CN110516340A - Process based on milling system stiffness variation damps unified model modeling method - Google Patents
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Abstract
The invention discloses a kind of, and the process based on milling system stiffness variation damps unified model modeling method, for solving the technical problem of existing process damping unified model modeling method accuracy difference.Technical solution is to carry out vibration displacement, speed, depth of cut and the solution for invading volume using actual measurement cutting force and milling system modal parameter；The inverse process for recycling cutting force to calculate instead releases shearing force coefficient and plough shear force coefficient under the known case of chipload and cutting force；The shearing force coefficient of calibration and plough shear force coefficient is recycled to calculate process damping matrix caused by process damping matrix caused by dynamic shear force matrix, shearing force and plough shear force；Finally the process damping matrix according to caused by dynamic shear force matrix, shearing force and plough shear force caused by process damping matrix establish milling system dynamical motion equation, stability solution is carried out to the equation of motion, the stability lobes diagram that damping mechanism is cut comprising cutting speed direction change damping mechanism and plough is obtained, accuracy is good.
Description
Technical field
The present invention relates to a kind of processes to damp unified model modeling method, in particular to a kind of to be become based on milling system rigidity
The process of change damps unified model modeling method.
Background technique
The damping effect occurred in cutting process can be explained by two kinds of mechanism.One is cutter flank and workpiece
Machined corrugated surface mutual extrusion and the plough of friction cut mechanism, and another kind is to consider the variation of actual cut directional velocity to cutting
The cutting speed direction change mechanism that power is modified.For the milling process of rigid workpiece, when cutter flank presses to workpiece
When corrugated surface, workpiece has sufficiently large rigidity to resist itself deflection deformation, and providing makes cutter flank be pressed into workpiece
The chance on surface, plough cut effect and occupy leading position in rigid workpiece milling process.For the milling process of thin-wall workpiece, work
Part wall thickness direction rigidity is very weak, once cutter has the tendency that pressing to workpiece surface, workpiece will generate normal direction deflection deformation to support
The intrusion of cutter processed, this makes plough cut effect and weaken significantly to the contribution that thin-wall workpiece milling process damps；At the same time, workpiece
Strong vibration on wall thickness direction is so that violent variation occurs for cutting speed direction, and considerably increases the change of cutting speed direction
Change the dominant position that effect damps thin-wall workpiece process.For the workpiece of any rigidity, milling process damping is actually same
When influenced by both mechanism, and two kinds of mechanism can become the contribution of cutting process total damping with milling system rigidity
Change.Therefore, establishing the process damping unified model based on milling system stiffness variation, there is important theory significance and engineering to answer
With value.
" L.Tunc, E.Budak, Identification and modeling of the process damping of document 1
in milling,Transactions of ASME Journal of Manufacturing Science and
Engineering 135 (2013) 021001. " discloses a kind of milling process Damping Modeling method that mechanism is cut based on plough.It should
Method solves the solution of encroachment area and ploughs the calibration of shear force coefficient, and reasonable prediction goes out low turn in the milling process of rigid workpiece
Fast stability inferior Limit cutting depth.But there is no consider cutting speed direction change effect to process resistance for the method for Tunc and Budak
The influence of Buddhist nun.
" J.Feng, M.Wan, T.Q.Gao, W.H.Zhang, Mechanism of process the damping in of document 2
milling of thin-walled workpiece,International Journal of Machine Tools and
Manufacture 134 (2018) 1-19. " disclose it is a kind of based on cutting speed direction change mechanism milling process damping build
Mould method.This method considers that vibration of the tool-workpiece system in direction of feed and feeding normal direction is modified cutting force, In
The correct conclusion that limit of stability cutting-in reduces with revolving speed and increased is obtained in the milling process of thin-wall workpiece.But Feng's et al.
There is no consider to plough to cut the contribution that effect damps process for method.
The typical feature of above-mentioned bibliography is: during process Damping Modeling, for rigid workpiece, only with being based on
Plough cuts the process Damping Modeling method of mechanism；For thin-wall workpiece, only with the process based on cutting speed direction change mechanism
Damping Modeling method.It is modeled since the influence without considering two kinds of mechanism simultaneously damps process, for any rigidity work
The milling process of part can not accurately predict the limit of stability cutting-in under its slow-speed of revolution.
Summary of the invention
In order to overcome the shortcomings of that existing process damping unified model modeling method accuracy is poor, the present invention provides one kind and is based on
The process of milling system stiffness variation damps unified model modeling method.This method is first with actual measurement cutting force and milling system
Modal parameter carries out vibration displacement, speed, depth of cut and the solution for invading volume；Then the inverse mistake calculated using cutting force
Journey instead releases shearing force coefficient and plough shear force coefficient under the known case of chipload and cutting force；Recycle cutting for calibration
Caused by shear force coefficient and plough shear force coefficient calculate process damping matrix caused by dynamic shear force matrix, shearing force and plough shear force
Process damping matrix；Finally the process damping matrix according to caused by dynamic shear force matrix, shearing force and plough shear force caused by mistake
Journey damping matrix establishes milling system dynamical motion equation, carries out stability solution to the equation of motion, obtains comprising cutting speed
Degree direction change damping mechanism and plough cut the stability lobes diagram of damping mechanism.The present invention is based on the mistakes of milling system stiffness variation
Journey damping unified model modeling method considers that cutting speed direction change effect and plough cut the damping of process caused by effect simultaneously,
Milling process accuracy suitable for any rigidity workpiece is good.
A kind of the technical solution adopted by the present invention to solve the technical problems: process resistance based on milling system stiffness variation
Buddhist nun's unified model modeling method, its main feature is that the following steps are included:
Step 1: carry out mould measurement to cutter and workpiece by proof force hammering blow method, obtain cutter, workpiece it is intrinsic
Frequency matrix ωT、ωW, damping ratio matrix ζT、ζWWith mode formation matrix UT、UW.Wherein ωTIt is cutter intrinsic frequency matrix, ωW
It is inherent frequency of workpiece matrix, ζTIt is cutter damping ratio matrix, ζWIt is workpiece damping ratio matrix, UTIt is cutting tool mode formation matrix,
UWIt is workpiece mode formation matrix.
Step 2: carrying out without flutter-stabilization milling experiment, using on dynamometer measurement tool feeding direction and feeding normal direction
Cutting force FxAnd Fy.Axial cutting-in apIt selects between 1-2mm, radial cutting-in aeSelection to guarantee in cutting process at most only
There is a blade to participate in cutting.Wherein FxIt is that cutting force, F are surveyed on tool feeding directionyIt is that cutting is surveyed in tool feeding normal direction
Power, apIt is axial cutting-in, aeIt is radial cutting-in.
Step 3: the vibration displacement and vibration velocity that are calculate by the following formula on tool feeding direction:
In formula, xTIt is vibration displacement on tool feeding direction,It is vibration velocity on tool feeding direction, Δ t is cutting
Power sampling time interval, MT,xIt is dominant mode quality, C on tool feeding direction at point of a knifeT,xIt is tool feeding direction at point of a knife
Upper dominant mode structural damping, KT,xIt is dominant mode rigidity, R on tool feeding direction at point of a knife1、R2、R3、R4、L1、L2、L3With
L4It is intermediate variable.MT,x、CT,xAnd KT,xIt tests to obtain by proof force hammering blow.
Step 4: repeating step 3, the vibration displacement y in tool feeding normal direction is calculatedTAnd vibration velocityWherein yTIt is
Vibration displacement in tool feeding normal direction,It is vibration velocity in tool feeding normal direction.
Step 5: repeating step 3 to step 4, the vibration displacement x in workpiece direction of feed is calculatedWAnd vibration velocity
Workpiece feeds the vibration displacement y in normal directionWAnd vibration velocityWherein xWIt is vibration displacement in workpiece direction of feed,It is work
Vibration velocity in part direction of feed, yWIt is vibration displacement in workpiece feeding normal direction,It is vibration velocity in workpiece feeding normal direction.
Step 6: being calculate by the following formula actual cut speed and actual cut angle:
Ri,j=R+ ρ cos [λ-φ (z) -2 (j-1) π/N]
In formula, Ri,jIt is j-th of cutter tooth radius for considering cutter deflection, R is nominal tool radius, and ρ and λ are cutter deflections
Parameter, φ (z) are angle of lags, and N is the cutter number of teeth,It is actual cut speed, Ω is the speed of mainshaft, θi,jIt is nominal ablation
Angle,It is actual cut angle.
Step 7: being calculate by the following formula depth of cut:
In formula,It is depth of cut, m is cutter deflection bring cutter tooth interval number, ftIt is per tooth feeding, Ri,j-mIt is to examine
Consider-m cutter tooth radiuses of jth of cutter deflection, τmIt is cutter deflection bring cutter tooth gap periods.
Step 8: being calculate by the following formula encroachment area:
In formula, S is encroachment area, rhIt is cutter radius of corner, βsIt is the angle of departure, γ is tool clearance, lwIt is flank mill
Damage strip length.
Step 9: being calculate by the following formula cutting force and radial cutting force:
In formula, FtIt is cutting force, FrIt is radial cutting force.
Step 10: being calculate by the following formula tangential shearing force coefficient, radial shear force coefficient, tangential plough shear force coefficient and radial direction
Plough shear force coefficient:
[Kts Ktp Krs Krp]T=[BTB]-1BTc
In formula, matrix B1, B and c be intermediate variable, l is total sampling number in a cutter tooth cutting period, KtsIt is tangential
Shear force coefficient, KtpIt is tangential plough shear force coefficient, KrsIt is radial shear force coefficient, KrpIt is radial plough shear force coefficient.
Step 11: milling cutter is carried out infinitesimal along axial, it is right to be calculate by the following formula j-th of cutter tooth institute on i-th of unit
The window function answered:
G in formulai,jIt is window function corresponding to j-th of cutter tooth, θ on i-th of unitstIt is entrance angle, θexIt is to cut out angle.
Step 12: being calculate by the following formula dynamic shear force matrix, shear history damping matrix corresponding to i-th of unit
Journey damping matrix is cut through with plough:
D in formulaiIt is dynamic shear force matrix, P corresponding to i-th of units,iIt is shearing corresponding to i-th of unit
Journey damping matrix, Pp,iIt is that plough corresponding to i-th of unit cuts through journey damping matrix, N is milling cutter tooth number, zi,jIt is single i-th
Unit axial height corresponding to the upper the j cutter tooth of member, matrixMatrixMatrixMatrixMatrixMatrix
Step 13: being calculate by the following formula the dynamic shear force matrix acted within the scope of entire axial cutting-in, shearing
Journey damping matrix and plough cut through journey damping matrix:
In formula,It is dynamic shear force matrix corresponding to entire axial cutting-in range,It is entire axial cutting-in range
Corresponding shear history damping matrix,It is that plough corresponding to entire axial cutting-in range cuts through journey damping matrix, matrixMatrixSquare
Battle arrayMatrix
MatrixMatrixSubscript q is the unit number in entire axial cutting-in, matrix
Step 14: establishing milling system dynamical motion equation according to the following equation:
In formula, ΓTFor cutting tool mode motion vector, ΓWFor workpiece modal displacement vector.Stability solution is carried out to equation,
Draw out the stability lobes diagram that damping effect is cut comprising cutting speed direction change damping effect and plough.
The beneficial effects of the present invention are: this method is vibrated first with actual measurement cutting force and milling system modal parameter
Displacement, speed, depth of cut and the solution for invading volume；Then the inverse process calculated using cutting force in chipload and is cut
It cuts and instead releases shearing force coefficient and plough shear force coefficient under the known case of power；Recycle shearing force coefficient and the plough shear force system of calibration
Number calculates process damping matrix caused by process damping matrix caused by dynamic shear force matrix, shearing force and plough shear force；Finally
Milling is established according to process damping matrix caused by process damping matrix caused by dynamic shear force matrix, shearing force and plough shear force
The system dynamics equation of motion carries out stability solution to the equation of motion, obtains damping mechanism comprising cutting speed direction change
The stability lobes diagram of damping mechanism is cut with plough.The present invention is based on the damping unified model modelings of the process of milling system stiffness variation
Method considers that cutting speed direction change effect and plough cut the damping of process caused by effect simultaneously, is suitable for any rigidity workpiece
Milling process accuracy it is good.
It elaborates with reference to the accompanying drawings and detailed description to the present invention.
Detailed description of the invention
Fig. 1 is the calculated result of embodiment of the present invention method depth of cut.
Fig. 2 is the calculated result of embodiment of the present invention method encroachment area.
Fig. 3 is the calculated result of embodiment of the present invention method cutting force.
Fig. 4 is the calculated result of embodiment of the present invention method radial cutting force.
Fig. 5 is embodiment of the present invention method prediction the stability lobes diagram and the comparison diagram for surveying flutter data.
Specific embodiment
Referring to Fig.1-5.Use flat carbide end mill with climb cutting cutting way in three coordinate vertical machining centres
Carry out experimental verification.Workpiece material is aluminium alloy 7050, having a size of 6 × 35 × 105 millimeters of aluminium sheet.Cutter tooth number N=4 tooth,
R=6 millimeters of radius, helixangleβ=30 degree, relief angle γ=9 degree, radius of corner rh=22 microns, angle of departure βs=50 degree, rear knife
Surface wear strip length lw=68 microns.Cutter axial direction cutting-in ap=1 millimeter, radial cutting-in ae=3 millimeters, per tooth feeds ft=
0.06 millimeter, entrance angle θst=120 degree, cut out angle θex=180 degree.The present invention is based on the resistances of the process of milling system stiffness variation
Specific step is as follows for Buddhist nun's unified model modeling method:
Step 1: carry out mould measurement to cutter and workpiece by proof force hammering blow method, obtain cutter, workpiece it is intrinsic
Frequency matrix ωT、ωW, damping ratio matrix ζT、ζWWith mode formation matrix UT、UW.Wherein ωTIt is cutter intrinsic frequency matrix, ωW
It is inherent frequency of workpiece matrix, ζTIt is cutter damping ratio matrix, ζWIt is workpiece damping ratio matrix, UTIt is cutting tool mode formation matrix,
UWIt is workpiece mode formation matrix.By proof force hammering blow experimental test, cutting tool mode parameter is referring to table 1, workpiece mode ginseng
Number is referring to table 2.
1 cutter Experimental Modal Parameters of table
2 workpiece Experimental Modal Parameters of table
Step 2: carrying out without flutter-stabilization milling experiment, using on dynamometer measurement tool feeding direction and feeding normal direction
Cutting force FxAnd Fy.Axial cutting-in apIt selects between 1-2mm, radial cutting-in aeSelection to guarantee in cutting process at most only
There is a blade to participate in cutting.Wherein FxIt is that cutting force, F are surveyed on tool feeding directionyIt is that cutting is surveyed in tool feeding normal direction
Power, apIt is axial cutting-in, aeIt is radial cutting-in.
Step 3: the vibration displacement and vibration velocity that are calculate by the following formula on tool feeding direction:
X in formulaTIt is vibration displacement on tool feeding direction,It is vibration velocity on tool feeding direction, Δ t is cutting force
Sampling time interval, MT,xIt is dominant mode quality, C on tool feeding direction at point of a knifeT,xIt is at point of a knife on tool feeding direction
Dominant mode structural damping, KT,xIt is dominant mode rigidity, R on tool feeding direction at point of a knife1、R2、R3、R4、L1、L2、L3And L4
It is intermediate variable.xT(tn) in t0The initial value x at momentT(t0)=0,In t0The initial value at momentMT,x、
CT,xAnd KT,xIt tests to obtain by proof force hammering blow.
Step 4: repeating step 3, the vibration displacement y in tool feeding normal direction is calculatedTAnd vibration velocityWherein yTIt is
Vibration displacement in tool feeding normal direction,It is vibration velocity in tool feeding normal direction.
Step 5: repeating step 3 to step 4, the vibration displacement x in workpiece direction of feed is calculatedWAnd vibration velocity
Workpiece feeds the vibration displacement y in normal directionWAnd vibration velocityWherein xWIt is vibration displacement in workpiece direction of feed,It is work
Vibration velocity in part direction of feed, yWIt is vibration displacement in workpiece feeding normal direction,It is vibration velocity in workpiece feeding normal direction.
Step 6: being calculate by the following formula actual cut speed and actual cut angle:
Ri,j=R+ ρ cos [λ-φ (z) -2 (j-1) π/N]
R in formulai,jIt is j-th of cutter tooth radius for considering cutter deflection, R is cutter nominal radius, and ρ and λ are cutter deflection ginsengs
Number, φ (z) is angle of lag, and N is the cutter number of teeth,It is actual cut speed, Ω is the speed of mainshaft, θi,jIt is nominal ablation angle,It is actual cut angle.
Step 7: being calculate by the following formula depth of cut:
In formulaIt is depth of cut, m is cutter deflection bring cutter tooth interval number, ftIt is per tooth feeding, Ri,j-mIt is to consider
- m cutter tooth radiuses of jth of cutter deflection, τmIt is cutter deflection bring cutter tooth gap periods.Depth of cut calculated result reference
Attached drawing 1.
Step 8: being calculate by the following formula encroachment area:
S is encroachment area, r in formulahIt is cutter radius of corner, βsIt is the angle of departure, γ is tool clearance, lwIt is flank mill
Damage strip length.Encroachment area calculated result is referring to attached drawing 2.
Step 9: being calculate by the following formula cutting force and radial cutting force:
F in formulatIt is cutting force, FrIt is radial cutting force.Cutting force calculated result is referring to attached drawing 3, radial cutting
Power calculated result is referring to attached drawing 4.
Step 10: being calculate by the following formula tangential shearing force coefficient, radial shear force coefficient, tangential plough shear force coefficient and radial direction
Plough shear force coefficient:
[Kts Ktp Krs Krp]T=[BTB]-1BTc
Matrix B in formula1, B and c be intermediate variable, l is total sampling number in a cutter tooth cutting period, KtsIt is tangential
Shear force coefficient, KtpIt is tangential plough shear force coefficient, KrsIt is radial shear force coefficient, KrpIt is radial plough shear force coefficient.Pass through calculating
Kts=1097 megapascal, Krs=588 megapascal, Ktp=1.25 × 1013Every cubic metre of ox, Krp=3.18 × 1013Every cubic metre of ox.
Step 11: milling cutter is carried out infinitesimal along axial, it is right to be calculate by the following formula j-th of cutter tooth institute on i-th of unit
The window function answered:
G in formulai,jIt is window function corresponding to j-th of cutter tooth, θ on i-th of unitstIt is entrance angle, θexIt is to cut out angle.
Step 12: being calculate by the following formula dynamic shear force matrix, shear history damping matrix corresponding to i-th of unit
Journey damping matrix is cut through with plough:
D in formulaiIt is dynamic shear force matrix, P corresponding to i-th of units,iIt is shearing corresponding to i-th of unit
Journey damping matrix, Pp,iIt is that plough corresponding to i-th of unit cuts through journey damping matrix, N is milling cutter tooth number, zi,jIt is single i-th
Unit axial height corresponding to the upper the j cutter tooth of member, matrixMatrixMatrixMatrixMatrixMatrix
Step 13: being calculate by the following formula the dynamic shear force matrix acted within the scope of entire axial cutting-in, shearing
Journey damping matrix and plough cut through journey damping matrix:
In formulaIt is dynamic shear force matrix corresponding to entire axial cutting-in range,It is entire axial cutting-in range institute
Corresponding shear history damping matrix,It is that plough corresponding to entire axial cutting-in range cuts through journey damping matrix, matrixMatrixSquare
Battle arrayMatrix
MatrixMatrixSubscript q is the unit number in entire axial cutting-in, matrix
Step 14: establishing milling system dynamical motion equation according to the following equation:
Γ in formulaTFor cutting tool mode motion vector, ΓWFor workpiece modal displacement vector.Stability solution is carried out to equation,
Draw out the stability lobes diagram that damping effect is cut comprising cutting speed direction change damping effect and plough.Referring to attached drawing 5, use
The stability lobes diagram that process of the present invention damping unified model modeling method obtains, energy quite well experimental result, it was demonstrated that
Propose the validity of the process damping unified model modeling method based on milling system stiffness variation.
Claims (1)
1. a kind of process based on milling system stiffness variation damps unified model modeling method, it is characterised in that including following step
It is rapid:
Step 1: carrying out mould measurement to cutter and workpiece by proof force hammering blow method, the intrinsic frequency of cutter, workpiece is obtained
Matrix ωT、ωW, damping ratio matrix ζT、ζWWith mode formation matrix UT、UW；Wherein ωTIt is cutter intrinsic frequency matrix, ωWIt is work
Part intrinsic frequency matrix, ζTIt is cutter damping ratio matrix, ζWIt is workpiece damping ratio matrix, UTIt is cutting tool mode formation matrix, UWIt is
Workpiece mode formation matrix；
Step 2: carrying out utilizing cutting on dynamometer measurement tool feeding direction and feeding normal direction without flutter-stabilization milling experiment
Cut power FxAnd Fy；Axial cutting-in apIt selects between 1-2mm, radial cutting-in aeSelection to guarantee in cutting process at most there was only one
A blade participates in cutting；Wherein FxIt is that cutting force, F are surveyed on tool feeding directionyIt is to survey cutting force in tool feeding normal direction,
apIt is axial cutting-in, aeIt is radial cutting-in；
Step 3: the vibration displacement and vibration velocity that are calculate by the following formula on tool feeding direction:
In formula, xTIt is vibration displacement on tool feeding direction,It is vibration velocity on tool feeding direction, Δ t is cutting force sampling
Time interval, MT,xIt is dominant mode quality, C on tool feeding direction at point of a knifeT,xIt is to be dominated on tool feeding direction at point of a knife
Modal structure damping, KT,xIt is dominant mode rigidity, R on tool feeding direction at point of a knife1、R2、R3、R4、L1、L2、L3And L4In being
Between variable；MT,x、CT,xAnd KT,xIt tests to obtain by proof force hammering blow；
Step 4: repeating step 3, the vibration displacement y in tool feeding normal direction is calculatedTAnd vibration velocityWherein yTIt is cutter
Vibration displacement in normal direction is fed,It is vibration velocity in tool feeding normal direction；
Step 5: repeating step 3 to step 4, the vibration displacement x in workpiece direction of feed is calculatedWAnd vibration velocityWorkpiece
Feed the vibration displacement y in normal directionWAnd vibration velocityWherein xWIt is vibration displacement in workpiece direction of feed,Workpiece into
To vibration velocity on direction, yWIt is vibration displacement in workpiece feeding normal direction,It is vibration velocity in workpiece feeding normal direction；
Step 6: being calculate by the following formula actual cut speed and actual cut angle:
Ri,j=R+ ρ cos [λ-φ (z) -2 (j-1) π/N]
In formula, Ri,jIt is j-th of cutter tooth radius for considering cutter deflection, R is nominal tool radius, and ρ and λ are cutter deflection parameters,
φ (z) is angle of lag, and N is the cutter number of teeth,It is actual cut speed, Ω is the speed of mainshaft, θi,jIt is nominal ablation angle,
It is actual cut angle；
Step 7: being calculate by the following formula depth of cut:
In formula,It is depth of cut, m is cutter deflection bring cutter tooth interval number, ftIt is per tooth feeding, Ri,j-mIt is to consider knife
Have-m cutter tooth radiuses of eccentric jth, τmIt is cutter deflection bring cutter tooth gap periods；
Step 8: being calculate by the following formula encroachment area:
In formula, S is encroachment area, rhIt is cutter radius of corner, βsIt is the angle of departure, γ is tool clearance, lwIt is major flank wear land
Length；
Step 9: being calculate by the following formula cutting force and radial cutting force:
In formula, FtIt is cutting force, FrIt is radial cutting force；
It is cut Step 10: being calculate by the following formula tangential shearing force coefficient, radial shear force coefficient, tangential plough shear force coefficient and radial plough
Force coefficient:
[Kts Ktp Krs Krp]T=[BT B]-1BTc
In formula, matrix B1, B and c be intermediate variable, l is total sampling number in a cutter tooth cutting period, KtsIt is tangentially to shear
Force coefficient, KtpIt is tangential plough shear force coefficient, KrsIt is radial shear force coefficient, KrpIt is radial plough shear force coefficient；
Step 11: milling cutter is carried out infinitesimal along axial, it is calculate by the following formula on i-th of unit corresponding to j-th of cutter tooth
Window function:
G in formulai,jIt is window function corresponding to j-th of cutter tooth, θ on i-th of unitstIt is entrance angle, θexIt is to cut out angle；
Step 12: being calculate by the following formula dynamic shear force matrix, shear history damping matrix corresponding to i-th of unit and plough
Cut through journey damping matrix:
D in formulaiIt is dynamic shear force matrix, P corresponding to i-th of units,iIt is the damping of shear history corresponding to i-th of unit
Matrix, Pp,iIt is that plough corresponding to i-th of unit cuts through journey damping matrix, N is milling cutter tooth number, zi,jIt is on i-th of unit
Unit axial height corresponding to a j cutter tooth, matrixMatrix
MatrixMatrixMatrixMatrix
Step 13: being calculate by the following formula the dynamic shear force matrix acted within the scope of entire axial cutting-in, shear history resistance
Buddhist nun's matrix and plough cut through journey damping matrix:
In formula,It is dynamic shear force matrix corresponding to entire axial cutting-in range,It is that entire axial cutting-in range institute is right
The shear history damping matrix answered,It is that plough corresponding to entire axial cutting-in range cuts through journey damping matrix, matrixMatrixSquare
Battle arrayMatrix
MatrixMatrixSubscript q is the unit number in entire axial cutting-in, matrix
Step 14: establishing milling system dynamical motion equation according to the following equation:
In formula, ΓTFor cutting tool mode motion vector, ΓWFor workpiece modal displacement vector；Stability solution is carried out to equation, is drawn
The stability lobes diagram of damping effect is cut comprising cutting speed direction change damping effect and plough out.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040193308A1 (en) * | 2003-03-31 | 2004-09-30 | Paul Darcy | Process and methodology for selecting cutting parameters for titanium |
| US20080065254A1 (en) * | 2004-11-01 | 2008-03-13 | University Of Florida Research Foundation, Inc. | Methods for Machining Process Parameter Estimation and Systems Thereof |
| CN106965032A (en) * | 2017-03-22 | 2017-07-21 | 西北工业大学 | Thin-wall part milling parameter suppressing method |
| CN107480354A (en) * | 2017-07-28 | 2017-12-15 | 东北大学 | A kind of turnery processing parameter optimization method for considering uncertain parameter |
| CN108804749A (en) * | 2018-04-19 | 2018-11-13 | 西北工业大学 | Thin-wall part milling process Damping Modeling method |
| CN109909806A (en) * | 2019-03-22 | 2019-06-21 | 南京理工大学 | A kind of method of hoisting machine people milling stable region |
-
2019
- 2019-08-21 CN CN201910774401.5A patent/CN110516340B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040193308A1 (en) * | 2003-03-31 | 2004-09-30 | Paul Darcy | Process and methodology for selecting cutting parameters for titanium |
| US20080065254A1 (en) * | 2004-11-01 | 2008-03-13 | University Of Florida Research Foundation, Inc. | Methods for Machining Process Parameter Estimation and Systems Thereof |
| CN106965032A (en) * | 2017-03-22 | 2017-07-21 | 西北工业大学 | Thin-wall part milling parameter suppressing method |
| CN107480354A (en) * | 2017-07-28 | 2017-12-15 | 东北大学 | A kind of turnery processing parameter optimization method for considering uncertain parameter |
| CN108804749A (en) * | 2018-04-19 | 2018-11-13 | 西北工业大学 | Thin-wall part milling process Damping Modeling method |
| CN109909806A (en) * | 2019-03-22 | 2019-06-21 | 南京理工大学 | A kind of method of hoisting machine people milling stable region |
Non-Patent Citations (3)
| Title |
|---|
| MIN WAN ET AL: "Mechanistic modeling of milling process damping including velocity and ploughing effects", 《PROCEDIA CIRP》 * |
| 杨昀: "薄壁件铣削系统动力学建模及稳定性预测方法研究", 《中国博士学位论文全文数据库电子期刊 工程科技II辑》 * |
| 赵慧楠: "基于过程阻尼的铣削加工薄壁件颤振稳定性及参数优化研究", 《中国优秀硕士学位论文全文数据库电子期刊 工程科技I辑》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114492013A (en) * | 2022-01-07 | 2022-05-13 | 西北工业大学 | Micro-milling process damping modeling method considering metal dead zone and material rebound |
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