CN105689719A - Method for calculating alloy droplet deposition cooling rate - Google Patents

Method for calculating alloy droplet deposition cooling rate Download PDF

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Publication number
CN105689719A
CN105689719A CN201610088272.0A CN201610088272A CN105689719A CN 105689719 A CN105689719 A CN 105689719A CN 201610088272 A CN201610088272 A CN 201610088272A CN 105689719 A CN105689719 A CN 105689719A
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liquid droplet
alloy liquid
cooldown rate
dendrite arm
secondary dendrite
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CN201610088272.0A
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徐轶
陈亚
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Southwest Jiaotong University
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Southwest Jiaotong University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F3/00—Manufacture of workpieces or articles from metallic powder characterised by the manner of compacting or sintering; Apparatus specially adapted therefor ; Presses and furnaces
    • B22F3/115—Manufacture of workpieces or articles from metallic powder characterised by the manner of compacting or sintering; Apparatus specially adapted therefor ; Presses and furnaces by spraying molten metal, i.e. spray sintering, spray casting
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y50/00—Data acquisition or data processing for additive manufacturing

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  • Engineering & Computer Science (AREA)
  • Manufacturing & Machinery (AREA)
  • Chemical & Material Sciences (AREA)
  • Materials Engineering (AREA)
  • Mechanical Engineering (AREA)
  • Investigating And Analyzing Materials By Characteristic Methods (AREA)

Abstract

The invention discloses a method for calculating the alloy droplet deposition cooling rate and belongs to the technical field of 3D printing technologies. According to the method for calculating the alloy droplet deposition cooling rate, on the basis of a thermodynamic equation, a mathematic model of the cooling rate and the dendritic structure character is built, and accordingly the cooling rate is calculated according to droplet structure evolution. In the solidification process, the influence of crystalline latent heat is taken into account, the droplet ejecting speed is combined, the heat exchanging condition of the droplet movement process and the external environment is considered, and the variable relationship of the cooling rate of droplets with different diameters is calculated. According to the dendrite spacing dimension, a semi-empirical formula of the cooling rate and the secondary dendrite spacing is built and derived through regression analysis; by observing and measuring the dendritic structure of the deposition droplets, the cooling rate of the deposition droplets in the 3D printing process is obtained. According to the calculation method, the relationship between the 3D printing material structure and the cooling rate can be built, and deposition droplet solidification structure evolution of 3D printing can be effectively predicted, adjusted and controlled. The method for calculating the alloy droplet deposition cooling rate is mainly used for 3D printing technology control.

Description

A kind of cooldown rate computational methods of alloy liquid droplet deposition
Technical field
The present invention relates to 3D marker's technology field。
Background technology
Symmetrical liquid drop 3D printing technique is that U.S. Orme proposed in 1993 and the one that grows up increases material manufacturing technology。It is based on the forming principle of " discrete-superposition ", produce homogeneous metal microdroplet by liquid drop ejector, control three-dimensional substrate motion simultaneously, make metal droplet accurate deposition at ad-hoc location and mutually merge, solidify, pointwise successively pile up, thus realizing the printing speed of complex three-dimensional structure。This technology have blasting materials scope wide, without constraint free forming with without advantages such as expensive special equipments, prepare at small complicated metalwork, circuit prints and is widely applied prospect with the field such as Electronic Packaging and structure-function integration part manufacture。
From symmetrical liquid drop through technological design, path is designed, deposition is designed into last 3D and is printed as product, molten drop experienced by liquid-solid, fusing-solidification, the transition process of forming core-growth, therefore to obtain the metal 3D printed product of excellent performance, process stabilizing, need material to have controlled dendritic solidification tissue and growth rhythm, and in process, drop cooldown rate has conclusive impact for dendritic solidification and growth。But due to the change of contact medium in real process, cooldown rate is difficult to quantitatively follow the trail of and quantify。
Print process controllability to increase 3D, reduce process costs, improve production efficiency, it is necessary to by the method setting up mathematical connection between cooldown rate and arborescent structure, thus realizing symmetrical liquid drop 3D printing tissue and solidification behavior are control effectively。
Summary of the invention
It is an object of the invention to provide the cooldown rate computational methods of a kind of alloy liquid droplet deposition, it can efficiently solve 3D and print the prediction of deposition droplet solidification microstructure evolution, it is to avoid repeat to test the problem groping the cost rising that technological parameter brings。
It is an object of the invention to be achieved through the following technical solutions: the cooldown rate computational methods of a kind of alloy liquid droplet deposition, comprise the following steps:
Step one, collect calculative alloy liquid droplet:
Print technical process and parameter based on symmetrical liquid drop 3D, change technological parameter and injection conditions so that the alloy liquid droplet natural cooling of different-grain diameter also solidifies, and prepares the alloy liquid droplet of different-grain diameter, after uniformly cooling, collects all alloy liquid droplets。
Step 2, measure alloy liquid droplet tissue secondary dendrite arm spacing:
Successively the alloy liquid droplet of different-grain diameter is carried out sample to inlay, and corrode as corrosive liquid with ethanol+hydrogen peroxide, Application Optics microscope carries out arborescent structure observation, for the alloy liquid droplet of any one particle diameter, measures and record the secondary dendrite arm spacing of different-grain diameter alloy liquid droplet tissue；Measure 40 groups of secondary dendrite arm spacings of n, and measure total length l, according to relational expression secondary dendrite arm spacingCalculate the alloy liquid droplet secondary dendrite arm spacing numerical value of corresponding particle diameter。
The linear relationship chart of step 3, drafting different-diameter drop and secondary dendrite arm spacing:
Different-grain diameter alloy liquid droplet reflects the impact of cooler environment, show the difference of certain cooldown rate, and secondary dendrite arm spacing reflects the size of cooldown rate, the relation of the alloy liquid droplet according to same size and tissue coagulation feature, measure the secondary dendrite arm spacing of different-diameter drop, count the relation of different-diameter alloy liquid droplet and secondary dendrite arm spacing, and draw the linear relationship chart of different-diameter alloy liquid droplet and secondary dendrite arm spacing。Step 4, calculate different-grain diameter alloy liquid droplet cooldown rate:
Based on uniform alloy drop 3D print procedure, according to influence factors such as Newtonian Cooling model and consideration latent heats, calculate the cooldown rate of different-grain diameter alloy liquid droplet；Utilize Newtonian Cooling modelConsider heat exchange coefficientAnd alloy liquid droplet course of injection thunder Lip river numberPrandtl numberNusselt number N u = 2 β k S ( m + 1 ) · ( T t m + 1 - T ∞ m + 1 ) ( T t - T ∞ ) + ( 0.4 Re 1 / 2 + 0.06 Re 2 / 3 ) · Pr 0.4 · ( μ ∞ μ S ) 1 / 4 Deng, and consider the influence factors such as latent heat, the cooldown rate of different-grain diameter alloy liquid droplet
The semiempirical formula of step 5, derivation alloy liquid droplet cooldown rate and secondary dendrite arm spacing:
The different-diameter alloy liquid droplet drawn according to step 3 and the linear relationship chart of secondary dendrite arm spacing, set up the numerical relation of alloy liquid droplet cooldown rate and secondary dendrite arm spacing, derive the semiempirical formula of alloy liquid droplet cooldown rate and secondary dendrite arm spacing: λ=a CR-n, meanwhile, to λ=a CR-nTaking the logarithm in formula two ends, obtains the logarithmic relationship formula lg λ=lga+blg (CR) of alloy liquid droplet cooldown rate and secondary dendrite arm spacing, carry out mathematical regression analysis, be fixed λ=a CR of value-n, and solve corresponding a and n value, obtain the semiempirical formula of complete cooldown rate and secondary dendrite arm spacing, and draw out the relation curve of secondary dendrite arm spacing and cooldown rate；Further according to the cooling jig in step 4, adopt matlab assembler language, input all material and parameter, run program and formula, calculate the cooldown rate that different-grain diameter alloy liquid droplet is corresponding。
Step 6, calculating increase alloy liquid droplet cooldown rate in material manufacture process:
Print alloy drop tissue in increasing material manufacture process at 3D to observe, measure secondary dendrite arm spacing/cellular crystal spacing, substitute into the semiempirical formula that step 5 is derived, thus calculating alloy liquid droplet cooldown rate in increasing material manufacture process。
The invention have the benefit that by the solidification relation that secondary dendrite arm spacing is set up with cooldown rate, can by tissue being observed and measuring, derive 3D print procedure alloy liquid droplet cooldown rate under complicated heat exchange environment, thus optimizing 3D to print technique and parameter。While saving material, improve the accuracy of 3D print job, add the degree of controllability of 3D printed material process of setting, be conducive to increasing 3D printing effect, it is achieved the effective control to 3D printed product tissue, improve tissue and the performance of 3D print member。
Accompanying drawing illustrates as follows:
Fig. 1 is the linear relationship chart of the CuSn6 alloy different-diameter drop measured of the present invention and secondary dendrite arm spacing。
Fig. 2 the present invention is directed to CuSn6 alloy to adopt after matlab assembler language is calculated, the cooldown rate figure of different-grain diameter drop。
Fig. 3 is the logarithmic relationship curve chart that the present invention is directed to secondary dendrite arm spacing that CuSn6 alloy derives and cooldown rate。
Fig. 4 is the graph of relation of the technical process CuSn6 alloy liquid droplet cooldown rate derived of the inventive method and Peculiarities of Solidification Structure。
Fig. 5 is the flow process frame diagram of the present invention。
Detailed description of the invention
The present invention is achieved by the following measures:
Embodiment 1
Step one, selection CuSn6 alloy are as experiment material, technical process and material parameter is printed based on symmetrical liquid drop 3D, adjusting process parameter and injection conditions, prepare the equally distributed alloy liquid droplet of different-grain diameter, alloy liquid droplet ejects and through motion path natural cooling, each alloy liquid droplet natural cooling is also frozen into molecule, is collected and carries out metallographic sample preparation。
Step 2, successively different-grain diameter CuSn6 alloying pellet is carried out sample and inlay, corrode as corrosive liquid with ethanol+hydrogen peroxide, Application Optics microscope carries out arborescent structure observation, drop for any one particle diameter, measure 40 groups of secondary dendrite arm spacings of n, and measure total length l, according to relational expression secondary dendrite arm spacingCalculate the alloy liquid droplet secondary dendrite arm spacing numerical value of corresponding particle diameter。
Step 3, according to measure different-diameter alloy liquid droplet secondary dendrite arm spacing, count the relation of different-diameter alloy liquid droplet and secondary dendrite arm spacing, as it is shown in figure 1, drafting CuSn6 alloying pellet different-grain diameter when secondary dendrite arm spacing graph of a relation。
Step 4, based on Newtonian Cooling modelConsider heat exchange coefficientAnd liquid drop jetting process thunder Lip river numberPrandtl numberNusselt number N u = 2 β k S ( m + 1 ) · ( T t m + 1 - T ∞ m + 1 ) ( T t - T ∞ ) + ( 0.4 Re 1 / 2 + 0.06 Re 2 / 3 ) · Pr 0.4 · ( μ ∞ μ S ) 1 / 4 Deng, and consider the influence factors such as latent heat, the cooldown rate of different-grain diameter alloy liquid dropletAdopt matlab assembler language, all programs of computing and formula, as in figure 2 it is shown, calculate the cooldown rate that different-grain diameter alloy liquid droplet is corresponding。
Step 5, relation according to alloy liquid droplet diameter and alloy liquid droplet solidification behavior secondary dendrite arm spacing, set up the numerical relation of alloy liquid droplet cooldown rate and secondary dendrite arm spacing, according to alloy liquid droplet secondary dendrite arm spacing and cooldown rate relational expression λ=a CR-n, it is necessary to solve a and n value corresponding in formula。To taking the logarithm of particle diameter alloy liquid droplet secondary dendrite arm spacing, corresponding particle diameter drop cooldown rate is taken the logarithm, draw the logarithmic relationship formula lg λ=lga+blg (CR) of alloy liquid droplet cooldown rate and secondary dendrite arm spacing, line number of going forward side by side regression analysis, as it is shown on figure 3, obtain y=-0.3138x+1.4449, and solve relational expression λ=27.85 CR of corresponding a=27.85 and n=0.3138 value, cooldown rate and secondary dendrite arm spacing-0.3138, and coefficient R2=0.9274, the linear dependence having had。
3D is printed increasing material manufacture CuSn6 alloy structure and observes by step 6, basis, and measure secondary dendrite arm spacing/cellular crystal be smaller than be equal to 1 μm, substitute into empirical equation, it is possible to calculate the cooldown rate increasing material manufacture process CuSn6 alloy liquid droplet and reach 2.27 × 104More than K/s。Relation curve such as secondary dendrite arm spacing that Fig. 4 is the CuSn6 alloy drawn out and cooldown rate。

Claims (4)

1. cooldown rate computational methods for alloy liquid droplet deposition, comprise the following steps:
Step one, collect calculative alloy liquid droplet:
Print technical process and parameter based on symmetrical liquid drop 3D, change technological parameter and injection conditions so that the alloy liquid droplet natural cooling of different-grain diameter also solidifies, and prepares the alloy liquid droplet of different-grain diameter, after uniformly cooling, collects all alloy liquid droplets；
Step 2, measure alloy liquid droplet tissue secondary dendrite arm spacing:
Successively the alloy liquid droplet of different-grain diameter being carried out sample to inlay, and corrode as corrosive liquid with ethanol+hydrogen peroxide, Application Optics microscope carries out arborescent structure observation, measures and record the secondary dendrite arm spacing of different-grain diameter alloy liquid droplet tissue；
The linear relationship chart of step 3, drafting different-diameter drop and secondary dendrite arm spacing:
Different-grain diameter alloy liquid droplet reflects the impact of cooler environment, show the difference of certain cooldown rate, and secondary dendrite arm spacing reflects the size of cooldown rate, the relation according to the drop of same size Yu tissue coagulation feature, draw the linear relationship chart of different-diameter drop and secondary dendrite arm spacing；
Step 4, calculate different-grain diameter alloy liquid droplet cooldown rate:
Based on uniform alloy drop 3D print procedure, according to influence factors such as Newtonian Cooling model and consideration latent heats, calculate the cooldown rate of different-grain diameter alloy liquid droplet；
The semiempirical formula of step 5, derivation drop cooldown rate and secondary dendrite arm spacing:
The different-diameter drop drawn according to step 3 and the linear relationship chart of secondary dendrite arm spacing, set up the numerical relation of drop cooldown rate and secondary dendrite arm spacing, derive the semiempirical formula of drop cooldown rate and secondary dendrite arm spacing: λ=a CR-n, meanwhile, through the Mathematical treatment of logarithmic transformation, and carry out regression analysis, draw the logarithmic relationship curve chart of alloy liquid droplet cooldown rate and secondary dendrite arm spacing, and solve correlation coefficient a and n；
Step 6, calculating increase alloy liquid droplet cooldown rate in material manufacture process:
Print alloy drop tissue in increasing material manufacture process at 3D to observe, measure secondary dendrite arm spacing/cellular crystal spacing, substitute into the semiempirical formula that step 5 is derived, thus calculating alloy liquid droplet cooldown rate in increasing material manufacture process。
2. the cooldown rate computational methods of a kind of alloy liquid droplet as claimed in claim 1 deposition, is characterized in that: described linear relationship chart is the linear relationship chart drawing different-diameter alloy liquid droplet with secondary dendrite arm spacing。
3. the cooldown rate computational methods of a kind of alloy liquid droplet as claimed in claim 1 deposition, is characterized in that: according to fluid and Thermodynamics Formulas, calculate the cooldown rate of different-grain diameter alloy liquid droplet。
4. the cooldown rate computational methods of a kind of alloy liquid droplet as claimed in claim 1 deposition, is characterized in that: described logarithmic relationship figure is based on particle diameter-dendrite-cooldown rate relation, the alloy liquid droplet secondary dendrite arm spacing of drafting and the logarithmic relationship curve chart of cooldown rate。
CN201610088272.0A 2016-02-17 2016-02-17 Method for calculating alloy droplet deposition cooling rate Pending CN105689719A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108108529A (en) * 2017-12-01 2018-06-01 东方电气集团东方汽轮机有限公司 A kind of reverse calculation algorithms of the easy measurement cast interface coefficient of heat transfer
CN108444921A (en) * 2018-03-19 2018-08-24 长沙理工大学 A kind of increasing material manufacturing component online test method based on signal correlation analysis
CN116992794A (en) * 2023-09-27 2023-11-03 北京科技大学 Atomized amorphous powder yield calculation method and application

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CN101169386A (en) * 2007-11-30 2008-04-30 江苏大学 Calculation method for predicating directional solidification first dendrite distance
EP2402473A2 (en) * 2010-06-30 2012-01-04 Alstom Technology Ltd Process for producing a single-crystal component made of a nickel-based superalloy

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108108529A (en) * 2017-12-01 2018-06-01 东方电气集团东方汽轮机有限公司 A kind of reverse calculation algorithms of the easy measurement cast interface coefficient of heat transfer
CN108108529B (en) * 2017-12-01 2021-07-06 东方电气集团东方汽轮机有限公司 Inverse calculation method for simply and conveniently measuring heat exchange coefficient of casting interface
CN108444921A (en) * 2018-03-19 2018-08-24 长沙理工大学 A kind of increasing material manufacturing component online test method based on signal correlation analysis
CN116992794A (en) * 2023-09-27 2023-11-03 北京科技大学 Atomized amorphous powder yield calculation method and application
CN116992794B (en) * 2023-09-27 2023-12-22 北京科技大学 Atomized amorphous powder yield calculation method and application

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Application publication date: 20160622