CN109190260A - A kind of laser-arc hybrid welding in industry Three dimensional transient simulation method - Google Patents
A kind of laser-arc hybrid welding in industry Three dimensional transient simulation method Download PDFInfo
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- B23K—SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
- B23K26/00—Working by laser beam, e.g. welding, cutting or boring
- B23K26/346—Working by laser beam, e.g. welding, cutting or boring in combination with welding or cutting covered by groups B23K5/00 - B23K25/00, e.g. in combination with resistance welding
- B23K26/348—Working by laser beam, e.g. welding, cutting or boring in combination with welding or cutting covered by groups B23K5/00 - B23K25/00, e.g. in combination with resistance welding in combination with arc heating, e.g. TIG [tungsten inert gas], MIG [metal inert gas] or plasma welding
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Abstract
A kind of laser-arc hybrid welding in industry Three dimensional transient simulation method, it solves that overall calculation is not implemented existing for present laser arc welding analogy method, the problem of being unable to true reappearance composite welding process, the present invention includes establishing geometrical model, initialization, renewal time step-length, update physical parameter, solve electromagnetic field, space interruption is decomposed, calculate gas zones state, calculate workpiece area state, update molten bath free interface step and judgment step, overall region space interruption is decomposed into gas zones and workpiece area by the instantaneous interface of workpiece and solved respectively by the present invention, and the two-way sequence coupling in two regions is realized by the way of the load of boundary in Minimum-time step.The present invention realizes the whole exact numerical solution of the aperture, molten bath, plasma, metallic vapour development law of the electric arc combined welding of laser-TIG, can be used for theoretical research and the process optimization of hybrid Laser-Arc Welding.
Description
Technical field
The invention belongs to weld numerical value emulation method, and in particular to a kind of laser-arc hybrid welding in industry Three dimensional transient numerical value
Analogy method.
Technical background
Laser-arc hybrid welding in industry can be realized and have complementary advantages in conjunction with the advantage of two kinds of heat sources of laser and electric arc;With electric arc
Welding is compared, and laser-arc hybrid welding in industry is with fusion penetration is big, speed is high, residual stress and deformation are small;Compared with laser welding,
The enhancing of laser-arc hybrid welding in industry bridging capability, composition of weld line are easily adjusted, and cold short phase tendency reduces, and aperture stability improves.Swash
Unique advantage possessed by optical-electronic arc composite welding can be realized the efficient welding manufacture of high quality, and becoming one kind has
The welding technique of wide application prospect has important application in fields such as ocean, nuclear powers.
Laser-arc hybrid welding in industry process as shown in Figure 1, laser, electric arc directly as Source on material, make material
The multiple physical states transformation such as fusing, gasification and ionization occurs for material, generates molten bath, aperture, photic metallic vapour/plasma, electric arc etc.
Gas ions etc. are simultaneously deposited, and there is the vigorous physicals variation such as very high temperature, high pressure, high speed, instantaneous in grade region, these are complicated
Physical process and feature make it difficult to further investigate composite welding mechanism using experimental method.Laser-electric arc simultaneously
Composite welding combines two kinds of heat sources, and technological parameter further increases, and also gives and obtains optimum process ginseng by experimental method
Number brings more difficulties.It can be to each physical quantity of laser-arc hybrid welding in industry process using the method for numerical simulation
And its development law carries out visual quantitative analysis, can disclose aperture in welding process, molten bath, plasma, metal steam
The development law of vapour at any time, therefore application of the numerical simulation in laser-arc hybrid welding in industry research is of great significance.
Laser-arc hybrid welding in industry process is extremely complex, and physical modeling is difficult, the density of interface two sides, temperature, potential,
Speed etc. mutates in little space scale, causes interface nearby to have the characteristics that big gradient, nonlinearity, using system
One two-phase flow model solved solves difficulty, and is difficult to obtain the accurate solution of interface location.For above-mentioned difficulties, this field skill
Art personnel or ignore electric arc and metallic vapour only calculates molten bath, sees Z Gao, et al.Analysis of weld pool
dynamic during stationary laser–MIG hybrid welding.The International Journal
Of Advanced Manufacturing Technology, 2009,44 (9-10): 870 or ignores molten bath and only calculates electricity
Arc is shown in Y.T.Cho, et al.Numerical analysis of hybrid plasma generated by Nd:YAG
Laser and gas tungsten arc.Optics&Laser Technology, 2011,43 (3): 711-720, currently, still
Do not have and the report realized is calculated to the whole numerical value of Laser-Arc Hybrid Welding.However the row of composite welding process plasma
Will directly to determine to the thermodynamic activity in molten bath, and metallic vapour caused by the local explosive vaporization in molten bath will also change etc. from
The composition and property of daughter.Therefore, it only calculates molten bath or only calculates the mode of electric arc, it is multiple that result obtained is unable to true reappearance
Welding process is closed, the research of the interaction mechanism of laser-arc hybrid welding in industry is also unfavorable for.
Summary of the invention
The present invention provides a kind of laser-arc hybrid welding in industry Three dimensional transient simulation method, solves present laser electric arc
Overall calculation is not implemented existing for welding analog method, is unable to the problem of true reappearance composite welding process, can be realized to sharp
Fusing, solidification, evaporation behavior in the electric arc combined welding process of light-TIG, arc-plasma, laser plume brightness gas and metal
The heat transfer flow and electromagnetic field in molten bath, which develop, carries out integration simulation calculating, more really can reproduce physics comprehensively
Process, facilitate carry out deeper into theoretical research, can further promote the engineering application of laser-arc hybrid welding in industry.
A kind of laser-arc hybrid welding in industry Three dimensional transient simulation method provided by the present invention, including establish geometry
Model step, renewal time step-length step, updates physical parameter step, solves between electromagnetic field step, space initialization step
Disconnected decomposition step calculates gas zones state step, calculates workpiece area state step, updating molten bath free interface step and sentence
Disconnected step, it is characterised in that:
One, geometrical model step is established:
Geometrical model is established using 3 d modeling software, the geometrical model is cuboid, and the geometrical model includes work
Part region, electrode zone and gas zones, workpiece area are cuboid, and length and width is identical as the geometrical model;Electrode zone
It is the cylindrical body of cone for cylindrical body or one end, when electrode zone is cylindrical body, electrode zone central axes and vertical direction are pressed from both sides
Angle is 0 °~60 °, and when electrode zone is the cylindrical body that one end is cone, cone basal diameter is identical as cylinder diameter;
Electrode zone threshold value workpiece area vertical distance 1mm~10mm;The gas zones are that the geometrical model removes workpiece area
Remaining region outside domain, electrode zone;
Region of the geometrical model in addition to electrode zone is zoning;
Grid dividing is carried out using grid dividing software to the zoning again, the grid is cuboid or pros
The side length of body, cuboid or square is 10 μm~500 μm;
Two, initialization step:
The boundary condition of given zoning: 300~1000K of environment temperature, 3000~3500K of electrode temperature, environment pressure
0.1~10atm of power, workpiece bottom potential 0V;
Set the physical quantity initial value of each grid element center point in entire zoning: potential 0V, current density 0A/m2、
Magnetic field strength 0T, speed 0m/s, 300~1000K of temperature, 0.1~10atm of pressure, metallic vapour mass percentage 0;
Accumulation interval variable t is setsum=0, calculate deadline tend=0.1~10s;
Time step Δ t is setiFor initial time step delta t0, Δ t0=1 × 10-7~1 × 10-6S carries out step 4;
Three, renewal time step-length step:
Calculate the maximum time step-length of gas zones stability Calculation
The maximum time step-length of workpiece area stability Calculation is calculated againIt takes
(Δt0,Δtg,Δtm) three minimum value as update time step Δ ti, carry out step 4;
Wherein, i=1,2 ..., indicate that the i-th step calculates, maximal condition number Cmax=0.5~1.0, ug_x,ug_y,ug_zRespectively
The gas velocity of gas zones grid element center pointComponent in three directions of x, y, z, um_x,um_y,um_zRespectively workpiece area
The molten bath speed of domain grid element center pointComponent in three directions of x, y, z;Δ x, Δ y, Δ z are respectively grid in x, y, z three
The size in a direction;
Four, physical parameter step is updated:
Set the physical parameter in entire zoning:
Gas zones are full of by the mixed gas of protective gas and metallic vapour, and the protective gas is argon gas, helium
And one or more of carbon dioxide, metallic vapour are the metallic vapour of workpiece material;Metal in mixed gas is calculated for the first time
Quality of steam percentage composition and temperature are initial value, future time walk in mixed gas metallic vapour mass percentage and temperature by
Sub-step (7.2) and (7.3) obtain;
The conductivityσ of mixed gase, density pg, viscosity, mug, specific heat capacity Cpg, thermal coefficient kgAnd gas net radiation coefficient εN
It is made of at each grid element center mixed gas and temperature directly determines;
Workpiece area workpiece material is ferrous alloy or non-ferrous alloy;Corresponding conductivityσe, density pm, viscosity, mum、
Specific heat capacity Cpm, thermal coefficient km, thermal expansion coefficient β, surface tension coefficient γ, hot capillary force coefficientWork gestureSpoke
Penetrate rate εrIt is directly determined at each grid element center by workpiece material and temperature;
Five, electromagnetic field step is solved:
Solve the electromagnetic field in entire zoning:
It is passed through welding current in welding process, electromagnetic field will be generated in entire zoning, 30 are given by electrode~
The welding current of 300A calculates the potential for obtaining all grid element center points in entire zoningCurrent densityAnd magnetic strength
Answer intensityDistribution, accounting equation are as follows:
Wherein, permittivity of vacuum μ0, the magnetic of grid element center point loses powerGradient operatorDivergence operatorCurl is calculated
SonLaplace operatorConductivityσeGas zones mixed gas and workpiece area work then is respectively adopted when calculating
The corresponding conductivity of part material;
Six, decomposition step is interrupted in space:
The molten bath free interface using workpiece area upper surface as interface, subsequent calculating to update is calculated for the first time to carry out as interface
Space interruption is decomposed, and is gas zones and workpiece area by overall calculation region division, and gas zones are electric arc-metallic vapour
Area, workpiece area are workpiece solid-liquid area;Definition interfaces boundary point is molten bath free interface two sides grid element center point line and molten bath
The crosspoint of free interface;
Seven, gas zones state step is calculated:
Successively calculate flow field, temperature field and the metallic vapour distribution of gas zones, including following sub-step:
(7.1) it calculates gas zones flow field: calculating the gas velocity of all grid element center points of gas zonesGas pressure
Power Pg, calculation formula is as follows:
WhereinFor acceleration of gravity;
At the molten bath free interface of gas zones and workpiece area, the gas velocity of interface boundary point is setIt is gentle
Body pressure Pg_sIt is respectively as follows:
Wherein, kickback pressure P is evaporatedr, obtained using the Recoil Pressure Model based on environmental pressure;
(7.2) it calculates gas zones temperature field: calculating the gas temperature T of all grid element center points of gas zonesg, calculate public
Formula is as follows:
Wherein, kb: Boltzmann constant, e: elementary charge, t: the time,Differential operator;
At the molten bath free interface of gas zones and workpiece area, the hot-fluid that interface boundary point enters gas zones is calculated
qgas:
Wherein Tgs、TmsThe respectively temperature of the gas zones and workpiece area of interface boundary point, is obtained using ghost fluid method
It takes;keffFor the effective thermal conductivity of interface boundary point, keff=0.5 × (kg(Tgs)+kg(Tms)), kg(Tgs)、kg(Tms) respectively
For temperature Tgs、TmsCorresponding Measurement of Gas Thermal Conductivity;δ be molten bath free interface boundary layer effective thickness, δ be 0.1mm~
0.4mm;
(7.3) it calculates the diffusion of gas zones metallic vapour: calculating the metallic vapour of all grid element center points in gas zones
Mass percentage Cvapor, calculation formula is as follows:
Wherein, D is metallic vapour mass diffusion coefficient, which can be obtained by the second sticky approximation method;
At the molten bath free interface of gas zones and workpiece area, each interface boundary point metallic vapour quality percentage is set
Content Cvapor:
Eight, workpiece area state step is calculated:
Successively calculate the flow field and temperature field of workpiece area, including following sub-step:
(8.1) it calculates workpiece area flow field: calculating the molten bath speed of all grid element center points of workpiece areaMolten bath pressure
Power Pm, calculation formula is as follows:
Wherein, the temperature T of workpiece area grid element center pointm, environment temperature is taken when calculating for the first time;Future time step, which calculates, adopts
With the calculated value of a time step (7.2);
Reference temperature Tref, take workpiece material melting temperature;K, C is respectively seepage coefficient and relaxation coefficient, with liquid fraction fl
It is closely related:
Wherein, d be and interdendritic away from the closely related constant of size, d=0.05mm~0.5mm;Liquid fraction flWith temperature
It spends in a linear relationship:
Wherein, Tl、TsIt is the liquidus temperature and solidus temperature of workpiece material respectively;
At the molten bath free interface of gas zones and workpiece area, the molten bath normal pressure P of interface boundary point is calculatedfWith
Molten bath tangential force
WhereinThe respectively normal vector and tangent vector of molten bath free interface, κ are molten bath free interface curvature, Peff
It is gas zones to the effective pressure of workpiece area, takes Peff=max (Pr,Pg);
(8.2) it calculates workpiece area temperature field: calculating the temperature T of all grid element center points of workpiece aream, calculation formula is such as
Under:
Wherein, energy absorption q of the workpiece to laserlaser, obtained using ray trace method;The laser is optical-fiber laser
Or Nd:YAG laser, power 100W~10000W, spot radius 0.1mm~0.5mm;
At the molten bath free interface of gas zones and workpiece area, the hot-fluid that interface boundary point enters workpiece area is calculated
qmatel:
Wherein, σ is this special fence-Boltzmann constant, T∞For environment temperature, qevapFor evaporative heat loss;
Nine, molten bath free interface step is updated:
Pass through the molten bath speed of all grid element center points of workpiece areaEach grid element center point is to interface in zoning
Distance φ, the contour surface of φ=0 obtained is the molten bath free interface updated, and calculation formula is as follows:
The normal vector and curvature of molten bath free interface solve as follows:
In the step 5~step 9, related accounting equation all uses finite difference method or limited bulk side
Method progress is discrete, and in time step Δ tiInside solved;
Ten, judgment step:
By tsum+ΔtiValue be assigned to tsum, judge whether tsum< tend, it is to go to step three, renewal time step-length, otherwise
Terminate to calculate.
In the step 1, the 3 d modeling software is the AutoCAD of U.S. Autodesk software company, Germany
The UG of the Siemens PLM Software company or Pro/E of U.S. parameters technology company;The cuboid of the geometrical model,
Long 5mm~500mm, wide 5mm~500mm, high 5mm~200mm;The cuboid of workpiece area, high 1mm~100mm;Electrode zone
When for cylindrical body, cylinder diameter 1mm~4mm, high 1mm~150mm, when electrode zone is the cylindrical body that one end is cone,
30 °~120 ° of cone angle, cylinder diameter 1mm~4mm, high 1mm~150mm;The grid dividing software is U.S. Altair public
Take charge of hypermesh, the Gridgen of Pointwise company of the U.S. or the Patran of MSC.Software company of the U.S..
6, in the step 4, the conductivityσ of the mixed gas determined with temperature is made of mixed gase, density pg, it is viscous
Spend μg, specific heat capacity Cpg, thermal coefficient kgAnd gas net radiation coefficient εNIt quotes from Mougenot J, et al.Plasma-weld
pool interaction in tungsten inert-gas configuration.Journal of Physics D:
Applied Physics, 2013,46 (13): 135206 or Murphy A B, et al.Modelling of thermal
plasmas for arc welding:the role of the shielding gas properties and of metal
Vapour.Journal of Physics D:Applied Physics, 2009,42 (19): 194006 or Murphy A
B.The effects of metal vapour in arc welding.Journal of Physics D:Applied
Physics,2010,43(43):434001;
The corresponding conductivityσ of workpiece material directly determined by workpiece material and temperaturee, density pm, viscosity, mum, specific heat capacity
Cpm, thermal coefficient km, thermal expansion coefficient β, surface tension coefficient γ, hot capillary force coefficientWork gestureRadiance εr
It is calculated and is obtained using the material property software for calculation JMatPro of Sente Software company of Britain, or quoted from Wei H
L,et al.Origin of grain orientation during solidification of an aluminum
Alloy.Acta Materialia, 2016,115:123-131, or reference is from Wu C S.Computer simulation
of three-dimensional convection in travelling MIG weld pools.Engineering
computations,1992,9(5):529-537。
In the sub-step (7.1), the Recoil Pressure Model based on environmental pressure is shown in: S.Pang, et
al.Explanation of penetration depth variation during laser welding under
variable ambient pressure.Journal of Laser Applications,2015,27(2):022007;Institute
It states in sub-step (7.2), the ghost fluid method is shown in: Fedkiw R P, et al.A non-oscillatory Eulerian
approach to interfaces in multimaterial flows(the ghost fluid method).Journal
of computational physics,1999,152(2):457-492;In the sub-step (7.3), the second sticky approximation side
Method is shown in: A.B.Murphy.A comparison of treatments of diffusion in thermal
plasmas.Journal of Physics D:Applied Physics,1996,29(7):1922。
In the sub-step (8.2), the ray trace method is shown in: the Laser Deep Penetration Welding arbitrary shape such as Pang Shengyong is small
The energy density in hole calculates laser technology, 2010,34 (05): 614-618;In the step (8.2), the evaporative heat loss
qevapCalculation method is shown in: Wu D, et al.Understanding of spatter formation in fiber laser
welding of 5083 aluminum alloy.International Journal of Heat&Mass Transfer,
2017,113:730-740。
The present invention can use the realization of the high level languages such as C++ computer, and by computer come simulated laser-arc welding
The Three-Dimensional Dynamic behavior of electric arc, molten bath, aperture, metallic vapour in termination process.
The present invention entire zoning Unified Solution when solving electromagnetic field is solving flow field, temperature field and metal steam
The whole meter that multiphase (liquid phase, solid phase, electric arc, metallic vapour) coexists instantaneous free interface when vapour concentration by workpiece molten bath
Calculation region division is gas zones (electric arc-metallic vapour area), workpiece area (workpiece solid-liquid phase region), in Minimum-time step
Calculating separately two, there are the intermittent regions of physical mathematics, and respectively calculating data in a manner of the load of boundary in interface position
It sets and carries out two-way sequence coupling.The method proposed through the invention can solve the tired of non-linear solution near interface very well
Difficulty, realize laser-arc hybrid welding in industry during molten bath and arc-plasma heat transfer flow, the diffusion row of metallic vapour
For free interface develops and electromagnetic field carries out integration simulation and calculates, and more really can reproduce physics mistake comprehensively
Journey, facilitate carry out deeper into theoretical research, can further promote the engineering application of laser-arc hybrid welding in industry.
Detailed description of the invention
Fig. 1 is laser-arc hybrid welding in industry process schematic;
Fig. 2 is flow diagram of the invention;
Fig. 3 is that overall space is interrupted decomposition diagram, and dotted line indicates molten bath free interface;
Fig. 4 is the temperature field simulation of the embodiment of the present invention 1 as a result, digital quantity unit is K in figure;
Fig. 5 is the modeling of velocity field of the embodiment of the present invention 1 as a result, digital quantity unit is m/s in figure;
Fig. 6 is the metallic vapour mass percentage analog result of the embodiment of the present invention 1;
Fig. 7 is the current density distribution simulation of the embodiment of the present invention 1 as a result, digital quantity unit is A/m in figure2。
Specific embodiment
Below in conjunction with specific embodiments and the drawings, the present invention is further described.
Embodiment 1, flow chart is as shown in Fig. 2, include establishing geometrical model step, initialization step, renewal time
Step-length step updates physical parameter step, solves electromagnetic field step, space interruption decomposition step, calculates gas zones state step
Suddenly, calculate workpiece area state step, update molten bath free interface step and judgment step:
One, geometrical model step is established:
Geometrical model is established using 3 d modeling software, the geometrical model is cuboid, and long 14mm, wide 10mm are high
12mm;The geometrical model includes workpiece area, electrode zone and gas zones, and workpiece area is cuboid, length and width and institute
It is identical to state geometrical model, high 4mm;Electrode zone is cylindrical body, cylinder diameter 2mm, high 3mm, electrode zone central axes and perpendicular
Straight angular separation is 30 °, electrode zone threshold value workpiece area vertical distance 5mm;The gas zones are the geometry mould
Remaining region of the type in addition to workpiece area, electrode zone;The 3 d modeling software is Germany Siemens PLM Software
The UG of company;
Region of the geometrical model in addition to electrode zone is zoning;
Grid dividing is carried out using grid dividing software to the zoning again, the grid is square, square
Side length be 100 μm;The grid dividing software is U.S. Altair company hypermesh;
Two, initialization step:
The boundary condition of given zoning: environment temperature 300K, electrode temperature 3000K, environmental pressure 1atm, workpiece bottom
Portion potential 0V;
Set the physical quantity initial value of each grid element center point in entire zoning: potential 0V, current density 0A/m2、
Magnetic field strength 0T, speed 0m/s, temperature 300K, pressure 1atm, metallic vapour mass percentage 0;
Accumulation interval variable t is setsum=0, calculate deadline tend=1.5s;
Time step Δ t is setiFor initial time step delta t0, Δ t0=1 × 10-7S carries out step 4;
Three, renewal time step-length step:
Calculate the maximum time step-length of gas zones stability Calculation
The maximum time step-length of workpiece area stability Calculation is calculated againIt takes
(Δt0,Δtg,Δtm) three minimum value as update time step Δ ti, carry out step 4;
Wherein, i=1,2 ..., indicate that the i-th step calculates, maximal condition number Cmax=0.8, ug_x,ug_y,ug_zRespectively gas
The gas velocity of area grid central pointComponent in three directions of x, y, z, um_x,um_y,um_zRespectively workpiece area net
The molten bath speed of lattice central pointComponent in three directions of x, y, z;Δ x, Δ y, Δ z are respectively grid in three sides of x, y, z
To size;
Four, physical parameter step is updated:
Set the physical parameter in entire zoning:
Gas zones are full of by the mixed gas of protective gas and metallic vapour, and the protective gas is argon gas, metal
Steam is the metallic vapour of workpiece material;Calculating metallic vapour mass percentage and temperature in mixed gas for the first time is initial value,
Future time walks metallic vapour mass percentage and temperature in mixed gas and is obtained by sub-step (7.2) and (7.3);
The conductivityσ of mixed gase, density pg, viscosity, mug, specific heat capacity Cpg, thermal coefficient kgAnd gas net radiation coefficient εN
It is made of at each grid element center mixed gas and temperature directly determines;The gaseous mixture determined with temperature is formed by mixed gas
The conductivityσ of bodye, density pg, viscosity, mug, specific heat capacity Cpg, thermal coefficient kgAnd gas net radiation coefficient εNIt quotes from Mougenot
J,et al.Plasma–weld pool interaction in tungsten inert-gas
configuration.Journal of Physics D:Applied Physics,2013,46(13):135206;
Workpiece area workpiece material is 316L stainless steel;Corresponding conductivityσe, density pm, viscosity, mum, specific heat capacity Cpm, lead
Hot coefficient km, thermal expansion coefficient β, surface tension coefficient γ, hot capillary force coefficientWork gestureRadiance εrEach
It is directly determined at grid element center by workpiece material and temperature;The workpiece material directly determined by workpiece material and temperature is electric accordingly
Conductance σe, density pm, viscosity, mum, specific heat capacity Cpm, thermal coefficient km, thermal expansion coefficient β, surface tension coefficient γ, hot capillary force system
NumberWork gestureRadiance εrUsing the material property software for calculation JMatPro of Sente Software company of Britain
It calculates and obtains;
Five, electromagnetic field step is solved:
Solve the electromagnetic field in entire zoning:
It is passed through welding current in welding process, electromagnetic field will be generated in entire zoning, 150A is given by electrode
Welding current, calculate the potential for obtaining all grid element center points in entire zoningCurrent densityIt is strong with magnetic induction
DegreeDistribution, accounting equation are as follows:
Wherein, permittivity of vacuum μ0, the magnetic of grid element center point loses powerGradient operatorDivergence operatorCurl is calculated
SonLaplace operatorConductivityσeGas zones mixed gas and workpiece area work then is respectively adopted when calculating
The corresponding conductivity of part material;
Six, decomposition step is interrupted in space:
The molten bath free interface using workpiece area upper surface as interface, subsequent calculating to update is calculated for the first time to carry out as interface
Space interruption is decomposed, as shown in figure 3, being gas zones and workpiece area by overall calculation region division, gas zones are electric arc-
Metallic vapour area, workpiece area are workpiece solid-liquid area;Definition interfaces boundary point is molten bath free interface two sides grid element center point company
The crosspoint of line and molten bath free interface;
Seven, gas zones state step is calculated:
Successively calculate flow field, temperature field and the metallic vapour distribution of gas zones, including following sub-step:
(7.1) it calculates gas zones flow field: calculating the gas velocity of all grid element center points of gas zonesGas pressure
Power Pg, calculation formula is as follows:
WhereinAcceleration of gravity;
At the molten bath free interface of gas zones and workpiece area, the gas velocity of interface boundary point is setIt is gentle
Body pressure Pg_sIt is respectively as follows:
Wherein, kickback pressure P is evaporatedr, obtained using the Recoil Pressure Model based on environmental pressure;It is described to be based on environment pressure
The Recoil Pressure Model of power is shown in: S.Pang, et al.Explanation of penetration depth variation
during laser welding under variable ambient pressure.Journal of Laser
Applications,2015,27(2):022007;
(7.2) it calculates gas zones temperature field: calculating the gas temperature T of all grid element center points of gas zonesg, calculate public
Formula is as follows:
Wherein, kb: Boltzmann constant, e: elementary charge, t: the time,Differential operator;
At the molten bath free interface of gas zones and workpiece area, the hot-fluid that interface boundary point enters gas zones is calculated
qgas:
Wherein Tgs、TmsThe respectively temperature of the gas zones and workpiece area of interface boundary point, is obtained using ghost fluid method
It takes;keffFor the effective thermal conductivity of interface boundary point, keff=0.5 × (kg(Tgs)+kg(Tms)), kg(Tgs)、kg(Tms) respectively
For temperature Tgs、TmsCorresponding Measurement of Gas Thermal Conductivity;δ is the effective thickness in the boundary layer of molten bath free interface, δ=0.1mm;
The ghost fluid method is shown in: Fedkiw R P, et al.A non-oscillatory Eulerian approach to
interfaces in multimaterial flows(the ghost fluid method)[J].Journal of
computational physics,1999,152(2):457-492;
(7.3) it calculates the diffusion of gas zones metallic vapour: calculating the metallic vapour of all grid element center points in gas zones
Mass percentage Cvapor, calculation formula is as follows:
Wherein, D is metallic vapour mass diffusion coefficient, which can be obtained by the second sticky approximation method;Described second
Sticky approximation method is shown in: A.B.Murphy.A comparison of treatments of diffusion in thermal
plasmas.Journal of Physics D:Applied Physics,1996,29(7):1922;
At the molten bath free interface of gas zones and workpiece area, each interface boundary point metallic vapour quality percentage is set
Content Cvapor:
Eight, workpiece area state step is calculated:
Successively calculate the flow field and temperature field of workpiece area, including following sub-step:
(8.1) it calculates workpiece area flow field: calculating the molten bath speed of all grid element center points of workpiece areaMolten bath pressure
Power Pm, calculation formula is as follows:
Wherein, the temperature T of workpiece area grid element center pointm, environment temperature is taken when calculating for the first time;Future time step, which calculates, adopts
With the calculated value of a time step (7.2);
Reference temperature Tref, take workpiece material melting temperature;K, C is respectively seepage coefficient and relaxation coefficient, with liquid fraction fl
It is closely related:
Wherein, d be and interdendritic away from the closely related constant of size, d=0.1mm;Liquid fraction flIt is linear with temperature
Relationship:
Wherein, Tl、TsIt is the liquidus temperature and solidus temperature of workpiece material respectively;
At the molten bath free interface of gas zones and workpiece area, the molten bath normal pressure P of interface boundary point is calculatedfWith
Molten bath tangential force
WhereinThe respectively normal vector and tangent vector of molten bath free interface, κ are molten bath free interface curvature, Peff
It is gas zones to the effective pressure of workpiece area, takes Peff=max (Pr,Pg);
(8.2) it calculates workpiece area temperature field: calculating the temperature T of all grid element center points of workpiece aream, calculation formula is such as
Under:
Wherein, energy absorption q of the workpiece to laserlaser, obtained using ray trace method, the laser swashs for optical fiber
Light, power 2000W, spot radius 0.3mm;The ray trace method is shown in: the Laser Deep Penetration Welding arbitrary shape such as Pang Shengyong
The energy density of aperture calculates laser technology, 2010,34 (05): 614-618;
At the molten bath free interface of gas zones and workpiece area, the hot-fluid that interface boundary point enters workpiece area is calculated
qmatel:
Wherein, σ is this special fence-Boltzmann constant, T∞For environment temperature, qevapFor evaporative heat loss;The heat of evaporation
Lose qevapCalculation method is shown in: Wu D, et al.Understanding of spatter formation in fiber
laser welding of 5083 aluminum alloy.International Journal of Heat&Mass
Transfer,2017,113:730-740;
Nine, molten bath free interface step is updated:
Pass through the molten bath speed of all grid element center points of workpiece areaEach grid element center point is to interface in zoning
Distance φ, the contour surface of φ=0 obtained is the molten bath free interface updated, and calculation formula is as follows:
The normal vector and curvature of molten bath free interface solve as follows:
In the step 5~step 9, it is discrete that related accounting equation all uses finite difference method to carry out, and
In time step Δ tiInside solved;
Ten, judgment step:
By tsum+ΔtiValue be assigned to tsum, judge whether tsum< tend, it is to go to step three, renewal time step-length, otherwise
Terminate to calculate.
After calculating, analogue data obtained in simulation process is carried out using open source visualization procedure Paraview
Visualization processing, Fig. 4~Fig. 7 are the laser-arc hybrid welding in industry temperature field of the present embodiment simulation, velocity field, metallic vapour point
Cloth and current density are distributed transient results.
Embodiment 2, flow chart is as shown in Figure 1, include establishing geometrical model step, initialization step, renewal time
Step-length step updates physical parameter step, solves electromagnetic field step, space interruption decomposition step, calculates gas zones state step
Suddenly, calculate workpiece area state step, update molten bath free interface step and judgment step:
One, geometrical model step is established:
It is same as Example 1;
Two, initialization step:
The boundary condition of given zoning: environment temperature 1000K, electrode temperature 3500, environmental pressure 10atm, workpiece
Bottom potential 0V;
Set the physical quantity initial value of each grid element center point in entire zoning: potential 0V, current density 0A/m2、
Magnetic field strength 0T, speed 0m/s, temperature 1000K, pressure 10atm, metallic vapour mass percentage 0;
Accumulation interval variable t is setsum=0, calculate deadline tend=10s;
Time step Δ t is setiFor initial time step delta t0, Δ t0=1 × 10-6S carries out step 4;
Three, renewal time step-length step:
It is same as Example 1;
Four, physical parameter step is updated:
Set the physical parameter in entire zoning:
Gas zones are full of by the mixed gas of protective gas and metallic vapour, and the protective gas is helium, metal
Steam is the metallic vapour of workpiece material;Calculating metallic vapour mass percentage and temperature in mixed gas for the first time is initial value,
Future time walks metallic vapour mass percentage and temperature in mixed gas and is obtained by sub-step (7.2) and (7.3);
The conductivityσ of mixed gase, density pg, viscosity, mug, specific heat capacity Cpg, thermal coefficient kgAnd gas net radiation coefficient εN
It is made of at each grid element center mixed gas and temperature directly determines;The gaseous mixture determined with temperature is formed by mixed gas
The conductivityσ of bodye, density pg, viscosity, mug, specific heat capacity Cpg, thermal coefficient kgAnd gas net radiation coefficient εNIt quotes from Murphy A
B,et al.Modelling of thermal plasmas for arc welding:the role of the
shielding gas properties and of metal vapour.Journal of Physics D:Applied
Physics,2009,42(19):194006;
Workpiece area workpiece material is 304 stainless steels;Corresponding conductivityσe, density pm, viscosity, mum, specific heat capacity Cpm, it is thermally conductive
Coefficient km, thermal expansion coefficient β, surface tension coefficient γ, hot capillary force coefficientWork gestureRadiance εrIn each net
Lattice are directly determined at center by workpiece material and temperature;The corresponding conductance of workpiece material directly determined by workpiece material and temperature
Rate σe, density pm, viscosity, mum, specific heat capacity Cpm, thermal coefficient km, thermal expansion coefficient β, surface tension coefficient γ, hot capillary force coefficientWork gestureRadiance εrIt quotes certainly: Wu C S.Computer simulation of three-dimensional
convection in travelling MIG weld pools.Engineering computations,1992,9(5):
529-537;
Five, electromagnetic field step is solved:
It is same as Example 1;
Six, decomposition step is interrupted in space:
It is same as Example 1;
Seven, gas zones state step is calculated:
(7.1) same as Example 1;
(7.2) δ=0.4mm is taken, remaining is same as Example 1;
(7.3) same as Example 1;
Eight, workpiece area state step is calculated:
It is same as Example 1;
Nine, molten bath free interface step is updated:
It is same as Example 1;
Ten, judgment step:
It is same as Example 1;
After calculating, using the visualization processing software Tecplot 360 of Tecplot company of the U.S. in simulation process
Analogue data obtained carries out visualization processing, can get laser-arc hybrid welding in industry temperature field, velocity field, metallic vapour
Distribution and current density are distributed transient results.
Embodiment 3, flow chart is as shown in Figure 1, include establishing geometrical model step, initialization step, renewal time
Step-length step updates physical parameter step, solves electromagnetic field step, space interruption decomposition step, calculates gas zones state step
Suddenly, calculate workpiece area state step, update molten bath free interface step and judgment step:
One, geometrical model step is established:
Geometrical model is established using 3 d modeling software, the geometrical model is cuboid, and long 500mm, wide 400mm are high
200mm;The geometrical model includes workpiece area, electrode zone and gas zones, and workpiece area is cuboid, length and width with
The geometrical model is identical, high 40mm;Electrode zone is cone, and cone angle is 120 °, and cone basal diameter and cylindrical body are straight
Diameter is identical, cylinder diameter 4mm, high 150mm, and electrode zone central axes and vertical direction angle are 60 °, electrode zone end away from
From workpiece area vertical distance 10mm;Region of the geometrical model in addition to electrode zone is zoning;The three-dimensional is built
Mould software is the Pro/E of U.S. parameters technology company;
The gas zones are remaining region of the geometrical model in addition to workpiece area, electrode zone;
Grid dividing is carried out using grid dividing software to the zoning again, the grid is cuboid, cuboid
Side length is 500 μm a length of, width is 200 μm, 200 μm a height of;The grid dividing software is U.S. Pointwise company
Gridgen;
Step 2~step 4 is same as Example 1;
Five, electromagnetic field step is solved:
It is passed through welding current in welding process, electromagnetic field will be generated in entire zoning, 300A is given by electrode
Welding current;Remaining is same as Example 1;
Step 6~step 7 is same as Example 1;
Eight, workpiece area state step is calculated:
(8.1) d=0.5mm is taken, remaining is same as Example 1;
(8.2) laser is Nd:YAG laser, power 10000W, spot radius 0.5mm;Remaining is same as Example 1;
Step 9~step 10 is same as Example 1;
Embodiment 4, flow chart is as shown in Figure 1, include establishing geometrical model step, initialization step, renewal time
Step-length step updates physical parameter step, solves electromagnetic field step, space interruption decomposition step, calculates gas zones state step
Suddenly, calculate workpiece area state step, update molten bath free interface step and judgment step:
One, geometrical model step is established:
Geometrical model is cuboid, long 5mm, wide 5mm, high 4mm;The high 1mm of workpiece area;Electrode zone is cone, cone
Angle is 30 °, and cone basal diameter is identical with cylinder diameter, cylinder diameter 1mm, high 1mm, electrode zone central axes with erect
Straight angular separation is 60 °, electrode zone threshold value workpiece area vertical distance 2mm;
The grid is square, and the side length of square is 20 μm;
Remaining is same as Example 1;
Two, initialization step:
Calculate deadline tend=0.1s;Remaining is same as Example 1;
Step 3~step 4 is same as Example 1;
Five, electromagnetic field step is solved:
It is passed through welding current in welding process, electromagnetic field will be generated in entire zoning, gives 30A's by electrode
Welding current;Remaining is same as Example 1;
Step 6~step 7 is same as Example 1;
Eight, workpiece area state step is calculated:
(8.1) d=0.05mm is taken, remaining is same as Example 1;
(8.2) laser is optical-fiber laser, power 100W, spot radius 0.1mm;Remaining is same as Example 1;
Step 9~step 10 is same as Example 1;
Numerical simulation to the laser-TIG hybrid weldering under the conditions of embodiment technological parameter is realized using the method for the present invention
It calculates, can be realized while the development law of solid phase during composite welding, liquid phase, metallic vapour, plasma is asked
Solution.To in embodiment embodiment and embodiment by simply modifying, can be realized using the method for the present invention to difference
The numerical simulation of the laser-TIG hybrid weldering of protective gas type, different workpieces material and different technical parameters, has fine
Scalability, in terms of the mechanism study of composite welding and engineering process parameter formulation have application potential.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention is not limited to and this,
In the technical scope disclosed by the present invention, the variation that can be readily occurred in or substitution are all by anyone skilled in the art
It is covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of protection of the claims
It is quasi-.
Claims (5)
1. a kind of laser-arc hybrid welding in industry Three dimensional transient simulation method, including establish geometrical model step, initialization
Step, renewal time step-length step update physical parameter step, solve electromagnetic field step, space interruption decomposition step, calculate gas
Body region state step, calculating workpiece area state step, update molten bath free interface step and judgment step, feature exist
In:
One, geometrical model step is established:
Geometrical model is established using 3 d modeling software, the geometrical model is cuboid, and the geometrical model includes workpiece area
Domain, electrode zone and gas zones, workpiece area are cuboid, and length and width is identical as the geometrical model;Electrode zone is circle
Cylinder or one end are the cylindrical body of cone, and when electrode zone is cylindrical body, electrode zone central axes are with vertical direction angle
0 °~60 °, when electrode zone is the cylindrical body that one end is cone, cone basal diameter is identical as cylinder diameter;Electrode
Area end is apart from workpiece area vertical distance 1mm~10mm;The gas zones are that the geometrical model removes workpiece area, electricity
The overseas remaining region in polar region;
Region of the geometrical model in addition to electrode zone is zoning;
Grid dividing is carried out using grid dividing software to the zoning again, the grid is cuboid or square, length
Cube or the side length of square are 10 μm~500 μm;
Two, initialization step:
The boundary condition of given zoning: 300~1000K of environment temperature, 3000~3500K of electrode temperature, environmental pressure 0.1
~10atm, workpiece bottom potential 0V;
Set the physical quantity initial value of each grid element center point in entire zoning: potential 0V, current density 0A/m2, magnetic field it is strong
Spend 0T, speed 0m/s, 300~1000K of temperature, 0.1~10atm of pressure, metallic vapour mass percentage 0;
Accumulation interval variable t is setsum=0, calculate deadline tend=0.1~10s;
Time step Δ t is setiFor initial time step delta t0, Δ t0=1 × 10-7~1 × 10-6S carries out step 4;
Three, renewal time step-length step:
Calculate the maximum time step-length of gas zones stability Calculation
The maximum time step-length of workpiece area stability Calculation is calculated againTake (Δ
t0,Δtg,Δtm) three minimum value as update time step Δ ti, carry out step 4;
Wherein, i=1,2 ..., indicate that the i-th step calculates, maximal condition number Cmax=0.5~1.0, ug_x,ug_y,ug_zRespectively gas
The gas velocity of area grid central pointComponent in three directions of x, y, z, um_x,um_y,um_zRespectively workpiece area net
The molten bath speed of lattice central pointComponent in three directions of x, y, z;Δ x, Δ y, Δ z are respectively grid in three sides of x, y, z
To size;
Four, physical parameter step is updated:
Set the physical parameter in entire zoning:
Gas zones are full of by the mixed gas of protective gas and metallic vapour, and the protective gas is argon gas, helium and two
One or more of carbonoxide, metallic vapour are the metallic vapour of workpiece material;Metallic vapour in mixed gas is calculated for the first time
Mass percentage and temperature are initial value, and metallic vapour mass percentage and temperature are by sub-step in future time step mixed gas
Suddenly (7.2) and (7.3) obtain;
The conductivityσ of mixed gase, density pg, viscosity, mug, specific heat capacity Cpg, thermal coefficient kgAnd gas net radiation coefficient εNEvery
It is made of at a grid element center mixed gas and temperature directly determines;
Workpiece area workpiece material is ferrous alloy or non-ferrous alloy;Corresponding conductivityσe, density pm, viscosity, mum, specific heat
Hold Cpm, thermal coefficient km, thermal expansion coefficient β, surface tension coefficient γ, hot capillary force coefficientWork gestureRadiance
εrIt is directly determined at each grid element center by workpiece material and temperature;
Five, electromagnetic field step is solved:
Solve the electromagnetic field in entire zoning:
It is passed through welding current in welding process, electromagnetic field will be generated in entire zoning, 30~300A is given by electrode
Welding current, calculate the potential for obtaining all grid element center points in entire zoningCurrent densityAnd magnetic induction intensityDistribution, accounting equation are as follows:
Wherein, permittivity of vacuum μ0, the magnetic of grid element center point loses powerGradient operatorDivergence operatorCurl operatorLaplace operatorConductivityσeGas zones mixed gas and workpiece area workpiece then is respectively adopted when calculating
The corresponding conductivity of material;
Six, decomposition step is interrupted in space:
The molten bath free interface using workpiece area upper surface as interface, subsequent calculating to update is calculated for the first time carries out space as interface
Interruption is decomposed, and is gas zones and workpiece area by overall calculation region division, and gas zones are electric arc-metallic vapour area, work
Part region is workpiece solid-liquid area;Definition interfaces boundary point is that molten bath free interface two sides grid element center point line and molten bath are free
The crosspoint at interface;
Seven, gas zones state step is calculated:
Successively calculate flow field, temperature field and the metallic vapour distribution of gas zones, including following sub-step:
(7.1) it calculates gas zones flow field: calculating the gas velocity of all grid element center points of gas zonesGas pressure Pg,
Calculation formula is as follows:
WhereinFor acceleration of gravity;
At the molten bath free interface of gas zones and workpiece area, the gas velocity of interface boundary point is setWith gas pressure
Power Pg_sIt is respectively as follows:
Wherein, kickback pressure P is evaporatedr, obtained using the Recoil Pressure Model based on environmental pressure;
(7.2) it calculates gas zones temperature field: calculating the gas temperature T of all grid element center points of gas zonesg, calculation formula is such as
Under:
Wherein, kb: Boltzmann constant, e: elementary charge, t: the time,Differential operator;
At the molten bath free interface of gas zones and workpiece area, the hot-fluid q that interface boundary point enters gas zones is calculatedgas:
Wherein Tgs、TmsThe respectively temperature of the gas zones and workpiece area of interface boundary point, is obtained using ghost fluid method;
keffFor the effective thermal conductivity of interface boundary point, keff=0.5 × (kg(Tgs)+kg(Tms)), kg(Tgs)、kg(Tms) it is respectively temperature
Spend Tgs、TmsCorresponding Measurement of Gas Thermal Conductivity;δ be molten bath free interface boundary layer effective thickness, δ be 0.1mm~
0.4mm;
(7.3) it calculates the diffusion of gas zones metallic vapour: calculating the metallic vapour quality of all grid element center points in gas zones
Percentage composition Cvapor, calculation formula is as follows:
Wherein, D is metallic vapour mass diffusion coefficient, which can be obtained by the second sticky approximation method;
At the molten bath free interface of gas zones and workpiece area, each interface boundary point metallic vapour mass percentage is set
Cvapor:
Eight, workpiece area state step is calculated:
Successively calculate the flow field and temperature field of workpiece area, including following sub-step:
(8.1) it calculates workpiece area flow field: calculating the molten bath speed of all grid element center points of workpiece areaMolten bath pressure Pm,
Calculation formula is as follows:
Wherein, the temperature T of workpiece area grid element center pointm, environment temperature is taken when calculating for the first time;Future time step is calculated using upper
The calculated value of one time step (7.2);
Reference temperature Tref, take workpiece material melting temperature;K, C is respectively seepage coefficient and relaxation coefficient, with liquid fraction flClosely
It is related:
Wherein, d be and interdendritic away from the closely related constant of size, d=0.05mm~0.5mm;Liquid fraction flIt is in line with temperature
Sexual intercourse:
Wherein, Tl、TsIt is the liquidus temperature and solidus temperature of workpiece material respectively;
At the molten bath free interface of gas zones and workpiece area, the molten bath normal pressure P of interface boundary point is calculatedfThe molten bath and
Tangential force
WhereinThe respectively normal vector and tangent vector of molten bath free interface, κ are molten bath free interface curvature, PeffFor gas
Region takes P to the effective pressure of workpiece areaeff=max (Pr,Pg);
(8.2) it calculates workpiece area temperature field: calculating the temperature T of all grid element center points of workpiece aream, calculation formula is as follows:
Wherein, energy absorption q of the workpiece to laserlaser, obtained using ray trace method;The laser be optical-fiber laser or
Nd:YAG laser, power 100W~10000W, spot radius 0.1mm~0.5mm;
At the molten bath free interface of gas zones and workpiece area, the hot-fluid that interface boundary point enters workpiece area is calculated
qmatel:
Wherein, σ is this special fence-Boltzmann constant, T∞For environment temperature, qevapFor evaporative heat loss;
Nine, molten bath free interface step is updated:
Pass through the molten bath speed of all grid element center points of workpiece areaDistance of each grid element center point to interface in zoning
The contour surface of φ, φ=0 obtained are the molten bath free interface updated, and calculation formula is as follows:
The normal vector and curvature of molten bath free interface solve as follows:
In the step 5~step 9, related accounting equation all use finite difference method or Finite Volume Method into
Row is discrete, and in time step Δ tiInside solved;
Ten, judgment step:
By tsum+ΔtiValue be assigned to tsum, judge whether tsum< tend, it is to go to step three, otherwise renewal time step-length terminates
It calculates.
2. laser-arc hybrid welding in industry Three dimensional transient simulation method as described in claim 1, it is characterised in that: described
In step 1, the 3 d modeling software is AutoCAD, the Germany Siemens PLM of U.S. Autodesk software company
The UG of the Software company or Pro/E of U.S. parameters technology company;The cuboid of the geometrical model, long 5mm~
500mm, wide 5mm~500mm, high 5mm~200mm;The cuboid of workpiece area, high 1mm~100mm;Electrode zone is cylinder
When body, cylinder diameter 1mm~4mm, high 1mm~150mm, when electrode zone is the cylindrical body that one end is cone, 30 ° of cone angle
~120 °, cylinder diameter 1mm~4mm, high 1mm~150mm;
The grid dividing software be U.S. Altair company hypermesh, Pointwise company of the U.S. Gridgen or
The Patran of MSC.Software company of the U.S..
3. laser-arc hybrid welding in industry Three dimensional transient simulation method as described in claim 1, it is characterised in that: described
In step 4, the conductivityσ of the mixed gas determined with temperature is made of mixed gase, density pg, viscosity, mug, specific heat capacity Cpg、
Thermal coefficient kgAnd gas net radiation coefficient εNIt quotes from Mougenot J, et al.Plasma-weld pool
interaction in tungsten inert-gas configuration.Journal of Physics D:Applied
Physics, 2013,46 (13): 135206 or Murphy A B, et al.Modelling of thermal plasmas
for arc welding:the role of the shielding gas properties and of metal
Vapour.Journal of Physics D:Applied Physics, 2009,42 (19): 194006 or Murphy A
B.The effects of metal vapour in arc welding.Journal of Physics D:Applied
Physics,2010,43(43):434001;
The corresponding conductivityσ of workpiece material directly determined by workpiece material and temperaturee, density pm, viscosity, mum, specific heat capacity Cpm, lead
Hot coefficient km, thermal expansion coefficient β, surface tension coefficient γ, hot capillary force coefficientWork gestureRadiance εrUsing English
The material property software for calculation JMatPro of Sente Software company of state, which is calculated, to be obtained, or is quoted from Wei H L, et
al.Origin of grain orientation during solidification of an aluminum
Alloy.Acta Materialia, 2016,115:123-131, or reference is from Wu C S.Computer simulation
of three-dimensional convection in travelling MIG weld pools.Engineering
computations,1992,9(5):529-537。
4. laser-arc hybrid welding in industry Three dimensional transient simulation method as described in claim 1, it is characterised in that: described
In sub-step (7.1), the Recoil Pressure Model based on environmental pressure is shown in: S.Pang, et al.Explanation of
penetration depth variation during laser welding under variable ambient
pressure.Journal of Laser Applications,2015,27(2):022007;In the sub-step (7.2), institute
It states ghost fluid method to see: Fedkiw R P, et al.A non-oscillatory Eulerian approach to
interfaces in multimaterial flows(the ghost fluid method).Journal of
computational physics,1999,152(2):457-492;In the sub-step (7.3), the second sticky approximation method
See: A.B.Murphy.A comparison of treatments of diffusion in thermal
plasmas.Journal of Physics D:Applied Physics,1996,29(7):1922。
5. laser-arc hybrid welding in industry Three dimensional transient simulation method as described in claim 1, it is characterised in that: described
In sub-step (8.2), the ray trace method is shown in: the energy density of the Laser Deep Penetration Welding arbitrary shape aperture such as Pang Shengyong
Calculate laser technology, 2010,34 (05): 614-618;In the step (8.2), the evaporative heat loss qevapCalculation method
See: Wu D, et al.Understanding of spatter formation in fiber laser welding of
5083aluminum alloy.International Journal of Heat&Mass Transfer,2017,113:730-
740。
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CN117195663B (en) * | 2023-11-03 | 2024-02-20 | 山东理工大学 | Simulation method for removing electric spark machining materials in liquid based on three-phase flow interface tracking |
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