edge line, milling edge is divided into M differentiation element, and M values are positive integer；
If the corner amount of k-th of differentiation element on j-th of milling edgeExpression formula is：
Wherein：Corner amountFor the corner amount of k-th of differentiation element on j-th of milling edge, θr(k, t) is milling edge kth
The rotation angle that a differentiation element is measured in cartesian coordinate Y direction, 0≤k≤M；NfIndicate the knife contained by rose cutter
Number of teeth amount, n indicate the rotating speed of cutter, and t is the time；J values are positive integer；
Differentiation element region transient state milling level product
Wherein：It is transient state depth of cut, Δ a is the length of a differentiation element；
Tangential force Ft, radial load Fr, axial force FaDifferentiation element on milling cutter milling sword is
dFt=KtcdAc dFr=KrcdAc dFa=KacdAc (5)
K in formulatcFor the Milling force parameter of tangential force, KrcFor the Milling force parameter of radial load, KacFor the Milling Force system of axial force
Number；
Tangential force Ft, radial load FrAnd axial force FaIt is converted into the dynamic milling force in three directions under cutter cartesian coordinate：
In formulaFor the dynamic milling force of cartesian coordinate X-direction,For the dynamic of cartesian coordinate Y direction
Milling Force,For the dynamic milling force of cartesian coordinate Z-direction, apFor cutter axial direction cutting depth,For corner amount,
KrFor the Milling force parameter of radial load and the ratio between the Milling force parameter of tangential force, Kr=Krc/Ktc；KaFor the Milling Force system of axial force
The ratio between the Milling force parameter of number and tangential force, Ka=Kac/Ktc；Δxj=(xc(t)-xc(t-T))-(xw(t)-xw(t-T)), Δ yj
=(yc(t)-yc(t-T))-(yw(t)-yw(t-T)), Δ zj=(zc(t)-zc(t-T))-(zw(t)-zw(t-T)), Δ xj、Δ
yj、ΔzjIt is regeneration efficity vibration；
Wherein xc(t) it is the X-direction dynamic displacement of the current cutter tooth of milling cutter, xc(t-T) it is the X-direction in milling cutter previous cutter tooth period
Dynamic displacement, xw(t) it is X-direction dynamic displacement of the workpiece under current cutter tooth milling, xw(t-T) be workpiece in previous cutter tooth
X-direction dynamic displacement under period milling；
yc(t) it is the Y-direction dynamic displacement of the current cutter tooth of milling cutter, yc(t-T) it is the Y-direction in milling cutter previous cutter tooth period dynamic
Displacement, yw(t) it is Y-direction dynamic displacement of the workpiece under current cutter tooth milling, yw(t-T) be workpiece in the previous cutter tooth period
Y-direction dynamic displacement under milling；
zc(t) it is the Z-direction dynamic displacement of the current cutter tooth of milling cutter, zc(t-T) it is the Z-direction in milling cutter previous cutter tooth period dynamic
Displacement, zw(t) it is Z-direction dynamic displacement of the workpiece under current cutter tooth milling, zw(t-T) be workpiece in the previous cutter tooth period
Z-direction dynamic displacement under milling；T is the period；
[F (t)]=apKtc[A(t)]{Δr} (7)
Wherein：F (t) be withFor the column vector of element, { Δ r } is with Δ xj、Δyj、Δzj
For the column vector of element, dynamic milling force direction coefficient matrix [A (t)] is that angular frequency is ω, and the period is the periodic function of T；ω
=NfΩ, T=2 π/ω；Ω is cutter spindle rotational angular velocity, unit rad/s；
[A (t)] is subjected to Fourier expansion, obtains mean direction coefficient matrix：
In formula, NfIndicate the cutter tooth quantity contained by rose cutter,For the entrance angle of cutter cutter tooth,For cutting for cutter cutter tooth
Angle of departure,For coefficient matrix,For corner amount；
By formula (8), time-varying dynamic milling equation [F (t)] is converted to do not change over time but with tool-workpiece contact state phase
The form of pass：
[F (t)]=apKtc[A(0)]{Δr} (9)
Wherein,
{ Δ r }={ rc(t)}-{rc(t-T)}-({rw(t)}-{rw(t-T)})
In formula, rc(t) it is X-direction, Y-direction, the dynamic displacement column vector of Z-direction of the current cutter tooth of milling cutter, rc(t-T) it is milling cutter
X-direction, Y-direction, the dynamic displacement column vector of Z-direction in previous cutter tooth period；
rw(t) it is X-direction, Y-direction, the dynamic displacement column vector of Z-direction of the workpiece under current cutter tooth milling, rw(t-T) it is work
X-direction, Y-direction, the dynamic displacement column vector of Z-direction of the part under previous cutter tooth period milling；
The curvature expression formula of variable curvature mold cavity curve (x (u), y (u)) is
In formula, u is the parametric variable in variable curvature mold cavity curve parametric equation, and ρ (u) is the curvature of parameter u corresponding points, is become
The bending direction of curvature curve indicates that negative curvature represented is concave curve, positive number curvature generation by the positive and negative of curvature of curve
Table is convex curve；X (u), y (u) are the parametric curve under cartesian coordinate, and x ' (u), y ' (u) are in cartesian coordinate system
Under parametric curve x (u), y (u) differential；X " (u), y " (u) is parametric curve x (u), y under cartesian coordinate system
(u) second-order differential；Parameter u is the independent variable of parametric curve；
When cutter climb cutting, the horizontal entrance angle of cutter tooth and cuts out angle and be respectivelyWith
When cutter upmilling, the horizontal entrance angle of cutter tooth and cuts out angle and be respectivelyWith
If the frequency response function of cutter subsystem is Gc(jω)；
The frequency response function of workpiece subsystem is Gw(jω)；
The vibration displacement vector of Tool in Milling is transformed to frequency domain by time domain, the coupling regeneration displacement of milling point is { Δ (j ω) }
={ rc(jω)}-{roc(jω)}-({rw(jω)}-{row(j ω) })=(1-ejωT)[Gc(jω)+Gw(jω)]{Fc}ejωT
In formula, rc(j ω) is the frequency domain vibration displacement vector of the X-direction of the current cutter tooth of milling cutter, Y-direction, Z-direction, roc(j ω) is
The X-direction of the current cutter tooth of milling cutter, the time domain vibration displacement vector of Y-direction, Z-direction, rw(j ω) is workpiece in current cutter tooth milling
Under X-direction, Y-direction, Z-direction frequency domain vibration displacement vector, row(j ω) be workpiece the X-direction of current cutter tooth, Y-direction,
The time domain vibration displacement vector of Z-direction, FcFor the frequency domain of Milling Force；ω T are the phase steric retardation between cutter tooth cycle T after generating vibration
Afterwards, it obtains：
{Fc}ejωT=ap[A(0)](1-ejωT)[Gc(jω)+Gw(jω)]{Fc}ejωT (13)
Enable ap[A(0)](1-ejωT)[Gc(jω)+Gw(j ω)] determinant be 0, obtain ap[A(0)](1-ejωT)[Gc(jω)+
Gw(j ω)] particular solution：
det{[I]-ap[A(0)](1-ejωT)[Gc(jω)+Gw(j ω)] }=0 (14)
The characteristic value of formula (14) is：
A is obtained according to (14) and (15)p[A(0)](1-ejωT)[Gc(jω)+Gw(j ω)] characteristic equation be：
det{[I]+Λ[A(0)][Gc(jω)+Gw(j ω)] }=0 (16)
In formula, det { } is square formation function；
Assuming that only considering the direct transmission function of tool-workpiece system, ignore the intersection transmission function of tool-workpiece system, it is special
Sign equation (16) is just reduced to a cubic function：
a3Λ3+a2Λ2+a1Λ+1=0 (17)
The characteristic value Λ of characteristic equation is acquired, because transmission function is plural number, a3Λ3+a2Λ2+a1The characteristic value of Λ+1=0 has reality
Portion and imaginary part, therefore characteristic value Λ=ΛR+iΛI；
In formula, ΛRIt is characterized the real part of value, ΛIIt is characterized the imaginary part of value, i2=-1 is plural number；a1、a2、a3For coefficient；
Acquiring the critical axial cutting depth at milling tool flutter frequency is：
Speed of cutter spindle is converted to obtain by delay period：
In formula：K is the integer for the oscillation mark that milling tool circular arc leaves, that is, the number of stable region curve flap；N is knife
Has the speed of mainshaft.
3. a kind of method for predicting flutter in mold cavity numerical control milling according to claim 2, it is characterised in that：It is described to work as
When cutter climb cutting, the horizontal entrance angle of cutter tooth and cuts out angle and be respectivelyWithFormula is：
In formula, RcFor tool radius, aeFor radial cutting depth；
When cutter upmilling, the horizontal entrance angle of cutter tooth and cuts out angle and be respectivelyWithFormula is：
4. a kind of method for predicting flutter in mold cavity numerical control milling according to claim 3, it is characterised in that：The knife
Has the frequency response function of subsystem
In formula, Gxxc(j ω) is direct frequency response function of the cutter subsystem in X-direction excitation, X-direction response, Gxyc(j ω) is knife
Have direct frequency response function of the subsystem in X-direction excitation, Y-direction response, Gxzc(j ω) is cutter subsystem in X-direction excitation, Z
The direct frequency response function of directional response, Gyxc(j ω) is the direct frequency response letter that cutter subsystem encourages in the Y direction, X-direction responds
Number, Gyyc(j ω) is the direct frequency response function that cutter subsystem encourages in the Y direction, Y-direction responds, Gyzc(j ω) is cutter subsystem
The system direct frequency response function that excitation, Z-direction respond in the Y direction, Gzxc(j ω) is that cutter subsystem is rung in Z-direction excitation, X-direction
The direct frequency response function answered, Gzyc(j ω) is direct frequency response function of the cutter subsystem in Z-direction excitation, Y-direction response, Gzzc
(j ω) is direct frequency response function of the cutter subsystem in Z-direction excitation, Z-direction response；
The frequency response function of workpiece subsystem
In formula, Gxxw(j ω) is direct frequency response function of the workpiece subsystem in X-direction excitation, X-direction response, Gxyw(j ω) is work
Part subsystem is in the direct frequency response function that X-direction encourages, Y-direction responds, Gxzw(j ω) is workpiece subsystem in X-direction excitation, Z
The direct frequency response function of directional response, Gyxw(j ω) is the direct frequency response letter that workpiece subsystem encourages in the Y direction, X-direction responds
Number, Gyyw(j ω) is the direct frequency response function that workpiece subsystem encourages in the Y direction, Y-direction responds, Gyzw(j ω) is workpiece subsystem
The system direct frequency response function that excitation, Z-direction respond in the Y direction, Gzxw(j ω) is that workpiece subsystem is rung in Z-direction excitation, X-direction
The direct frequency response function answered, Gzyw(j ω) is direct frequency response function of the workpiece subsystem in Z-direction excitation, Y-direction response, Gzzw
(j ω) is direct frequency response function of the workpiece subsystem in Z-direction excitation, Z-direction response.
5. a kind of method for predicting flutter in mold cavity numerical control milling according to claim 4, it is characterised in that：The step
The critical axial cutting depth obtained based on step 2 in rapid three judges whether mold cavity numerical control milling occurs flutter；Specific mistake
Cheng Wei：
It repeats step 2 and obtains the critical axial cutting depth under all rotating speeds, obtained all critical axial cuttings are deep
Spend aplimIt is defined as array, cutter cutter tooth entrance angle is calculated using formula (11) and formula (12) and cuts out angle, in conjunction with cutter
The speed of mainshaft forms milling stability flap array, according to cutter cutter tooth entrance angle, cuts out angle and speed of cutter spindle is found
The axial cutting depth a of corresponding neutrality in milling stability flap arrayplim, aplimWith practical axial cutting depth ap
It compares；
If apLess than aplim, predict that milling is stablized, chatter phenomenon do not occur；If apMore than or equal to aplim, prediction generation flutter
Phenomenon.
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