CN105868461B - A kind of ingredient calculation method of laser melting coating multi-component alloys coating - Google Patents
A kind of ingredient calculation method of laser melting coating multi-component alloys coating Download PDFInfo
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Abstract
The present invention provides a kind of ingredient calculation method of laser melting coating multi-component alloys coating, each parameter of initialization zoning first is basic status；Then in cladding calculating process, according to required required precision, time step is set, step number is solved as total divided by time step to complete the time required for cladding track, then calculating is iterated in each time step: last iteration calculating process, and continue to judge whether the concentration field of each component in molten bath in each time step tends towards stability, when unstable, continue to iterate to calculate；Stablize when then stop iterating to calculate, iterate to calculate at this time it is obtained as a result, as in current time molten bath each component concentration value.The present invention predicts the concentration value of each component in the laser cladding process of multicomponent reinforced alloys by Computer Numerical Simulation, and then achievees the purpose that optimize laser cladding technological parameter.
Description
Technical field
The present invention relates to Material Fields to calculate and apply when more particularly to a kind of utilization laser melting coating multi-component alloys coating
The calculation method of concentration shared by each component in layer.
Background technique
Laser melting coating has heat affected area pole as a kind of advanced modification technology, compared to traditional process for modifying surface
The small, advantages such as the small, dilution rate of deformation is controllable, solidification crystal grain is tiny.Its conventional modification mode is made with high power density laser
For heat source, base material formation molten bath is radiated and melted, while various powders material is injected into molten bath, is formed after the solidification of molten bath
The cladding layer that performance and structure greatly improve.
The physics and chemical phenomenon of large amount of complex can occur in laser melting coating, in molten bath, such as heat transfer, flowing, component pair
Stream diffusion, evaporation, sputtering etc., so that the corresponding relationship obtained between technological parameter and high quality cladding layer is very difficult, at present
Conventional Calculation Method when to can only obtain addO-on therapy be two kinds, the concentration value of each component in molten bath.
Summary of the invention
The invention aims to provide and it is a kind of using laser melting coating multi-component alloys coating when, calculate each group in coating
The calculation method of concentration shared by point.
Particularly, the present invention provides a kind of ingredient calculation method of laser melting coating multi-component alloys coating, including walks as follows
It is rapid:
Step 100, each parameter for initializing zoning is basic status, then according to scheduled requirement to workpiece surface
Carry out cladding calculating；
Step 200, in cladding calculating process, time step is arranged according to required required precision, to complete cladding rail
Time required for mark solves step number as total divided by time step, and calculating, institute are then iterated in each time step
The process for stating iterative calculation includes following four steps:
Step 201, by present laser effective power density, the molten bath velocity field of previous moment, density of material, thermal conductivity and
In the Equations of Three-dimension of convection transfer rate lead-in zone convective term, to obtain the temperature field in current time molten bath；
Step 202, it is by the temperature field in current molten bath, the molten bath velocity field of previous moment, the concentration stream of each component, diffusion
It is flat that number, thermal diffusion coefficient, molar fraction and molal weight import the multicomponent mixing based on Maxwell-Stefan diffusion model
In equal convective-diffusion equation, the concentration field at current time that respectively obtains each component in molten bath；
Step 203, by the concentration field in temperature field and each component, the molten bath velocity field of previous moment, and it is added to molten bath
In each component quality stream import Arbitrary Lagrangian-Eulerian equation, to obtain current molten bath upper surface
Vertical displacement vectors field in vertical direction；
Step 204, by the concentration field in temperature field and each component, the vertical displacement vectors of molten bath upper surface in vertical direction
, density of material, viscosity import Navier-Stokes equation and obtain the velocity vector field in current molten bath；
Step 300, iteration calculating process, and continue to judge that the concentration field of each component in molten bath in each time step is
It is no to tend towards stability, when unstable, continue to iterate to calculate；Then stop iterating to calculate when stablizing, iterates to calculate obtained knot at this time
Fruit, the concentration value of each component as in current time molten bath.
Further, the Equations of Three-dimension are as follows:
Wherein, ρ is the density of liquid metal, CpFor material thermal capacitance,It is temperature to the derivative of time, u is liquid metal
Speed,For temperature gradient, k is material thermal conductivity.
Further, the multicomponent mixing average convection diffusion equation of the Maxwell-Stefan diffusion model are as follows:
Ni=ji+ρuωi (2)
Wherein jiConcentration stream when a certain component is spread in molten bath in all components is represented, i is the label of the component, ρ generation
The mixed density of each component in table molten bath, u represent convection velocity of each component in molten bath.
Further, the concentration gradient between each component itself concentration gradient, each component is handled in a manner of source item, is currently melted
The temperature gradient in pond caused component diffusion in molten bath.
Further, the j in described (1) formulaiIt is obtained by following formula:
In formulaI component is represented because of diffusion caused by component itself concentration gradient,Represent i group
Diffusion caused by concentration gradient between point,Represent the diffusion due to caused by temperature gradient of i component, ωiRepresent the matter of i component
Score is measured,Represent each component mixing average diffusion coefficient, M in molten bathnMixing average molar mass is represented,Represent thermal expansion
Coefficient is dissipated, T represents temperature field of molten pool,The gradient of the mass fraction of i component is represented,The gradient in temperature field is represented,Represent the gradient of mixing average molar mass.
Further, each component mixing average diffusion coefficient in the molten bath in described (3) formulaIt is obtained by following formula:
Wherein, xkRepresent the molar fraction of k component, DjkRepresent Maxwell-Stefan diffusion coefficient matrix.
Further, the mixing average molar mass M in described (3) formulanIt is obtained by following formula:
Wherein, MiRepresent the molal weight of i component.
Further, the Arbitrary Lagrangian-Eulerian equation are as follows:
Wherein, u represents molten bath flowing velocity, and n represents surface normal, MfRepresentation quality adding rate, ρ represent molten metal
Density.
Further, the Navier-Stokes equation are as follows:
Wherein, I represents unit matrix, and μ represents metal liquid viscosity.F represents body force.
Further, DjkFor j rank symmetric coefficient matrix, the numerical value of j and k are equal and are equal to the mark that component is corresponded in molten bath
Number, the value on diagonal line is 1.
Each component is dense in the laser cladding process that the present invention passes through Computer Numerical Simulation prediction multicomponent reinforced alloys
Angle value, and then achieve the purpose that optimize laser cladding technological parameter.The present invention is spread using based on Maxwell-Stefan for the first time
The transport phenomenon of laser cladding process is described in the multicomponent mixing average convection diffusion equation of model, improves multicomponent
The precision and reliability that ingredient calculates.
Detailed description of the invention
Fig. 1 is calculation method flow diagram according to an embodiment of the present invention；
Fig. 2 is the grid dividing schematic diagram of zoning according to an embodiment of the invention；
Fig. 3 is main schematic diagram of calculation flow according to an embodiment of the invention；
Fig. 4 is the fluid flow result and experimental result comparison diagram of middle calculating according to an embodiment of the present invention；
Fig. 5 is the element sulphur concentration results and experimental result comparison diagram of middle calculating according to an embodiment of the present invention.
Specific embodiment
As shown in Figure 1, the calculation method of one embodiment of the invention generally includes the following steps:
Step 100, each parameter for initializing zoning is basic status, then according to scheduled requirement to workpiece surface
Carry out cladding calculating；
The initial parameters referred here to include: each component that temperature field is initialized as room temperature, molten bath speed and bath
Movement velocity is initialized as 0, and multicomponent concentration field is initialized as the concentration of each component in the base.
Step 200, in cladding calculating process, time step is arranged according to required required precision, to complete cladding rail
Time required for mark solves step number as total divided by time step, and calculating, institute are then iterated in each time step
The process for stating iterative calculation includes following four step:
Step 201, by present laser effective power density, the molten bath velocity field of previous moment, density of material, thermal conductivity and
In the Equations of Three-dimension of convection transfer rate lead-in zone convective term, to obtain the temperature field in current time molten bath；
When calculating, the movement routine of laser heat source is identical as actual machining path.
Wherein, Equations of Three-dimension used in the present embodiment are as follows:
In formula, ρ is the density of liquid metal, CpFor material thermal capacitance,It is temperature to the derivative of time, u is liquid metal
Speed,For temperature gradient, k is material thermal conductivity.
Since the molten bath thermal conduction rate difference in three directions that laser generates is very big, so temperature field embodies three
Characteristic is tieed up, temperature difference is very big in three directions, and two dimension or one-dimension temperature field cannot replace.In addition, laser generation is molten
Since surface tension gradient can generate strong convection current, influence of the convection current to heat transfer (temperature field) be can't be ignored in pond.Using band
The Equations of Three-dimension of convective term can satisfy and be applicable in completely the molten bath under above-mentioned condition.
Step 202, it is by the temperature field in current molten bath, the molten bath velocity field of previous moment, the concentration stream of each component, diffusion
It is flat that number, thermal diffusion coefficient, molar fraction and molal weight import the multicomponent mixing based on Maxwell-Stefan diffusion model
In equal convective-diffusion equation, the concentration field at current time that respectively obtains each component in molten bath.
The multicomponent mixing average convection diffusion equation of the Maxwell-Stefan diffusion model used in the present embodiment are as follows:
Ni=ji+puωi (2)
Wherein jiConcentration stream when a certain component is spread in molten bath in all components is represented, i is the label of the component；ρ generation
The mixed density of each component in table molten bath, u represent convection velocity of each component in molten bath.
Molten bath can be calculated using the multicomponent mixing average convection diffusion equation with Maxwell-Stefan diffusion model
The case where adding three kinds or more component is in the prior art the cladding layer capability for realizing optimization, generally comprises in molten bath
Two kinds or more of component, and traditional double base component diffusion equation can only calculate two kinds of components, thus it is not suitable for two kinds or more
Component.Further, since strong convection can be generated in molten bath between each component, and for the phenomenon, traditional double base diffusion of components
The equation equation can not equally consider, cause final calculation result error larger.
In addition, diffusion of each component in molten bath calculates, the prior art generally uses the diffusion model based on Fick, the expansion
Scattered model can not consider the interaction between various ingredients, and Maxwell-Stefan diffusion model, then can consider simultaneously each
The temperature gradient of concentration gradient, current molten bath between component itself concentration gradient, each component caused component diffusion in molten bath.
In the present embodiment, the j of concentration stream when a certain component is spread in molten bath in all components is representediIt can be under
Formula obtains:
In formulaI component is represented because of diffusion caused by component itself concentration gradient,Represent i group
Diffusion caused by concentration gradient between point,Represent the diffusion due to caused by temperature gradient of i component, ωiRepresent the matter of i component
Score is measured,Represent each component mixing average diffusion coefficient, M in molten bathnMixing average molar mass is represented,Represent thermal expansion
Coefficient is dissipated, T represents temperature field of molten pool.AndThe gradient of the mass fraction of i component is represented,The gradient in temperature field is represented,Represent the gradient of mixing average molar mass.
Each component mixing average diffusion coefficient in molten bathIt can be obtained by following formula:
Wherein, xkRepresent the molar fraction of k component, DjkRepresent Maxwell-Stefan diffusion coefficient matrix.
Mix average molar mass MnIt can be obtained by following formula:
Wherein, MiRepresent the molal weight of i component.
In this step, concentration gradient between each component itself concentration gradient, each component, current is handled in a manner of source item
The temperature gradient in molten bath caused diffusion of components in molten bath.The temperature field that is previously obtained be can use to calculate temperature gradient,
And then obtain the temperature gradient (soret effect) in the current molten bath caused diffusion of components in molten bath.
Step 203, by the concentration field of temperature field and each component, previous moment molten bath velocity field and be added to molten bath
In each component quality stream, import Arbitrary Lagrangian-Eulerian equation, to obtain current molten bath upper surface
Vertical displacement vectors field in vertical direction；
Arbitrary Lagrangian-Eulerian equation in this step are as follows:
Wherein, u represents molten bath flowing velocity, and n represents surface normal, MfRepresentation quality adding rate, ρ represent molten metal
Density.
In the equation: the position of molten bath upper surface in vertical direction caused by (un) is represented due to bath flowing
It moves,The displacement of molten bath upper surface in vertical direction caused by representing due to powder quality addition.
Step 204, by the concentration field in temperature field and each component, the vertical displacement vectors of molten bath upper surface in vertical direction
, density of material, viscosity import Navier-Stokes equation and obtain the velocity vector field in current molten bath；
In this step, Navier-Stokes equation are as follows:
Wherein, I represents unit matrix, and μ represents metal liquid viscosity, and wherein F represents body force, including buoyancy (due to temperature
Caused by variable density caused by degree is different) and the drag force that generates of molten bath solidification (molten bath solidification leads to the increasing of metal liquid viscosity
Caused by big).
(7) formula is mass-conservation equation, and (8) formula is momentum conservation equation, passes through the speed of the available metal fluid of two formulas
Spend field.
Step 300, iteration calculating process, and continue to judge that the concentration field of each component in molten bath in each time step is
It is no to tend towards stability, when unstable, continue to iterate to calculate；Then stop iterating to calculate when stablizing, iterates to calculate obtained knot at this time
Fruit, the concentration value of each component as in current time molten bath.
In the present embodiment, the condition of convergence of iterative calculation:
It is divided by with the result that the result that current iteration calculates is calculated with last iteration, it is full when value is between 0.99-1.01
The sufficient condition of convergence.Wherein result includes: temperature field, velocity field and each component concentration field.
Zoning in the present embodiment should be identical as actual workpiece to be machined size, solves the temperature in zoning
When field, velocity field, concentration field, finite difference calculus or finite volume method or finite element method can be used, is adopted in embodiment
Use finite element method.D in this examplejkFor j rank symmetric coefficient matrix, the numerical value of j and k it is equal and be equal to molten bath in correspond to component
Label, the value on diagonal line is 1.
It also needs to carry out grid dividing to zoning before iterative calculation, can be drawn according to pool size and required precision selection
The size of sub-unit.In addition, before calculating, it is also necessary to determine the movement routine of laser heat source according to actual machining path.
Illustrate realization process of the invention with specific example below.
The laser power of the present embodiment is 700W, laser absorption rate 0.27, laser beam movement velocity (scanning speed) 10mm/
S, powder feeding rate 5.9g/min, the multicomponent element of calculating include: powdered ingredients (Co 75wt%, Cr 20wt%, W 5wt%) and
Matrix composition (Fe 99.96wt%, S 0.04%).When powder is added to molten bath, Convention diffusion phenomenon will occur, lead to element
The concentration distribution of the redistribution of ingredient, each ingredient after the solidification of molten bath is that the present embodiment will be calculated and be predicted.Matrix and powder
The thermal physical property parameter that powder material varies with temperature is calculated by JMatPro software.
Zoning is 20*10*6, and grid is as shown in Figure 2.The process of execution is as shown in Figure 3.
A. physical field initializes: temperature field is initialized as room temperature, velocity field is initialized as 0, the initialization of multicomponent concentration field
For the concentration of each component in the base.
Wherein, Fe concentration of element is initialized as 99.96wt% in substrate, and S constituent content is initialized as 0.04wt%.Other
Powdered ingredients are initialized as 0, are that other addO-on therapies do not fuse into matrix also.
B. start iterative process: setting time step always solves step number, convergence tolorence.
Wherein, time step is 1 × 10-5Second, total to solve the time 0.5 second, convergence tolorence 1 × 10-3。
The time step of setting should be less than sizing grid (50 microns) divided by molten bath flowing velocity (about 0.5m/s).Range
Generally less than 1 × 10-4Second.
C. it calculates temperature field: using laser effective power density as energy input, calculating the three-dimensional heat transfer side with convective term
Journey obtains instantaneous scalar temperature field T.
Wherein, the concrete form of Equations of Three-dimension are as follows:
Density p takes 7400kg/m in this example3, thermal capacitance CpTake 600kJ/kg/K.K takes 22W/ (mK)
T andIt is variable to be solved, is determined when u is a upper time step by Navier-Stokes.
D. it calculates multicomponent concentration field: being based on temperature field T, be input with the concentration stream of each ingredient, calculating is based on
The multicomponent mixing average convection diffusion equation of Maxwell-Stefan diffusion model, wherein considering component certainly in a manner of source item
Concentration gradient between body concentration gradient, component, component diffusion caused by temperature gradient (soret effect).It is instantaneous to obtain each component
Concentration field: w1, w2... ..., wn。
Wherein, the specific calculating of the multicomponent mixing average convection diffusion equation based on Maxwell-Stefan diffusion model
Process are as follows:
N5=j5+7400uω5 (2)
Mn=0.4 (5)
Wherein jiThe diffusion concentration stream of i component is represented, i=5, ρ represent molten metal density (7400kg/m in this example3)、u
Represent convection velocity, ωiRepresent mass fraction, the N of i componentiRepresent i component total concentration stream,Represent mixing average diffusion
Coefficient, MnRepresentative mixing average molar mass,Thermal diffusion coefficient is represented, 0.01kg/m/s, T is taken to represent molten bath temperature in this example
Degree, xkRepresent the molar fraction of k component.
DjkMaxwell-Stefan diffusion coefficient matrix is represented, is 5 rank symmetrical matrixes in this example, is calculated to simplify, this
Constant matrices is taken in example, constant is 1 × 10-7。MiRepresent the molal weight of i component, MFe=56g/mol, MS=32g/mol, MCo
=59g/mol, MCr=52g/mol, MW=183g/mol.
ωiIt is variable to be solved.Temperature field T is obtained by Equations of Three-dimension, by Navier- when u is a upper time step
Stokes is determined.
E. air liquid interface displacement field and molten bath velocity field are calculated: being based on temperature field T and each component concentration field: Fe, Ms, Mco,
MCr, MWIt is input with powder quality stream, calculates gas/liquid circle using Arbitrary Lagrangian-Eulerian (ALE) method
Face displacement field obtains interfacial displacement vector field X, while obtaining molten bath speed arrow by solving Navier-Stokes (N-S) equation
Measure field U.
Wherein, the rate travel of ALE mobile grid are as follows:
In equation, u represents molten bath flowing velocity, and n represents surface normal, MfRepresentation quality adding rate takes in this example
10kg/m2/ s, ρ represent molten metal density (7400kg/m3).It is determined when u is a upper time step by Navier-Stokes.
Wherein, the concrete form of the N-S equation of solution are as follows:
In equation, I represents unit matrix, and μ represents metal liquid viscosity, and this example takes 0.005Pas.F represents body force,
Molten bath drag force is only considered in this example.F=0, ρ=7400, u are variables to be solved.
F. judge the condition of convergence: meeting the condition of convergence and then calculate completion, be unsatisfactory for the condition of convergence then return step c.
Wherein, the condition of convergence refers to that calculating residual error is less than tolerance or calculates solution time of the time greater than setting.With
The result that the result that current iteration calculates is calculated with last iteration is divided by, and when value is between 0.99-1.01, meets convergence item
Part.
The cross section result of molten bath flowing after the present embodiment calculating and the comparison diagram of experiment in Fig. 4 as shown in figure 4, show
Molten bath interface, molten bath directional velocity, molten bath maximum speed under the different scanning speed that the present embodiment calculates, with experimental result
It coincide good.Wherein S1 to S9 respectively represents scanning speed 1mm/s to 9mm/s.
Fig. 5 indicates the comparing result of the element sulphur concentration calculated and the element sulphur concentration tested with AES methods experiment,
In, Fig. 5 (a) to (d) respectively indicates the calculating and experimental result indicated under scanning speed 2mm/s, 4mm/s, 6mm/s, 8mm/s.
As can be seen that the present embodiment calculated result and the experimental result of concentration of element are coincide well in figure.
So far, although those skilled in the art will appreciate that present invention has been shown and described in detail herein multiple shows
Example property embodiment still without departing from the spirit and scope of the present invention, still can according to the present disclosure directly
Determine or deduce out many other variations or modifications consistent with the principles of the invention.Therefore, the scope of the present invention is understood that and recognizes
It is set to and covers all such other variations or modifications.
Claims (10)
1. a kind of ingredient calculation method of laser melting coating multi-component alloys coating, which comprises the steps of:
Step 100, each parameter for initializing zoning is basic status, then requires to carry out workpiece surface according to scheduled
Cladding calculates；
Step 200, in cladding calculating process, time step is arranged according to required required precision, to complete cladding track institute
The time needed solves step number as total divided by time step, and calculating is then iterated in each time step, described to change
The process that generation calculates includes following four steps:
Step 201, by molten bath velocity field, density of material, thermal conductivity and the convection current of present laser effective power density, previous moment
In the Equations of Three-dimension of coefficient of heat transfer lead-in zone convective term, to obtain the temperature field in current time molten bath；
Step 202, by the temperature field in current molten bath, the molten bath velocity field of previous moment, the concentration stream of each component, diffusion coefficient,
Thermal diffusion coefficient, molar fraction and molal weight import average pair of the multicomponent mixing based on Maxwell-Stefan diffusion model
It flows in diffusion equation, the concentration field at current time that respectively obtains each component in molten bath；
Step 203, it by the concentration field in temperature field and each component, the molten bath velocity field of previous moment, and is added in molten bath
The quality stream of each component imports Arbitrary Lagrangian-Eulerian equation, is being hung down with obtaining current molten bath upper surface
The upward vertical displacement vectors field of histogram；
Step 204, by the concentration field in temperature field and each component, the vertical displacement vectors field of molten bath upper surface in vertical direction,
Density of material, viscosity import Navier-Stokes equation and obtain the velocity vector field in current molten bath；
Step 300, iteration calculating process, and continue to judge whether the concentration field of each component in molten bath in each time step becomes
In stabilization, when unstable, continue to iterate to calculate；Then stop iterating to calculate when stablizing, iterate to calculate at this time obtained as a result, i.e.
For the concentration value of each component in current time molten bath.
2. ingredient calculation method according to claim 1, which is characterized in that
The Equations of Three-dimension are as follows:
Wherein, ρ is the density of liquid metal, CpFor material thermal capacitance,It is temperature to the derivative of time, u is liquid metal speed,For temperature gradient, k is material thermal conductivity.
3. ingredient calculation method according to claim 1, which is characterized in that
The multicomponent mixing average convection diffusion equation of the Maxwell-Stefan diffusion model are as follows:
Ni=ji+ρuωi (2)
Wherein jiConcentration stream when a certain component is spread in molten bath in all components is represented, i is the label of the component, and ρ represents molten bath
The middle mixed density of each component, u represent convection velocity of each component in molten bath.
4. ingredient calculation method according to claim 3, which is characterized in that
The temperature gradient of concentration gradient between each component itself concentration gradient, each component, current molten bath is handled in a manner of source item
The caused component diffusion in molten bath.
5. ingredient calculation method according to claim 3, which is characterized in that
J in (1) formulaiIt is obtained by following formula:
In formulaI component is represented because of diffusion caused by component itself concentration gradient,It represents between i component
Diffusion caused by concentration gradient,The diffusion due to caused by temperature gradient of i component is represented, ω i represents the quality point of i component
Number,Each component mixing average diffusion coefficient in molten bath is represented, Mn represents mixing average molar mass,Represent thermal diffusion system
Number, T represent temperature field of molten pool,The gradient of the mass fraction of i component is represented,The gradient in temperature field is represented,Generation
The gradient of table mixing average molar mass.
6. ingredient calculation method according to claim 5, which is characterized in that
Each component mixing average diffusion coefficient in molten bath in (3) formulaIt is obtained by following formula:
Wherein, xkRepresent the molar fraction of k component, DjkRepresent Maxwell-Stefan diffusion coefficient matrix.
7. ingredient calculation method according to claim 5, which is characterized in that
Mixing average molar mass M in (3) formulanIt is obtained by following formula:
Wherein, MiRepresent the molal weight of i component.
8. ingredient calculation method according to claim 1, which is characterized in that
The Arbitrary Lagrangian-Eulerian equation are as follows:
Wherein, u represents molten bath flowing velocity, and n represents surface normal, MfRepresentation quality adding rate, ρ represent molten metal density.
9. ingredient calculation method according to claim 1, which is characterized in that
The Navier-Stokes equation are as follows:
Wherein, I represents unit matrix, and μ represents metal liquid viscosity, and F represents body force.
10. ingredient calculation method according to claim 6, which is characterized in that
DjkFor j rank symmetric coefficient matrix, the numerical value of j and k are equal and are equal to the label that component is corresponded in molten bath, on diagonal line
Value is 1.
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