CN108491352A - Ablation depth method for solving based on laser energy DYNAMIC DISTRIBUTION model - Google Patents
Ablation depth method for solving based on laser energy DYNAMIC DISTRIBUTION model Download PDFInfo
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Abstract
The present invention is based on the ablation depth method for solving of laser energy DYNAMIC DISTRIBUTION model to belong to special process field, be related to it is a kind of based on pulse laser machining when piece surface energy dynamics distributed model laser maximum ablation depth method for solving.This method integrates Energy distribution along laser direction of feed, obtains Energy distribution equation of the single-pulse laser along vertical feed direction first according to Gaussian pulse laser in Energy distribution equation in plane of girdling the waist；According to parts to be processed geometric properties and laser processing technology parameter, the Geometrical change rule of laser facula motion track and the discrete distribution characteristics of pulse laser are determined, obtain piece surface energy dynamics distributed model when pulse laser machining；Further according to laser ablation thermal energy balance rule, the laser maximum ablation depth method for solving based on piece surface pulsed laser energy DYNAMIC DISTRIBUTION model is given.This method solves the problems, such as processing pulse laser discrete light spot Energy distribution problem, and it is accurate that method solves, easy to operate.
Description
Technical field
The invention belongs to special process fields, and piece surface energy dynamics are distributed when being related to one kind based on pulse laser machining
The laser maximum ablation depth method for solving of model.
Background technology
As a kind of contactless special processing technology, laser processing have it is high in machining efficiency, without tool wear, without processing
The advantages such as stress are widely used in the fields such as surface processing, increasing material manufacturing, cutting.During pulse laser machining metal material,
Laser energy is constantly accumulated in metal material surface, and material absorbs pulsed laser energy, and the removal of material is realized in heating, fusing.
Therefore, piece surface regularity of energy distribution is that a significant process in laser processing procedure is joined during pulse laser machining
Number, the accurate description of regularity of energy distribution is to Study of Laser processing quality influence factor and laser processing ablation pattern affecting laws
It is of great significance and directive function.Existing research mostly uses single-pulse laser energy distribution model or simulation result as theoretical
Foundation, is distributed pulse laser machining process piece surface energy dynamics and carries out approximate description, and the model established has ignored arteries and veins
Piece surface spread in energy characteristic distributions in laser processing procedure are rushed, do not consider that parts to be processed geometric properties change, with reality
Energy distribution deviation is larger, can not utilize piece surface energy when having achievement in research to pulse laser machining complex geometry feature
Distribution carries out Accurate Prediction, and then is accurately solved to laser ablations shape characteristics such as maximum ablation depths and bring difficulty.
A kind of " the precise and tiny drilling technology parameter optimization method of laser " of Yu Gang et al. patent publication No.s CN102737137A, should
Patent is according to ideal hole type characteristic, using the method for single-pulse laser thermal energy TRANSFER MODEL numerical simulation under different technical parameters
Laser boring effect is predicted, and carries out laser boring experiment using the laser processing parameter of simulation and prediction, by comparing real
Difference between border laser boring pass and ideal pass, adjusts machined parameters, simulation and prediction work is repeated, until being met
It is required that pass.However, this method is only applicable to laser boring, it is special to piece surface Energy distribution to lack each technological parameter of optimization
Point affecting laws research, and real work repeat measure it is larger, it is practical relatively low, have significant limitation.Document
“Micromachining of metals and thermal barriers coatings using a 532 nm
Nanosecond fiber laser ", Huang Qi etc., Physics Procedia, 2012,39 (8), 603-612 are used
532nm grades of pulse lasers have studied laser and cover the physical action between coated metal, close by experimental study light spot energy
The variation of the parameters such as degree obtains using maximum material removing rate as the optimal of target laser ablation straight trough geometric properties affecting laws
Machined parameters combine.This method is using single-pulse laser thermal energy ablating model as theoretical model, and verification waist radius variation is to laser
The influence of ablation straight trough removal rate.However, the theoretical model of this method is limited to single-pulse laser, can not accurate description laser it is dynamic
State process piece surface Energy distribution situation does not join each technique in laser processing when studying the influence of machined parameters
Several carry out to Energy distribution Influencing Mechanism is furtherd investigate, and has certain limitation.
Invention content
The present invention is directed to the limitation and defect of the existing prior art, has invented a kind of based on laser energy DYNAMIC DISTRIBUTION mould
The ablation depth method for solving of type, this method, which considers, changes incident laser fluence, laser feed speed and laser weight
Complex frequency establishes model in the DYNAMIC DISTRIBUTION of material surface energy to change laser, and influences laser processing ablation depth
Parameter related with Energy distribution.The DYNAMIC DISTRIBUTION model of piece surface energy, discloses when by establishing pulse laser machining
To control ablation depth as target, change piece surface energy dynamics changing rule caused by laser processing parameter.According to laser
Ablation thermal energy Balance, the laser maximum ablation depth for giving piece surface pulsed laser energy DYNAMIC DISTRIBUTION model solve
Method.This method solves the problems, such as processing pulse laser discrete light spot Energy distribution problem.
The technical scheme is that a kind of ablation depth method for solving based on laser energy DYNAMIC DISTRIBUTION model, special
Sign is that this method, which considers, changes incident laser fluence, laser feed speed and laser repetition rate, sharp to change
Light establishes model in the DYNAMIC DISTRIBUTION of material surface energy；First according to Gaussian pulse laser in the Energy distribution side in plane that girdles the waist
Journey integrates Energy distribution along laser direction of feed, obtains Energy distribution side of the single-pulse laser along vertical feed direction
Journey；Then according to parts to be processed geometric properties and laser processing technology parameter, determine that the geometry of laser facula motion track becomes
The discrete distribution characteristics of law and pulse laser obtains piece surface energy dynamics distributed model when pulse laser machining；Most
The influence that piece surface energy dynamics are distributed according to laser optics parameter and non-optical parameters afterwards, it is flat according to laser ablation thermal energy
Weigh rule, gives the laser maximum ablation depth method for solving based on piece surface pulsed laser energy DYNAMIC DISTRIBUTION model.
Method is as follows：
Step 1, pulsed laser energy distribution is integrated along machine direction
It is laser machined using basic mode Gaussian pulse laser, as the electromagnetic field E (x, y, z) that stable state is propagated, is met
Helmholtz equation：
In formula,For Laplace operator, in rectangular coordinate system,
S is wave number,λ is optical maser wavelength, in a vacuum n=1.
Basic mode Gaussian pulsed beam is in transmission process, and beam energy distribution at waist radius is minimum, and energy is close
Spend highest.With the increase of transmission range, beam energy distributed areas gradually increase, and energy density is gradually reduced.It is sat at right angle
In mark system, the intensity I distributions of fundamental-mode gaussian beam can be expressed as：
Wherein, w0For waist radius, A0For amplitude constant, w (z) is beam radius.Beam radius w (z) is with transmission range
The variation of Z is extended to the outside according to the hyperbolic rule that formula (3) describes, and wherein λ is optical maser wavelength.W (z) takes minimum at z=0
Value, i.e., beam radius is minimum at this time, is waist radius w0。
In the plane perpendicular to laser light incident direction, the energy F (x, y) of Gaussian beam by Gaussian function distributional pattern from
Center smoothly reduces outward, and single pulse energy (z=0) distribution formula in plane with a tight waist is：
Wherein, F0For laser energy density.
Shown in the Energy distribution of basic mode Gaussian pulsed beam such as formula (4), when being processed along the arc track that radius is R,
Dynamic power distribution causes hot spot overlapping region to change due to difference because of working process parameter variation.A pulse duration
Interior, single-pulse laser energy is constantly accumulated along machine direction in piece surface, and pulse laser adds along the arc track that radius is R
Single pulse energy can be integrated along machine direction, obtains distribution equation of the pulse laser along vertical machine direction by working hour.
When pulse laser is along the arc track processing that radius is R, it is specified that arteries and veins in a pulse duration (nanosecond)
Impulse light machine direction is X-direction.Therefore, if pulse laser single pulse energy distribution equation is distinguished along X-axis range of integration
For-x0And x0, then pulse laser is equation about y along the integral function of machine direction, therefore, laser energy with processing side
Distribution formula F in vertical Y directionyFor：
Basic mode gauss laser single pulse energy is distributed in waist radius always, i.e., to basic mode gauss laser along machine direction
When integral, range of integration is respectively-w0And w0, then according to formula (5), basic mode gauss laser is in the Y-axis vertical with machine direction
Integral result F on directionyFor：
In above formula, Gauss error function erf be non-basic function, by error function integral table it is found thatThen
Above formula can be reduced to：
Step 2, pulsed laser energy DYNAMIC DISTRIBUTION model solution
When basic mode Gaussian pulse laser machines, any point in piece surface arc track is r apart from center of circle O length,
And meet R≤r≤R+w, introduce hot spot relative position parameter k.Any point distance in piece surface laser beam ablation track
The length r of center of circle O meets with Circular test radius R：
R=R+kw (8)
In view of R≤r≤R+w, so -1≤k≤1 uses hot spot relative position parameter k that is, when k increases to+1 by -1
It can determine that on ablation track any position in laser processing procedure.
Known arc track radius R, adjacent spots distance are Δ x, then it is N to process pulse number needed for a complete curve
For：
Laser repetition rate is f, and laser feed rate is v, then adjacent spots distance is：
By formula (9) and formula (10), it is N and laser repetition rate f, laser to process pulse number needed for a complete curve
Relationship between feed rate v is：
Pulsed laser energy distribution as shown in formula (5), is processed, zero along machine direction integral along the arc track that radius is R
Cumlative energy F of the part surface along machine direction at hot spot relative position ksumFor：
Fsum=NFy|Y=kw (12)
Bringing formula (7) into formula (12) can obtain：
When pulse laser is processed along the arc track that radius is R, piece surface is along machine direction in hot spot relative position k
The spread in energy at place is distributed on the circular arc that radius of curvature is r, and the pulsed laser energy DYNAMIC DISTRIBUTION value at r is Fk, therefore, zero
Apart from center of circle O length it is a little that pulsed laser energy DYNAMIC DISTRIBUTION equation at r is in part surface laser light beam machining locus：
Formula (8), formula (13) is brought into formula (14) to obtain：
Formula (15) is pulsed laser energy DYNAMIC DISTRIBUTION model.By the model, laser optics parameter, non-optical is established
The affecting laws that parameter and part geometry changing features are distributed piece surface energy dynamics.
Step 3, the maximum ablation depth based on laser energy DYNAMIC DISTRIBUTION model solves
During pulse laser machining, laser maximum ablation depth is located at spot center, i.e. k=0.In the condition of k=0
Under, formula (15) is represented by：
Pulse laser realizes the removal of part material, it is necessary first to which the energy accumulation of piece surface reaches the ablation threshold of material
Value.Since the interaction process of laser and target material meets law of conservation of energy, single-pulse laser recession thickness lT
There are following relationships between ablation threshold：
ρCp(Tm-T0)lT=(1- β) Fth (17)
Wherein, ρ is part material density, and Cp is part material specific heat capacity, TmFor part material fusion temperature, T0For room temperature,
FthFor the Laser Ablation Threshold of part material, β is the reflectivity that specific wavelength laser machines certain material, lTMeet formula (18)：
Wherein, DTFor thermal diffusion coefficient, tpFor the pulse laser duration.
According to the law of thermodynamics, after laser energy is incident to piece surface and is absorbed by material part, it is more than ablation threshold
When the energy fusing of value part even vaporizes the material that thickness is H, energy balance relations can be expressed as：
Wherein, ρsFor part material solid-state lower density；ρlFor part material liquid lower density；ΔHslIt is melted for part material
Enthalpy；ΔHlvFor part material enthalpy of vaporization；H is the piece surface maximum ablation depth under pulsed laser energy density.
The piece surface maximum ablation depth based on pulsed laser energy DYNAMIC DISTRIBUTION can be obtained by formula (17), (18), (19)
For：
The remarkable result and benefit of the present invention is the Geometrical change rule and pulse for pulsed laser spot motion track
The discrete distribution characteristics of laser energy, the DYNAMIC DISTRIBUTION model of piece surface energy, describes when establishing pulse laser machining
The energy dynamics regularity of distribution during pulse laser machining, and using this DYNAMIC DISTRIBUTION model as bridge, to study pulse laser
Processing quality and ablation topography issues caused by machining energy changes in distribution rule provide the new method of Continuum Model solution
And new approaches, solving engineering, laser ablation depth caused by simulation and prediction and pulse model approximate description adds repeatedly in practice
Work error fundamentally solves pulse laser maximum ablation depth Solve problems.It is accurate that method solves, easy to operate.
Description of the drawings
Fig. 1-method overall flow figure；
Fig. 2-Gaussian pulse laser facula Energy distribution；Wherein, F0Indicate pulsed laser energy density, X, Y are indicated respectively
The position of pulse hot spot；
Fig. 3-pulse laser machining circular arc schematic diagram；Wherein, O1And O2The respectively pulse laser adjacent spots center of circle, O0For
Circular arc curvature center, R are laser processing trajectory tortuosity radius, and laser direction of feed is O1O2, w0For laser beam waist radius, with light
Spot center is coordinate origin, and laser direction of feed is X-axis, and vertical feed direction is that Y-axis establishes coordinate system as shown in the figure；
Fig. 4-laser energy density is to maximum ablation depth affecting laws verification result；Wherein, F0For laser energy density,
H is laser ablation depth capacity, and L is that theoretical values emulate change curve, and P is experiment processing result；
Fig. 5-laser repetition rate is to maximum ablation depth affecting laws verification result；Wherein, f is laser repetition rate, H
For laser ablation depth capacity, L is that theoretical values emulate change curve, and P is experiment processing result；
Fig. 6-laser feed speed is to maximum ablation depth affecting laws verification result；Wherein, v is laser feed speed, H
For laser ablation depth capacity, L is that theoretical values emulate change curve, and P is experiment processing result.
Specific implementation mode
Combination technology scheme and the attached drawing specific implementation mode that the present invention will be described in detail.
During pulse laser machining, since the geometric properties of the discrete characteristic distributions of laser energy and machining locus change,
Single-pulse laser energy distribution model or Energy distribution simulation result can not accurate description material surface energy DYNAMIC DISTRIBUTION, this hair
A kind of maximum ablation depth method for solving based on pulsed laser energy DYNAMIC DISTRIBUTION model of bright proposition, for pulsed laser light
The Geometrical change rule of spot motion track and the discrete distribution characteristics of pulsed laser energy, part when establishing pulse laser machining
The DYNAMIC DISTRIBUTION model of surface energy describes the energy dynamics regularity of distribution during pulse laser machining, and with this dynamic
Distributed model is bridge, for change laser processing technology state modulator ablation depth provide energy dynamics distribution it is theoretical according to
According to providing serialization for processing quality and ablation topography issues caused by research pulse laser machining Energy distribution changing rule
The new method and new approaches of model solution.Method overall flow figure is as shown in Figure 1.
With waist radius w0=20 μm of fundamental-mode gaussian beam swashs along the complex geometry feature arc track that radius is R
For light process, by MATLAB softwares and verification test, the solution procedure of process in detail.
First, its integral along machine direction is calculated according to pulsed laser energy distribution formula：It can be obtained by formula (4), beam
Waist radius w0Energy distribution formula of=20 μm of the basic mode Gaussian pulsed beam in plane with a tight waist be：
Wherein, F0For laser energy density.Attached drawing 2 show Gaussian pulse laser facula Energy distribution.
When pulse laser is along the arc track processing that radius is R, pulse laser single pulse energy distribution equation is integrated along X-axis
Bound is respectively-w0And w0.Basic mode gauss laser is obtained in the Y direction upper integral result vertical with machine direction according to formula (7)
For：
Secondly, according to hot spot motion track Geometrical change rule and the discrete distribution characteristics of pulsed laser energy, pulse is solved
Laser energy DYNAMIC DISTRIBUTION model：It is as shown in Fig. 3 to laser machine arc track, piece surface complex geometry feature arc track
Interior apart from center of circle O length is r, introduces hot spot relative position parameter k, and meets formula (8), pulsed laser energy r at moves
State Distribution Value is Fk.Obtaining pulsed laser energy DYNAMIC DISTRIBUTION equation by formula (15) is：
Finally, the pulsed laser energy DYNAMIC DISTRIBUTION model based on acquisition, it is dynamic to energy according to optics and non-optical parameters
State is distributed affecting laws, solves laser maximum ablation depth：During pulse laser machining, laser maximum ablation depth is located at light
At spot center, i.e. k=0.When k=0, formula (23) is represented by：
Known parts to be processed metal coating is copper, density p=8900kg/m3, specific heat capacity Cp=390J/kgK, material
Expect fusion temperature Tm=1358K, room temperature T0=295K, thermal diffusion coefficient DT=1.17cm2/ s, pulse laser duration tp=
15ns, solid-state lower density ρs=8900kg/m3, liquid lower density ρl=8000kg/m3, fusion enthalpy Δ Hsl=205kJ/kg, vaporization
Enthalpy Δ Hlv=305kJ/mol, reflectivity β=0.34, according to single-pulse laser recession thickness lTWith ablation threshold FthRelational expression
(17), formula (18), energy balance relations formula (19), the maximum ablation depth found out under pulsed laser energy density are：
Using the laser maximum ablation depth solution formula based on pulsed laser energy DYNAMIC DISTRIBUTION model, laser energy is obtained
The affecting laws of metric density, laser repetition rate and the variation of laser feed speed to maximum ablation depth.
Experiment selects wavelength for 532nm pulse lasers, pulse duration 15ns, and range of pulse repetition frequency is
10-40kHz.The material of laser processing is that polyimide substrate integrally covers copper product.Verification test is studied using control variate method
Single-factor influence rule is analyzed by MATLAB numerical simulations and test data fitting curve comparison.
Attached drawing 4 show changing rule relativity of the theoretical and practical maximum ablation depth with laser energy density, this
When the laser repetition rate that sets as 30kHz, laser feed speed is 2m/min；Attached drawing 5 show theoretical and practical maximum burning
Depth is lost with the changing rule relativity of laser repetition rate, and the laser energy density set at this time is 42J/cm2, laser into
It is 2m/min to speed.From two above emulation and the comparison of experimental result it is found that as laser energy density and laser repeat
The increase of frequency, laser maximum ablation depth increase, and MATLAB numerical simulations and actual experiment result are almost the same, test
The accuracy of energy dynamics distributed model and maximum ablation depth method for solving is demonstrate,proved.
The laser repetition rate set is 30kHz, laser energy density 42J/cm2.It is emulated and is tested by MATLAB
The laser maximum ablation depth of measurement is as shown in Fig. 6 with the variation comparison diagram of laser feed speed.Thus, it can be known that laser ablation
Depth is continuously decreased with the increase of laser feed speed, and reduction speed is slower and slower, and exponential rule demonstrates energy
The accuracy of DYNAMIC DISTRIBUTION model and maximum ablation depth method for solving.
To sum up, using this method establish model consider change incident laser fluence, laser feed speed and
Laser repetition rate with change laser material surface energy DYNAMIC DISTRIBUTION, and then influence ablation depth etc. of laser processing with
The related parameter of Energy distribution.Material surface energy DYNAMIC DISTRIBUTION maximum value is in laser repetition rate maximum, incident laser energy
It is got when density maximum and laser feed speed minimum, and as laser repetition rate reduces, incident laser fluence reduces
Increase with laser feed speed and reduces.
By above-mentioned experiment, using laser maximum ablation depth as token state, laser energy density, laser feeding speed are demonstrated
The variation of degree, laser repetition rate is to the accuracy based on pulsed laser energy DYNAMIC DISTRIBUTION continuous analysis model, experiment knot
Fruit illustrates that pulsed laser energy DYNAMIC DISTRIBUTION model can directly reflect during pulse laser actual processing, optical parameter and
Non-optical parameters change the affecting laws to material surface energy DYNAMIC DISTRIBUTION, and then give based on pulsed laser energy dynamic
The maximum ablation depth method for solving of distributed model, conventional is distributed continuous analysis in being laser machined to engineering actual pulse
There is innovative reference value.
Claims (1)
1. a kind of ablation depth method for solving based on laser energy DYNAMIC DISTRIBUTION model, which is characterized in that this method synthesis is examined
Consider and change incident laser fluence, laser feed speed and laser repetition rate, to change laser in material surface energy
DYNAMIC DISTRIBUTION establishes model；First according to Gaussian pulse laser in Energy distribution equation in plane of girdling the waist, along laser direction of feed
Energy distribution is integrated, Energy distribution equation of the single-pulse laser along vertical feed direction is obtained；Then according to be processed
Part geometry feature and laser processing technology parameter determine the Geometrical change rule and pulse laser of laser facula motion track
Discrete distribution characteristics obtains piece surface energy dynamics distributed model when pulse laser machining；Finally according to laser optics parameter
The influence being distributed to piece surface energy dynamics with non-optical parameters gives and is based on according to laser ablation thermal energy balance rule
The laser maximum ablation depth method for solving of piece surface pulsed laser energy DYNAMIC DISTRIBUTION model；The specific steps of method are such as
Under：
Step 1, pulsed laser energy distribution is integrated along machine direction
It is laser machined using basic mode Gaussian pulse laser, as the electromagnetic field E (x, y, z) that stable state is propagated, meets last of the twelve Earthly Branches nurse
Hereby equation suddenly：
In formula,For Laplace operator, in rectangular coordinate system,S is
Wave number,λ is optical maser wavelength, in a vacuum n=1；
Basic mode Gaussian pulsed beam is in transmission process, and beam energy distribution at waist radius is minimum, and energy density is most
It is high；With the increase of transmission range, beam energy distributed areas gradually increase, and energy density is gradually reduced；In rectangular coordinate system
In, the intensity I distributions of fundamental-mode gaussian beam can be expressed as：
Wherein, w0For waist radius, A0For amplitude constant, w (z) is beam radius；Beam radius w (z) is with transmission range Z's
Change the hyperbolic rule described according to formula (3) to extend to the outside, wherein λ is optical maser wavelength；W (z) is minimized at z=0,
I.e. beam radius is minimum at this time, is waist radius w0；
In the plane perpendicular to laser light incident direction, the energy F (x, y) of Gaussian beam presses Gaussian function distributional pattern from center
Smooth outward to reduce, single pulse energy (z=0) distribution formula in plane with a tight waist is：
Wherein, F0For laser energy density；
Shown in the Energy distribution of basic mode Gaussian pulsed beam such as formula (4), when being processed along the arc track that radius is R, dynamic
Energy distribution causes hot spot overlapping region to change due to difference because of working process parameter variation；It is single within a pulse duration
Pulsed laser energy is constantly accumulated along machine direction in piece surface, when pulse laser is processed along the arc track that radius is R,
Single pulse energy can be integrated along machine direction, obtains distribution equation of the pulse laser along vertical machine direction；
When pulse laser is along the arc track processing that radius is R, it is specified that pulse swashs in a pulse duration (nanosecond)
Light machine direction is X-direction；Therefore, if pulse laser single pulse energy distribution equation is along X-axis range of integration respectively-x0
And x0, then pulse laser is the equation about y along the integral function of machine direction, and therefore, laser energy hangs down with machine direction
Distribution formula F in straight Y directionyFor：
Basic mode gauss laser single pulse energy is distributed in waist radius always, i.e., is integrated along machine direction to basic mode gauss laser
When, range of integration is respectively-w0And w0, then according to formula (5), basic mode gauss laser is in the Y direction vertical with machine direction
On integral result FyFor：
In above formula, Gauss error function erf be non-basic function, by error function integral table it is found thatThen above formula
It can be reduced to：
Step 2, pulsed laser energy DYNAMIC DISTRIBUTION model solution
When basic mode Gaussian pulse laser machines, any point in piece surface arc track is r apart from center of circle O length, and full
Sufficient R≤r≤R+w introduces hot spot relative position parameter k；Any point is apart from center of circle O in piece surface laser beam ablation track
Length r and Circular test radius R meet：
R=R+kw (8)
It, i.e., can be with using hot spot relative position parameter k when k increases to+1 by -1 so -1≤k≤1 in view of R≤r≤R+w
Determine that on ablation track any position in laser processing procedure；
Known arc track radius R, adjacent spots distance are Δ x, then it is that N is to process pulse number needed for a complete curve：
Laser repetition rate is f, and laser feed rate is v, then adjacent spots distance is：
By formula (9) and formula (10), process that pulse number needed for a complete curve is N and laser repetition rate f, laser is fed
Relationship between rate v is：
Pulsed laser energy distribution as shown in formula (5), is processed, parts list along machine direction integral along the arc track that radius is R
Cumlative energy F of the face along machine direction at hot spot relative position ksumFor：
Fsum=NFy|Y=kw (12)
Bringing formula (7) into formula (12) can obtain：
When pulse laser is processed along the arc track that radius is R, piece surface is along machine direction at hot spot relative position k
Spread in energy is distributed on the circular arc that radius of curvature is r, and the pulsed laser energy DYNAMIC DISTRIBUTION value at r is Fk, therefore, parts list
Apart from center of circle O length it is a little that pulsed laser energy DYNAMIC DISTRIBUTION equation at r is in the laser beam machining locus of face：
Formula (8), formula (13) is brought into formula (14) to obtain：
Formula (15) is pulsed laser energy DYNAMIC DISTRIBUTION model；By the model, laser optics parameter, non-optical parameters are established
The affecting laws that piece surface energy dynamics are distributed with part geometry changing features；
Step 3, the maximum ablation depth based on laser energy DYNAMIC DISTRIBUTION model solves
During pulse laser machining, laser maximum ablation depth is located at spot center, i.e. k=0；Under conditions of k=0,
Formula (15) is represented by：
Pulse laser realizes the removal of part material, it is necessary first to which the energy accumulation of piece surface reaches the ablation threshold of material；
Since the interaction process of laser and target material meets law of conservation of energy, single-pulse laser recession thickness lTWith burning
There are following relationships between erosion threshold value：
ρCp(Tm-T0)lT=(1- β) Fth (17)
Wherein, ρ is part material density, and Cp is part material specific heat capacity, TmFor part material fusion temperature, T0For room temperature, FthFor
The Laser Ablation Threshold of part material, β are the reflectivity that specific wavelength laser machines certain material, lTMeet formula (18)：
Wherein, DTFor thermal diffusion coefficient, tpFor the pulse laser duration；
According to the law of thermodynamics, after laser energy is incident to piece surface and is absorbed by material part, it is more than ablation threshold portion
When the energy fusing divided even vaporizes the material that thickness is H, energy balance relations can be expressed as：
(ρsΔHsl+ρlΔHlv) H=(1- β) (Fk0-Fth) (19)
Wherein, ρsFor part material solid-state lower density；ρlFor part material liquid lower density；ΔHslFor part material fusion enthalpy；Δ
HlvFor part material enthalpy of vaporization；H is the piece surface maximum ablation depth under pulsed laser energy density；
Can obtain the piece surface maximum ablation depth based on pulsed laser energy DYNAMIC DISTRIBUTION by formula (17), (18), (19) is：
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| CN117787021A (en) * | 2024-02-28 | 2024-03-29 | 中国人民解放军海军工程大学 | Laser far field energy density estimation method |
| CN117787021B (en) * | 2024-02-28 | 2024-05-07 | 中国人民解放军海军工程大学 | Laser far field energy density estimation method |
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