CN113779793B - Heat source modeling method for selective laser melting based on ray tracing - Google Patents

Heat source modeling method for selective laser melting based on ray tracing Download PDF

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CN113779793B
CN113779793B CN202111060679.XA CN202111060679A CN113779793B CN 113779793 B CN113779793 B CN 113779793B CN 202111060679 A CN202111060679 A CN 202111060679A CN 113779793 B CN113779793 B CN 113779793B
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heat source
energy
powder
laser
model
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CN113779793A (en
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黄智�
贾卫博
王颢铭
李超
梁杰
钟岳
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • 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
    • B22F10/00—Additive manufacturing of workpieces or articles from metallic powder
    • B22F10/20—Direct sintering or melting
    • B22F10/28—Powder bed fusion, e.g. selective laser melting [SLM] or electron beam melting [EBM]
    • 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
    • B22F10/00—Additive manufacturing of workpieces or articles from metallic powder
    • B22F10/80—Data acquisition or data processing
    • B22F10/85—Data acquisition or data processing for controlling or regulating additive manufacturing processes
    • 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
    • B33Y50/02—Data acquisition or data processing for additive manufacturing for controlling or regulating additive manufacturing processes
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/10—Additive manufacturing, e.g. 3D printing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
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    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P10/00—Technologies related to metal processing
    • Y02P10/25—Process efficiency

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Abstract

The invention discloses a heat source modeling method for selective laser melting based on ray tracing, which is applied to the technical field of additive manufacturing, and aims at solving the problems that a process parameter determination method for SLM (selective laser melting) preparation parts in the existing additive manufacturing technology is time-consuming and labor-consuming and has high cost. Firstly, adopting Python programming to obtain a powder model, carrying out interaction between the obtained powder model and laser, calculating and counting the distribution situation of a heat source in the powder, and then carrying out fitting of the depth direction and the horizontal direction on the counting result to obtain the distribution rule of the heat source, thus obtaining a complete heat source model; the heat source model is applied to temperature field simulation, so that the accuracy of SLM simulation can be improved, and the product quality of SLM preparation parts can be improved.

Description

Heat source modeling method for selective laser melting based on ray tracing
Technical Field
The invention belongs to the technical field of additive manufacturing, and particularly relates to a selective laser melting technology.
Background
The selective laser melting technology (selective laser melting, SLM) is an additive manufacturing technology, has the advantages of short production period and high material utilization rate, and is increasingly applied to various fields such as aerospace, medical treatment and the like. The advantages and disadvantages of the SLM preparation part are greatly influenced by the technological parameters, but the traditional experimental trial-and-error method for determining the technological parameters is time-consuming, labor-consuming and high in cost, so that a large number of researchers study the SLM process by adopting a simulation method, the trial-and-error times are reduced, and the manufacturing cost is saved. Most of the current researches focus on three aspects of temperature field, stress strain and metallographic structure simulation. The temperature field is the basis of stress strain and metallographic structure research, and the simulation accuracy of the temperature field is influenced by the heat source model to the greatest extent, so that the improvement and optimization of the heat source model are the important importance of improving the simulation accuracy of the SLM.
The heat source models commonly used for the SLM at present are Gaussian heat source models, double-ellipsoid heat source models, cylindrical heat source models and ray tracing heat source models. The gaussian heat source model is a planar heat source model, and the simulation accuracy is not high because the penetration of energy in the depth direction is not considered. The double ellipsoidal heat source is a volumetric heat source with energy decreasing in the depth direction. The heat source consists of a front quarter ellipsoid and a rear quarter ellipsoid, and in practical application, the sizes of the front half ellipsoid and the rear half ellipsoid of the double ellipsoids are required to be adjusted by observing the shape of a molten pool, so that a proper heat source model is obtained. However, the molten pool morphology cannot be easily and accurately captured, so that the difficulty in selecting model parameters is great. The cylindrical heat source is a heat source, which satisfies gaussian distribution on a cylindrical section and gradually decays in an axial direction according to a certain rule. None of the above simulation models consider the effect of powder placement on the heat source. The ray tracing heat source model overcomes the defects of the former, and obtains the distribution condition of the heat source energy based on ray tracing in the powder so as to obtain the heat source model. However, the conventional heat source model only analyzes the change of the energy distribution in the depth direction, the conventional plane Gaussian energy distribution is directly used in the horizontal direction, and the change of the energy distribution in the horizontal direction is not deeply analyzed, so that errors can be generated in simulation.
Disclosure of Invention
In order to solve the technical problems, the invention provides a heat source modeling method for selective laser melting based on ray tracing, which can effectively improve the simulation precision of SLM.
The invention adopts the technical scheme that: a heat source modeling method for laser selective melting based on ray tracing comprises the following steps:
A. generating a powder model;
B. based on the powder model in the step A, dispersing laser into a plurality of tiny laser beams, tracking the propagation process of the laser beams in the powder, and recording and counting the energy absorption condition to obtain the energy distribution in the powder bed;
C. fitting the heat source energy distribution by adopting an improved heat source model expression;
D. parameters of the improved heat source model are obtained by fitting the energy of each layer, and a final heat source model is obtained by performing polynomial fitting on the parameters for 5 times.
And step A, simulating sedimentation of powder by adopting a sand rain method to obtain a powder model of the SLM powder layer.
Step B comprises the following sub-steps:
b1, generation of light beam
Assuming that the laser consists of n beamlets, each beamlet being represented by a straight line; the energy density distribution formula of the laser is as follows:
wherein P is laser power, r 0 Is the beam waist radius of the laser, (x, y) is the point position coordinate to be solved, (x) 0 ,y 0 ) The laser center position coordinates;
each beam has a power of
P(x,y)＝q(x,y)·s
Where n is the number of hypothetical beamlets and s is the cross-sectional area of each hypothetical beam;
b2 reflection of light beam on sphere
The initial point of the incident light is denoted as A, and the direction isThe starting point B and the direction of the reflection of the light beam on the sphere>The method of (2) is as follows:
wherein E is O 1 Projection in AB direction, F is A in O 1 Projection in the B direction;
b3 reflection of the light beam on the top surface of the substrate
The initial point of the incident light is C, the direction isStarting point D and direction of reflection of the light beam on the top surface of the substrate +.>The method of (2) is as follows:
wherein z is c Representing the z-axis coordinate of the point C, wherein H is the projection of C in the vertical direction;
b4 condition of ending propagation of light beam
The remaining energy P per propagation of the beam is determined by:
P i+1 ＝(1-ε)P i
wherein epsilon is the absorptivity and is 0.3. When the residual laser energy is lower than 1% or the laser emission statistical range is within, ending the tracking of the current beam propagation;
b5, energy statistics
Recording the position and energy value of each reflection point, repeating the test for a plurality of times and counting the energy mean value.
The step C specifically comprises the following sub-steps:
c1, performing polynomial fitting on the distribution condition of the heat source in the vertical direction z for five times:
f(z)＝az 5 +bz 4 +cz 3 +dz 2 +ez+f
wherein a, b, b, d, e, f is the coefficient to be determined;
and C2, fitting the distribution situation of the heat sources in the horizontal directions x and y:
wherein a is 1 、b 1 Is a coefficient to be determined.
The step D is specifically as follows: fitting the energy layering in the horizontal directions x and y to obtain a series of parameters a 1 、b 1 ；
By f 1 (z) represents a 1 Relationship with z, g 1 (z) represents b 1 Relationship with z;
respectively to f 1 (z) and g 1 (z) performing a polynomial fit of degree 5;
f obtained from fitting 1 (z) and g 1 (z) obtaining a final heat source model.
The final heat source model expression is:
z 0 the z-axis coordinate representing the initial point.
The invention has the beneficial effects that: the invention provides a new heat source model, and compared with the traditional heat source model, the heat source model has the advantages of simple parameter obtaining method and higher precision; the heat source model is applied to temperature field simulation, so that the simulation accuracy can be improved; the product quality of the SLM manufacturing part is effectively improved.
Drawings
Fig. 1 is a flow chart of the method of the present invention.
FIG. 2 is a graph showing the particle size distribution of the powder used in the present invention.
Fig. 3 is a powder model generated in step a.
Fig. 4 is a schematic diagram of the principle of beam reflection.
FIG. 5 is an energy statistics cloud;
wherein (a) is a front view; (b) is a left side view; (c) is a top view; (d) is an oblique view.
Fig. 6 is a graph of the results of a fifth order polynomial fit of the heat source in the vertical direction.
FIG. 7 is a graph showing the heat source distribution obtained by beam tracking in the horizontal direction at different depths, the heat source generated by the conventional modeling method, and the heat source generated by the present invention;
wherein (a) is a comparison plot at z=0 μm; (b) is a comparison plot at z=3 μm; (c) is a comparison plot at z=6 μm; (d) is a comparison plot at z=9 μm; (e) is a comparison plot at z=12 μm; (f) is a comparison plot at z=15 μm; (g) is a comparison plot at z=18 μm; (h) is a comparison plot at z=21 μm; (i) is a comparison plot at z=24 μm; (j) is a comparison plot at z=27 μm; (k) is a comparison plot at z=30μm.
FIG. 8 is a fitting result of the method of the present invention;
wherein (a) is f 1 (z)，a 1 A functional relationship with z; (b) G is g 1 (z)，b 1 Functional relation with z.
FIG. 9 is a graph comparing the loss function of a conventional modeling method with that of the present invention at the time of fitting.
Detailed Description
The present invention will be further explained below with reference to the drawings in order to facilitate understanding of technical contents of the present invention to those skilled in the art.
The invention carries out deep analysis on a heat source model considering powder influence, researches the distribution situation of energy in the horizontal direction and the vertical direction, and provides a flow chart of a heat source modeling method, which is shown in figure 1. Firstly, programming to obtain a powder model, carrying out interaction between the obtained powder model and laser, calculating and counting the distribution condition of a heat source in the powder, and then carrying out fitting of the depth direction and the horizontal direction on the counting result to obtain the distribution rule of the heat source, thus obtaining the complete heat source model. The method comprises the following specific steps:
A. generating a powder model:
according to the particle size distribution of the powder shown in fig. 2, sedimentation of the powder was simulated by using a sand rain method, and a powder model of the SLM powder layer was obtained as shown in fig. 3.
B. Heat source energy tracking:
during SLM, a portion of the laser light impinging on the powder is absorbed and a portion is reflected off, and the reflected energy may be absorbed by other powders. In order to obtain the distribution of laser energy in the powder bed, the laser is scattered into a plurality of tiny laser beams, the propagation process of the laser beams in the powder is tracked, and the energy absorption condition is recorded and counted to obtain the energy distribution in the powder bed. A schematic diagram of beam reflection is shown in fig. 4.
B1, generation of light beam
In this embodiment, it is assumed that the laser light is composed of n beamlets, each beamlet being represented by a straight line. The energy density distribution formula of the laser is as follows:
wherein P is laser power, r 0 Is the beam waist radius of the laser, (x, y) is the point position coordinate to be solved, (x) 0 ,y 0 ) Is the laser center position coordinates.
Each beam has a power of
P(x,y)＝q(x,y)·s
Where n is the number of hypothetical beamlets and s is the cross-sectional area of each hypothetical beam.
B2, reflection of the light beam on the sphere B5 is that
The initial point of the incident light is A, the direction isStarting point B and direction of reflection of the light beam on the sphere +.>The method of (2) is as follows:
wherein O is 1 、O 2 Is the sphere center of the powder 1, 2. E is O 1 Projection in the AB direction. F is A in O 1 Projection in the B direction.Respectively->Is a unit vector of (a). Those skilled in the art will note here thatRepresenting vectors AB, AE, BE, BF, BA, respectively;
b3 reflection of the light beam on the top surface of the substrate
The initial point of the incident light is C, the direction isStarting point D and direction of reflection of the light beam on the top surface of the substrate +.>The method of (2) is as follows:
wherein z is c Representing the z-axis coordinate of point C, H is the projection of C in the vertical direction.Respectively-> Is a unit vector of (a).
B4 condition of ending propagation of light beam
The remaining energy P per propagation of the beam is determined by:
P i+1 ＝(1-ε)P i
wherein epsilon is the absorptivity and is 0.3. And when the residual laser energy is lower than 1 percent or the laser emission statistical range is within, ending the tracking of the current beam propagation.
B5, energy statistics
The position and energy values of each reflection point are recorded according to the methods in B2, B3 and B4.
Repeated tests are carried out for a plurality of times and the energy average value is counted. The energy mean distribution has reached steady state when repeated 1000 times. The energy statistics cloud is shown in fig. 5.
C. Fitting analysis of heat source energy distribution
Assuming that the original volume of the powder+the voids is 1, when the powder is melted and solidified and the gas in the voids is discharged, the present volume becomes 1×relative density, and the relative density is η in this example.
C1, considering the change of the relative density eta after the powder is fused, the vertical dimension of the heat source model is eta times of the vertical dimension of the powder, the eta is about 51.2% through experimental measurement, the eta is about 47.3% through simulation calculation, and the eta is 50%. A five degree polynomial fit was performed on the energy distribution of the heat source in the vertical direction (z direction). The fitting results are shown in fig. 6.
f(z)＝az 5 +bz 4 +cz 3 +dz 2 +ez+f
Where f (z) represents the sum of the energies of the entire layers at the depth z and a, b, b, d, e, f is the coefficient to be determined.
And C2, fitting the distribution situation of the heat source in the horizontal direction (x and y directions). The conventional heat source model considers that the distribution of energy in the horizontal direction satisfies the formula:
wherein a is 0 Is a coefficient to be determined.
The invention discovers that the distribution of the heat source in the horizontal direction is different along with the r of z through a plurality of experimental observations 0 The heat source concentration degree is changed by adopting the following formula for fitting in order to further accurately express the heat source:
wherein a is 1 、b 1 For undetermined coefficients
D. Building a heat source model
As shown in fig. 7, the energy stratification in the horizontal direction is fitted to obtain a series of parameters a 1 、b 1 。f 1 (z)、g 1 (z) represents a respectively 1 、b 1 Relation with depth z, 5 th degree polynomial fitting was performed on it (5 th degree polynomial fitting formula same as step C1).
f 1 (z)＝Az 5 +Bz 4 +Cz 3 +Dz 2 +Ez+F
g 1 (z)＝A 1 z 5 +B 1 z 4 +C 1 z 3 +D 1 z 2 +E 1 z+F 1
Therein, A, B, C, D, E, F, A 1 、B 1 、C 1 、D 1 、E 1 、F 1 For the undetermined coefficients, the fit results are shown in FIG. 8.
Obtaining a final heat source model:
z 0 the z-axis coordinate representing the initial point, v x 、v y The speeds of the heat source in the x and y directions are respectively shown, and t is time.
The loss function generated when the invention is compared with the traditional method is shown in fig. 9, and obviously, the heat source model of the invention can better represent the distribution condition of laser energy.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Various modifications and variations of the present invention will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (4)

1. The heat source modeling method for selective laser melting based on ray tracing is characterized by comprising the following steps of:
A. generating a powder model;
B. based on the powder model in the step A, dispersing laser into a plurality of tiny laser beams, tracking the propagation process of the laser beams in the powder, and recording and counting the energy absorption condition to obtain the energy distribution in the powder bed;
C. fitting the heat source energy distribution by adopting an improved heat source model expression; the step C specifically comprises the following sub-steps:
c1, performing polynomial fitting on the distribution condition of the heat source in the vertical direction z for five times:
f(z)＝az 5 +bz 4 +cz 3 +dz 2 +ez+f
wherein a, b, b, d, e, f is the coefficient to be determined;
and C2, fitting the distribution situation of the heat sources in the horizontal directions x and y:
wherein a is 1 、b 1 Is a coefficient to be determined;
D. obtaining parameters of an improved heat source model by fitting energy of each layer, and obtaining a final heat source model by performing polynomial fitting on the parameters for 5 times; the final heat source model expression is:
z 0 the z-axis coordinate representing the initial point.
2. The heat source modeling method for selective laser melting based on ray tracing of claim 1, wherein the step A adopts a sand rain method to simulate sedimentation of powder, and a powder model of an SLM powder layer is obtained.
3. The method for modeling heat source for selective laser melting based on ray tracing of claim 1, wherein step B comprises the following sub-steps:
b1, generation of light beam
Assuming that the laser consists of n beamlets, each beamlet being represented by a straight line; the energy density distribution formula of the laser is as follows:
wherein P is laser power, r 0 Is the beam waist radius of the laser, (x, y) is the point position coordinate to be solved, (x) 0 ,y 0 ) The laser center position coordinates;
each beam has a power of
P(x,y)＝q(x,y)·s
Where n is the number of hypothetical beamlets and s is the cross-sectional area of each hypothetical beam;
b2 reflection of light beam on sphere
The initial point of the incident light is denoted as A, and the direction isThe starting point B and the direction of the reflection of the light beam on the sphere>The method of (2) is as follows:
wherein E is O 1 Projection in AB direction, F is A in O 1 Projection in the B direction;
b3 reflection of the light beam on the top surface of the substrate
The initial point of the incident light is C, the direction isStarting point D and direction of reflection of the light beam on the top surface of the substrate +.>The method of (2) is as follows:
wherein z is c Representing the z-axis coordinate of the point C, wherein H is the projection of C in the vertical direction;
b4 condition of ending propagation of light beam
The remaining energy P per propagation of the beam is determined by:
wherein epsilon is the absorptivity;
b5, energy statistics
And (3) recording the position and the energy value of each reflection point according to the methods in B2, B3 and B4, repeating the test for a plurality of times and counting the energy mean value.
4. The method for modeling heat source of selective laser melting based on ray tracing as defined in claim 1, wherein step D specifically comprises: fitting the energy layering in the horizontal directions x and y to obtain a series of parameters a 1 、b 1 ；
By f 1 (z) represents a 1 Relationship with z, g 1 (z) represents b 1 Relationship with z;
respectively to f 1 (z) and g 1 (z) performing a polynomial fit of degree 5;
f obtained from fitting 1 (z) and g 1 (z) obtaining a final heat source model.
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CN111695256A (en) * 2020-06-10 2020-09-22 河海大学常州校区 Modeling method of laser arc composite heat source based on energy distribution coefficient
CN113343521A (en) * 2021-05-27 2021-09-03 重庆大学 Method for predicting interlayer thermal stress distribution in selective laser melting process based on COMSOL

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