CN105279313B - A kind of curve end mill Prediction Method of Milling Forces based on inclined cutting - Google Patents
A kind of curve end mill Prediction Method of Milling Forces based on inclined cutting Download PDFInfo
- Publication number
- CN105279313B CN105279313B CN201510627974.7A CN201510627974A CN105279313B CN 105279313 B CN105279313 B CN 105279313B CN 201510627974 A CN201510627974 A CN 201510627974A CN 105279313 B CN105279313 B CN 105279313B
- Authority
- CN
- China
- Prior art keywords
- infinitesimal
- milling
- sword
- angle
- plane
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Landscapes
- Numerical Control (AREA)
- Milling Processes (AREA)
Abstract
The present invention provides a kind of curve end mill Prediction Method of Milling Forces based on inclined cutting, and by blade, differential, application curves Differential Geometry derive the computational methods of working reference plane on infinitesimal sword in an axial direction.By blade, differential, application curves Differential Geometry derive the computational methods of working reference plane on infinitesimal sword to this method in an axial direction.In the modus operandi Plane reference system of infinitesimal sword, using least-energy principle, establish the constraint between the milling parameters such as force vector, velocity vector, chip-flow angle, normal direction angle of friction, normal shear angle and shear stress, Milling force parameter is demarcated with the experiment of monodentate line milling, wherein normal direction angle of friction, normal shear angle and shear stress etc. are represented by the double-exponential function of instantaneous undeformed chip thickness.
Description
Technical field
The invention belongs to milling technology fields, are related to a kind of curve end mill Prediction Method of Milling Forces based on inclined cutting.
Background technology
Curve end mill is the common processing technology of the industrial circles such as aerospace, weapons, vehicle, and Milling Force is then technique
Calculate cutting power in customization, formulate cutting data, monitor the important physical amount of cutting state, be cause tool wear, breakage,
Fracture and work pieces process deformation, unstability primary factor.Therefore Milling Force prediction model when curve end mill is established, to realizing
High-quality and efficient production is of great significance.The movement in direction of feed is had ignored in the prior art, does not consider that working reference plane changes
When to tool working angle generate influence, and its propose mechanical model be only applicable to straight turning or line milling..
Invention content
The present invention provides a kind of curve end mill Prediction Method of Milling Forces based on inclined cutting, by blade differential in an axial direction,
Application curves Differential Geometry derives the computational methods of working reference plane on infinitesimal sword.
A kind of curve end mill Prediction Method of Milling Forces based on inclined cutting, includes the following steps：
Step 1 establishes frame of axes：Inertial coordinate frame OXYZ is established in workpiece boundary first, in cutter bottom centre O'
Moving coordinate frame O'X'Y'Z' is established, wherein plane OXY is overlapped with plane O'X'Y', and axis X', Y' are respectively parallel to axis X, Y, axis
Z' is overlapped with tool axis；Using cutter bottom centre O' as starting point, establishes cutter in process and instantaneously feed vector f and its method
To vector n；
Step 2, by cutter differential in an axial direction, with the infinitesimal sword I at axial height z on jth swordj,zFor research object, in step
In the rapid 1 inertial coordinate frame OXYZ established, infinitesimal sword Ij,zMovement locus with vector representation be rj,z(t)=pj,z(t)+qj,z
(φ)；
Wherein：pj,z(t) it is infinitesimal sword Ij,zCorresponding center cutter point O'zThe movement locus in inertial coordinate frame OXYZ
pj,z(t)={ x (t), y (t), z }；
qj,z(φ) is O'zThe movement locus q in the moving coordinate frame O'X'Y'Z' that step 1 is establishedj,z(φ)={ Rcos
φ,Rsinφ,z}；φ is cutter rotation angle, and R is tool radius；
Step 3, by differential geometry of curves, by p in step 2j,z(t) natural parameter expression is ps,z(s)={ x (t
(s)),y(t(s)),z}；
Wherein：Natural parameter difference quotientFrom
Right parameter s is regular curve arc length, is denoted as wherein fzFor feed engagement, znFor the cutter number of teeth；
Step 4, the infinitesimal sword I for obtaining step 2j,zVector motion track be expressed as the vector motion using φ as parameter
Track, i.e. rj,z(φ)=pj,z(φ)+qj,z(φ)；
Step 5, according to step 2 it can be seen that in infinitesimal sword Ij,zPlace, the normal vector of basal plane are expressed as nr=q'j,z(φ),
Wherein q'j,z(φ) is qj,zThe difference quotient of (φ)；According to step 4 it can be seen that the normal vector of working reference plane is expressed as nre=r'j,z
(φ), wherein r'j,z(φ) is rj,zThe difference quotient of (φ)；To can determine infinitesimal sword Ij,zThe working reference plane at place, relative to basal plane
Angle change be
Step 6, the working reference plane determined according to step 5 establish the reference of the work orthogonal plane under inclined cutting mode respectively
System and modus operandi Plane reference system, to establish infinitesimal sword Ij,zOn resultant force and its component between constrain；
Step 7, by least-energy principle, the angle of shearValue should make the cutting power minimalization on infinitesimal sword, and
Establish infinitesimal sword Ij,zConstraint between up cut shear, the section of shear and shear stress；
Step 8, milling parameter calibration, and make the limitation of line milling experimental condition；Wink is obtained in conjunction with the constrained solution that step 7 is established
When undeformed chip thickness under milling parameter, and calculate Milling force parameter, and then be expressed as infinitesimal sword Ij,zOn cutting angle
Milling Force；
It is integrated via transition matrix T, then and to each by step 9, the infinitesimal Milling Force for obtaining step 8 in an axial direction
Cutter tooth is summed, and the Milling Force on cutter can must be acted on.
Further, the line milling experimental condition is limited to：1. only having single-blade to participate in milling always；2. axial cutting-in
ap∈[1,2](mm)。
The present invention has the advantages that：
The present invention is directed to curve end mill processing process, proposes that a kind of milling force modeling method, applied differential geometry calculate micro-
Working reference plane on first sword is based on oblique cutting model, milling is established using least-energy principle in modus operandi Plane reference system
Cut the constraint between parameter.The influence of the parameters such as the equivalent amount of feeding, instantaneous direction of feed angle is also contemplated during milling force modeling.
With monodentate line milling Experimental Calibration Milling force parameter, circular arc and Bezier curve end are carried out respectively on PCrNi3MoVA workpiece
Milling is tested, and by comparison of test results, demonstrates the validity of the curve end mill Milling Force Model.
Description of the drawings
Fig. 1 is curve end mill processing process schematic；
Fig. 2 is infinitesimal Milling Force schematic diagram in curve end mill；
Fig. 3 is force vector, velocity vector and chip-flow angle relational graph in inclined cutting；(a) work orthogonal plane referential,
(b) modus operandi Plane reference system.
Specific implementation mode
The invention will be described further below in conjunction with the accompanying drawings.
Fig. 1 show curve end mill processing process schematic.OXYZ is the inertial coordinate frame for being fixed on workpiece boundary,
Middle cutter end face is overlapped with plane OXY.O'X'Y'Z' is the moving coordinate frame established at cutter bottom centre O', axis X', Y'
It is respectively parallel to axis X, Y, axis Z' is overlapped with tool axis.F, n be respectively in process cutter instantaneously feed vector and its method
To vector, starting point is overlapped with O'.
By cutter differential in an axial direction, with the infinitesimal sword I at axial height z on jth swordj,zFor research object, wherein O'zFor
Infinitesimal sword Ij,zCorresponding center cutter point.In Milling Processes, if O'zMovement locus is regular curve, can use vector representation
For
pj,z(t)={ x (t), y (t), z } (1)
Infinitesimal sword Ij,zMovement locus in moving coordinate frame O'X'Y'Z' can be with vector representation
qj,z(φ)={ Rcos φ, Rsin φ, z } (2)
Wherein φ is cutter rotation angle, and R is tool radius, it is clear that qj,z(φ) is regular curve.Therefore infinitesimal sword Ij,z
Movement locus in inertia frame OXYZ is also regular curve, can be with vector representation
rj,z(t)=pj,z(t)+qj,z(φ) (3)
pj,z(t) natural parameter expression is
ps,z(s)={ x (t (s)), y (t (s)), z } (4)
Wherein natural parameter
Difference quotient
Natural parameter s is regular curve arc length again, therefore is had
Wherein fzFor feed engagement, znFor the cutter number of teeth.Formula (4), (7) substitute into formula (3) and obtain
rj,z(φ)=pj,z(φ)+qj,z(φ) (8)
As Milling Process when, infinitesimal sword Ij,zUsing φ as the vector motion track of parameter in inertia frame OXYZ.
In infinitesimal sword Ij,zPlace, basal plane PrNormal vector be represented by
nr=q'j,z(φ) (9)
Working reference plane PreNormal vector be represented by
nre=r'j,z(φ) (10)
Wherein, q'j,z(φ)、r'j,z(φ) is respectively qj,z(φ)、rj,zThe difference quotient of (φ), then working reference plane PreRelative to
Basal plane PrAngle change μ be represented by
Milling force modeling and experiment are upmilling processing method.Fig. 2 is infinitesimal Milling Force schematic diagram in curve end mill, micro-
First sword is in cutting angle θj,zThe infinitesimal Milling Force at place is represented by
dFT,j,z(θj,z)=ε (θj,z)KT,j,zh(θj,z)dz
dFR,j,z(θj,z)=ε (θj,z)KR,j,zh(θj,z)dz (12)
dFA,j,z(θj,z)=ε (θj,z)KA,j,zh(θj,z)dz
Wherein, dFT,j,z、dFR,j,z、dFA,j,zInfinitesimal sword I is indicated respectivelyj,zOn tangential force, radial load and axial force；
KT,j,z、KR,j,z、KA,j,zTangential, radial and axial Cutting Force Coefficient is indicated respectively；Dz indicates infinitesimal sword height；h(θj,z) indicate
Infinitesimal sword Ij,zIn cutting angle θj,zThe momentary-cutting-thick at place, can approximate representation be
h(θj,z)=fasinθj,z
In formula, faFor curve end mill when equivalent feed engagement, feed engagement f can be expressed asz, instantaneously into being given to angle k
And the function of curvature of curve ρ, wherein
ε(θj,z) it is unit jump function,
θen、θexRespectively entrance angle and cut out angle；
Cutter rotational angle φ can be by cutting angle θj,zIt is expressed as：
φ=θj,z-k+ψj,z-(j-1)φp (16)
ψj,zIt is infinitesimal relative to the angle of lag at jth sword endpoint
ψj,z=ztan β/R (17)
β is cutter helical angle, angle between teeth φp=2 π/zn。
Convolution (15), by dFT,j,z、dFR,j,z、dFA,j,zAfter decomposing instantaneous direction of feed f and its normal direction n, through matrix T
Transformation can obtain infinitesimal Milling Force expression formula in inertial coordinate frame：
Wherein
Formula (17) is integrated in an axial direction and is summed to each cutter tooth, the Milling Force that can must be acted on cutter is：
Wherein apFor axial cutting-in.
Infinitesimal sword milling process is Oblique Cutting Process, is established in work orthogonal plane and modus operandi Plane reference system
Force vector, velocity vector under inclined cutting mode and chip-flow angle relation schematic diagram, wherein V are to consider feeding post exercise synthesis
Cutting speed vector, VsFor shear velocity vector, VcVelocity vector is considered to be worth doing for stream.
FfAnd FnRespectively rake face AγThe frictional force and normal pressure in chip are acted on, F, which is resultant force, obviously to be had
sinξλ=sin βasinη (23)
tan(ξn+γne)=tan βacosη (24)
βn=ξn+γne (25)
Wherein, ξλFor F and normal plane PnAngle, ξnIt is F in normal plane PnUpper and work cutting plane PseAngle, βaTo rub
Wipe angle, βnFor normal plane PnOn normal direction angle of friction, η is chip-flow angle, FTn,j,z、FRn,j,z、FAn,j,zRespectively FT,j,z、FR,j,z、
FA,j,zIn normal plane PnOn projection, be represented by
[FTn,j,z,FRn,j,z,FAn,j,z]T=T (λs)[FT,j,z,FR,j,z,FA,j,z]T (27)
γneFor working normal rake, it is represented by
γne=arctan (tan (γo+μ)cosλs) (28)
In formula, γoFor tool orthogonal rake, λsFor cutting edge inclination, that is, cutter helical angle.
Infinitesimal sword I under inclined cutting modej,zOn cutting power be represented by
By least-energy principle, the angle of shearValue should make the cutting power P on infinitesimalj,zMinimalization, and the angle of shearIt isFunction, so having
I.e.
In formulaFor normal shear angle,For shear velocity vector VsWith normal plane PnAngle.
In modus operandi Plane reference system, it is proposed that Milling force parameter be modified to：
τ in formulasFor shear stress, it is represented by
Wherein shearing force
As,j,zFor infinitesimal sword Ij,zThe section of shear at place
If line milling experimental condition meets：
I. single-blade participates in milling always；
II. axial cutting-in ap∈[1,2](mm)；
The sword for then participating in milling may be regarded as a milling edge infinitesimal, i.e. dz=ap, the Milling Force acquired at this time is i.e. equal to micro-
Milling Force on first sword, by the inverse matrix of T by its rotation transformation at tangential on infinitesimal sword, axially and radially three directions power
Formula (38) substitutes into formula (27) and acquires F in modus operandi Plane reference systemTn,j,z、FRn,j,zAnd FAn,j,zAfterwards, connection solution formula (23)
~(26), (32), (33), (35) can solve instantaneous undeformed chip thickness h (θj,z) under τs、βn、Equal milling parameters, then
Substitution formula (34) can acquire Instantaneous Milling force coefficient, wherein according to the chip removal rule that Stabler is proposed, can enable chip-flow angle η etc.
In cutting edge inclination λs。
Claims (2)
1. a kind of curve end mill Prediction Method of Milling Forces based on inclined cutting, which is characterized in that include the following steps：
Step 1 establishes frame of axes：Inertial coordinate frame OXYZ is established in workpiece boundary first, is established in cutter bottom centre O'
Moving coordinate frame O'X'Y'Z', wherein plane OXY are overlapped with plane O'X'Y', and axis X', Y' are respectively parallel to axis X, Y, axis Z' with
Tool axis overlaps；Using cutter bottom centre O' as starting point, establishes cutter in process and instantaneously feed vector f and normal vector
n；
Step 2, by cutter differential in an axial direction, with the infinitesimal sword I at axial height z on jth swordj,zFor research object, in step 1
In the inertial coordinate frame OXYZ of foundation, infinitesimal sword Ij,zMovement locus with vector representation be rj,z(t)=pj,z(t)+qj,z(φ)；
Wherein：pj,z(t) it is infinitesimal sword Ij,zCorresponding center cutter point O'zThe movement locus p in inertial coordinate frame OXYZj,z(t)
={ x (t), y (t), z }；
qj,z(φ) is O'zThe movement locus in the moving coordinate frame O'X'Y'Z' that step 1 is established；qJ, z(φ)=Rcos φ,
Rsin φ, z }, φ is cutter rotation angle, and R is tool radius；
Step 3, by differential geometry of curves, by p in step 2j,z(t) natural parameter expression is ps,z(s)={ x (t (s)), y
(t(s)),z}；
Wherein：Natural parameterDifference quotientNatural parameter
S is regular curve arc length, is denoted asWherein fzFor feed engagement, znFor the cutter number of teeth；
Step 4, the infinitesimal sword I for obtaining step 2j,zVector motion track be expressed as the vector motion track using φ as parameter,
That is rj,z(φ)=pj,z(φ)+qj,z(φ)；
Step 5, according to step 2 it can be seen that in infinitesimal sword Ij,zPlace, the normal vector of basal plane are expressed as nr=q'j,z(φ), wherein
q'j,z(φ) is qj,zThe difference quotient of (φ)；According to step 4 it can be seen that the normal vector of working reference plane is expressed as nre=r'j,z(φ),
Wherein r'j,z(φ) is rj,zThe difference quotient of (φ)；To can determine infinitesimal sword Ij,zThe working reference plane at place, the angle relative to basal plane
Degree changes
Step 6, the working reference plane determined according to step 5 establish respectively work orthogonal plane referential under inclined cutting mode and
Modus operandi Plane reference system, to establish infinitesimal sword Ij,zOn resultant force and its component between constrain；
Infinitesimal sword I under step 7, inclined cutting modej,zOn cutting power be represented by
By least-energy principle, the angle of shearValue should make the cutting power P on infinitesimalj,zMinimalization, and the angle of shearIt isFunction, in formulaFor normal shear angle,For shear velocity vector VsWith normal plane PnAngle；
Step 8, milling parameter calibration, and make the limitation of line milling experimental condition；It is obtained instantaneously not in conjunction with the constrained solution that step 7 is established
The milling parameter under depth of cut is deformed, and calculates Milling force parameter, and then is expressed as infinitesimal sword Ij,zMilling on cutting angle
Power；
It is integrated via transition matrix T, then and to each cutter tooth by step 9, the infinitesimal Milling Force for obtaining step 8 in an axial direction
Summation, can must act on the Milling Force on cutter.
2. a kind of curve end mill Prediction Method of Milling Forces based on inclined cutting as described in claim 1, which is characterized in that into
One step, the line milling experimental condition is limited to：1. only having single-blade to participate in milling always；2. axial cutting-in ap∈[1,2]
(mm)。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510627974.7A CN105279313B (en) | 2015-09-28 | 2015-09-28 | A kind of curve end mill Prediction Method of Milling Forces based on inclined cutting |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510627974.7A CN105279313B (en) | 2015-09-28 | 2015-09-28 | A kind of curve end mill Prediction Method of Milling Forces based on inclined cutting |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105279313A CN105279313A (en) | 2016-01-27 |
| CN105279313B true CN105279313B (en) | 2018-10-16 |
Family
ID=55148323
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510627974.7A Active CN105279313B (en) | 2015-09-28 | 2015-09-28 | A kind of curve end mill Prediction Method of Milling Forces based on inclined cutting |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105279313B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112818474A (en) * | 2020-08-06 | 2021-05-18 | 南京航空航天大学 | Robot milling stability prediction method based on Bessel function |
| CN113536543A (en) * | 2021-06-18 | 2021-10-22 | 北京理工大学 | Modeling method for cutting force of side-edge-free rear angle fine PCD milling cutter |
| CN117884694B (en) * | 2024-03-18 | 2024-06-18 | 哈尔滨理工大学 | Method for determining cross section direction of chip flute of end mill |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104268343A (en) * | 2014-09-28 | 2015-01-07 | 北京理工大学 | Method of cutting force prediction and temperature prediction for end-milling cutting |
| CN104298818A (en) * | 2014-09-26 | 2015-01-21 | 北京理工大学 | Method for predicting and simulating errors of end-milled surface |
| CN104392090A (en) * | 2014-09-26 | 2015-03-04 | 北京理工大学 | Construction method of aluminium alloy material end milling-cutting force and cutting processing deformation model |
-
2015
- 2015-09-28 CN CN201510627974.7A patent/CN105279313B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104298818A (en) * | 2014-09-26 | 2015-01-21 | 北京理工大学 | Method for predicting and simulating errors of end-milled surface |
| CN104392090A (en) * | 2014-09-26 | 2015-03-04 | 北京理工大学 | Construction method of aluminium alloy material end milling-cutting force and cutting processing deformation model |
| CN104268343A (en) * | 2014-09-28 | 2015-01-07 | 北京理工大学 | Method of cutting force prediction and temperature prediction for end-milling cutting |
Non-Patent Citations (2)
| Title |
|---|
| Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis;Bernard W. Ikua etc.;《Precision Engineering》;20011031;第25卷(第4期);266-273 * |
| The milling–milling machining method and its realization;Shenwang Li etc.;《The International Journal of Advanced Manufacturing Technology》;20150228;1151-1161 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105279313A (en) | 2016-01-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110270705B (en) | Micro-milling machining cutting force simulation prediction method considering cutter bounce influence | |
| CN105279313B (en) | A kind of curve end mill Prediction Method of Milling Forces based on inclined cutting | |
| Guo et al. | Research and improvement of the cutting performance of skiving tool | |
| Fergani et al. | Analytical modeling of residual stress and the induced deflection of a milled thin plate | |
| CN103646141B (en) | Cutting force modeling method for flat bottom spiral end mill orthogonal turning milling shaft parts | |
| Lin et al. | Modeling of cutting forces in end milling based on oblique cutting analysis | |
| CN102004818A (en) | Instantaneous milling force modeling method in free curve shape part peripheral milling process | |
| Xiaofen et al. | Analytical model of cutting force in axial ultrasonic vibration-assisted milling in-situ TiB2/7050Al PRMMCs | |
| Fergani et al. | Prediction of residual stress regeneration in multi-pass milling | |
| Malkov et al. | Improving thread accuracy in machining components for rocket and space technologies | |
| CN108733912A (en) | A kind of robot rotary ultrasonic drilling CFRP/ aluminium alloy laminated construction outlet burr height prediction technique | |
| Denkena et al. | Continuous generating grinding—material engagement in gear tooth root machining | |
| CN109604738A (en) | A kind of efficient side edge finish-milling processing method based on Niemann worm gear mathematical model | |
| Shen et al. | A study on cutting force in micro end milling with ultrasonic vibration | |
| Li et al. | Cutting force calculation for gear slicing with energy method | |
| Kudryashov et al. | Tool guarantee of intermittent cutting processes | |
| Tang et al. | Integrity of grinding face-gear with worm wheel | |
| Nosenko et al. | Mathematical models of operating time and cutting capacity for various stages of flat creep feed grinding of horizontal surface by circle of direct profile | |
| Meng et al. | Modeling and analysis of cutting force in vibration-assisted broaching (VAB) | |
| Ramaraj et al. | Analysis of the mechanics of machining with tapered end milling cutters | |
| Baburaj et al. | Development and experimental validation of a mechanistic model of cutting forces in micro-ball end milling of full slots | |
| Venkatesh et al. | Design, modelling and manufacturing of helical gear | |
| Tsai | Analysis and prediction of cutting forces in end milling by means of a geometrical model | |
| Zhygalov et al. | Investigation of the carbide-tipped tool wear hardened by method of aerodynamic impact | |
| Hsieh | Manufacturing models for design and NC grinding of truncated-cone ball-end cutters |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |