A surface prediction method for selective laser melting parts based on inherent strain method

Abstract

A surface prediction method for a selective laser melting molded part based on an inherent strain method, comprising: S10, sequentially setting printing layers from 1 to I; when the printing layer is the i-th layer, sequentially setting printing paths from 1 to J i S20, print the Jth layer of the i-th layer i The printing path is discretized, and at each discrete point, an ideal analytical expression prediction result of the surface on each discrete point is obtained using an analytical shape hypothesis. S30: The thermal field during the printing process is calculated using a quasi-static thermal model. S40: The total strain and thermoelastic strain of the printing process are calculated using a total strain model and a thermoelastic model, respectively. S50: Based on the total strain and thermoelastic strain obtained in step S40, the inherent strain of the printing process is obtained using an inherent strain model. S60: The ideal analytical expression prediction result of the surface obtained in step S20 is corrected using the inherent strain obtained in step S50 to obtain a surface prediction result. This method has short computation time and high prediction accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of metal additive manufacturing, and in particular to a surface prediction method for a selective laser melting molded part based on an inherent strain method. Background Art

[0002] Selective laser melting (SLM) is a metal additive manufacturing technology that has been widely used in the processing of metal parts in the fields of aerospace, medical, military, automotive, etc. The surface profile of SLM-molded parts has a great influence on the structural and functional performance of the molded parts. However, due to thermal stress, elastic-plastic deformation and other reasons, surface deviations between the designed and printed parts are inevitable during the SLM process, which limits the further development and application of this technology. Therefore, reliable and accurate surface prediction is a key step in SLM quality control. However, due to the complex physical processes and thermomechanical behavior in SLM, surface prediction of SLM-molded parts is still a great challenge.

[0003] At present, the commonly used surface prediction methods for SLM molded parts include experimental methods, numerical simulation methods and analytical methods. For example, Chinese invention patent publication number CN108399280A discloses a finite element simulation method for predicting the deformation of laser selective melting molded parts, Chinese invention patent publication number CN113976920A proposes a cross-scale control method and system for residual deformation of selective laser melting formed structures, and Chinese invention patent application CN115455776A discloses a physics-based inherent strain method for predicting residual stress and deformation in additive manufacturing. A comprehensive analysis of the existing surface prediction methods for SLM molded parts summarizes the characteristics of each method as follows: the experimental method requires a large amount of material and time; the numerical simulation method can save material, but still requires a lot of computing time; the analytical method can not only save material, but also greatly save computing time, and is the most promising surface prediction method for SLM molded parts. However, due to the complexity of the SLM process, if the various factors affecting the surface of the molded part are not fully considered during the analytical analysis process, the accuracy of the analytical method will be low and it will not meet the prediction requirements. Summary of the Invention

[0004] In order to solve the problems that the existing SLM molded part surface prediction method based on analytical method does not fully consider the various factors affecting the surface of the molded part, has low accuracy, and cannot meet the prediction requirements, the purpose of the present invention is to provide a selective laser melting molded part surface prediction method based on the inherent strain method. This method obtains the inherent strain based on the multi-physical field analytical analysis, and comprehensively considers the influence of the scanning trajectory within the layer, interlayer remelting and interlayer accumulation on the surface of the SLM molded part. It has short calculation time, high prediction accuracy, and strong practicality.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A surface prediction method for a selective laser melting part based on an inherent strain method comprises the following steps:

[0007] S10, set the printing layer from 1 to I in sequence; when the printing layer is the i-th layer, set the printing path from 1 to J in sequence i Where, I is the total number of printed layers, J i is the total number of printing paths for the i-th printing layer;

[0008] S20, print the Jth layer of the i-th layer i The printing paths are discretized, and the ideal analytical prediction result of the upper surface of each discrete point is obtained by using the analytical shape hypothesis at each discrete point;

[0009] S30, calculating the thermal field during the printing process using a quasi-static thermal model;

[0010] S40, calculating the total strain and thermoelastic strain of the printing process respectively using the total strain model and the thermoelastic model;

[0011] S50, based on the total strain and thermoelastic strain obtained in step S40, using an inherent strain model to obtain the inherent strain of the printing process;

[0012] S60 , using the inherent strain obtained in step S50 to correct the surface ideal analytical expression prediction result obtained in step S20 , to obtain a surface prediction result.

[0013] Preferably, in step S10, I and J i All of them are determined when planning the printing process parameters before actual printing. The determination principles are:

[0014] I=H / L t ;

[0015] J i =W i / D l ;

[0016] In the above two formulas, H is the total design height of the part, W i Design the width of the part at layer i, L t D is the set printing layer height. l The spacing of the printing path, H and W i Determined by the design size of the part.

[0017] Preferably, L t The value of D is 50~65μm, l The value is 40~60μm.

[0018] Preferably, in step S20, the spacing Δc between the discrete points is 10 μm; at each discrete point, the surface is a raised molten pool, and the key dimensions of the molten pool include: molten pool height h, molten pool depth d, molten pool width w and molten pool length l.

[0019] Preferably, the analytical shape of the molten pool is assumed to be a combined figure composed of two upper and lower semi-ellipses, the semi-ellipse opening of the upper half faces downward, the semi-ellipse opening of the lower half faces upward, the lengths of the openings of the two semi-ellipses are equal, and the two semi-ellipses are combined at the openings; wherein, the molten pool height h is the height of the semi-ellipse in the upper half of the molten pool, the molten pool depth d is the height of the semi-ellipse in the lower half, and the molten pool width w is the length of the opening of the semi-ellipse in the upper half of the molten pool.

[0020] Preferably, the critical size of the molten pool is determined by a selective laser melting molten pool size prediction method based on molten pool state division.

[0021] Preferably, in step S30, the quasi-static thermal model used to calculate the thermal field during the printing process is:

[0022]

[0023] Where T(x, y, z) is the thermal field during printing, (x, y, z) represents the coordinates of the scanning unit point relative to the current heat source position, and the current heat source position is the irradiation position of the laser; T r (x, y, z) represents the residual temperature; P, η, v, λ, and a represent the laser beam power, energy absorption rate, scanning speed, thermal conductivity, and thermal diffusivity, respectively; a is calculated by a = λ / ρc, where ρ represents density and c represents specific heat; R represents the distance from the scanning unit point to the heat source;

[0024] Among them, the x direction is the scanning direction, the z direction is the vertical direction of the substrate, and the y direction is perpendicular to the xz plane according to the right-hand coordinate system;

[0025] Among them, the residual temperature T r (x,y,z) is calculated as follows:

[0026]

[0027] Where, T a represents the ambient temperature and the virtual heat source laser power, w t It represents the distance between the scanning unit point and the current heat source position in the scanning direction, and t represents the scanning track number.

[0028] Preferably, in step S40, the total strain model used to calculate the total strain of the printing process is:

[0029]

[0030]

[0031]

[0032] Where, are the total strains in the x-, y-, and z-directions, respectively; E is the elastic modulus of the material; σ xx , σ yy , σ zz are the total stress in the x, y, and z directions, respectively, and v e is the Poisson's ratio of the material in elastic state, E p is the plastic modulus of the material;

[0033] Among them, σ xx , σ yy , σ zz Calculated by the following three formulas:

[0034]

[0035]

[0036]

[0037] Where α is the thermal expansion coefficient of the material;

[0038] In step S40, the thermoelastic model used to calculate the thermoelastic strain during the printing process is:

[0039]

[0040]

[0041]

[0042] Where, are the thermoelastic strains in the x, y, and z directions, respectively.

[0043] Preferably, in step S50, the inherent strain model used to calculate the inherent strain of the printing process is:

[0044]

[0045]

[0046]

[0047] Where, are the inherent strains in the x, y, and z directions, respectively.

[0048] Preferably, in step S60, the formula for obtaining the predicted surface result is:

[0049]

[0050]

[0051]

[0052]

[0053] According to step S10, the printing layers are sequentially set from 1 to I; when the printing layer is the i-th layer, the printing paths are sequentially set from 1 to J i The molten pool surface prediction results of all discrete points are obtained, and the set of molten pool surface prediction results of all discrete points is the final predicted SLM molded part surface prediction result.

[0054] Compared with existing technologies, this method offers the following advantages: It uses multi-physics analytical analysis to determine inherent strain, comprehensively considering the effects of intra-layer scanning trajectories, interlayer remelting, and interlayer accumulation on the surface of SLM-molded parts. This method shortens calculation time, achieves high prediction accuracy, and demonstrates strong practicality. This method addresses the problem that existing analytical methods for predicting the surface of SLM-molded parts fail to fully consider all factors affecting the part surface, resulting in low accuracy and an inability to meet prediction requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 The figure is a flow chart of a surface prediction method for selective laser melting molded parts based on the inherent strain method of the present invention.

[0056] Figure 2 Schematic diagram of the molten pool morphology based on the analytical shape assumption in step S20 of the present invention.

[0057] Figure 3 Schematic diagram of the key dimensions of the molten pool morphology based on the analytical shape assumption in step S20 of the present invention.

[0058] Figure 4 Schematic diagram of the process of selective laser melting melt pool size prediction method based on melt pool state division.

[0059] Figure 5 Schematic diagram of determining the molten pool state according to process parameters in step S22 of the selective laser melting molten pool size prediction method based on molten pool state division.

[0060] Figure 6 This is a comparison chart of the melt pool prediction results and experimental results of the first test case of the selective laser melting melt pool size prediction method based on melt pool state division.

[0061] Figure 7 This is a comparison chart of the melt pool prediction results and the experimental results of the second test case of the selective laser melting melt pool size prediction method based on melt pool state division.

[0062] Figure 8 Schematic diagram of surface prediction results obtained in the experimental example of the present invention.

[0063] Figure 9 Schematic diagram of an actual molded part corresponding to the surface prediction result obtained in the test example of the present invention. DETAILED DESCRIPTION

[0064] In order to make the above features and advantages of the present invention more obvious and easy to understand, embodiments are given below with reference to the accompanying drawings for detailed description.

[0065] like Figure 1 As shown, the present invention provides a surface prediction method for a selective laser melting molded part based on an inherent strain method, comprising the following steps:

[0066] S10, set the printing layer from 1 to I in sequence; when the printing layer is the i-th layer, set the printing path from 1 to J in sequence i Where, I is the total number of printed layers, J i is the total number of printing paths for the i-th printing layer;

[0067] S20, print the Jth layer of the i-th layer i The printing paths are discretized, and the ideal analytical prediction result of the upper surface of each discrete point is obtained by using the analytical shape hypothesis at each discrete point;

[0068] S30, calculating the thermal field during the printing process using a quasi-static thermal model;

[0069] S40, calculating the total strain and thermoelastic strain of the printing process respectively using the total strain model and the thermoelastic model;

[0070] S50, based on the total strain and thermoelastic strain obtained in step S40, using an inherent strain model to obtain the inherent strain of the printing process;

[0071] S60 , using the inherent strain obtained in step S50 to correct the surface ideal analytical expression prediction result obtained in step S20 , to obtain a surface prediction result.

[0072] Specifically, in step S10, I and J i All of them are determined when planning the printing process parameters before actual printing. The determination principles are:

[0073] I=H / L t ;

[0074] Ji =W i / D l ;

[0075] In the above two formulas, H is the total design height of the part, W i Design the width of the part at layer i, L t D is the set printing layer height. l The spacing of the printing path, H and W i Determined by the design size of the part. t The value of D is 50~65μm, l The value is 40~60μm.

[0076] Specifically, in step S20 , the spacing Δc between discrete points is 10 μm; at each discrete point, the surface is a raised molten pool, and the key dimensions of the molten pool include: molten pool height h, molten pool depth d, molten pool width w, and molten pool length l.

[0077] like Figure 2 As shown in , the analytical shape of the molten pool is assumed to be a combination of two semi-ovals, the upper semi-oval 1 opening facing downward, the lower semi-oval 2 opening facing upward, the openings of the two semi-ovals are equal in length, and the two semi-ovals are combined at the openings. Figure 3 As shown, the molten pool height h is the height of the semi-ellipse 1 in the upper half of the molten pool, the molten pool depth d is the height of the semi-ellipse 2 in the lower half, and the molten pool width w is the length of the opening of the semi-ellipse 1 in the upper half of the molten pool.

[0078] Specifically, the critical size of the molten pool is determined by the selective laser melting molten pool size prediction method based on the molten pool state division, e.g. Figure 4 As shown in FIG, the method for predicting the molten pool size of selective laser melting based on the molten pool state division includes the following steps:

[0079] S21, setting process parameters for dividing the molten pool state;

[0080] S22, determining the molten pool state according to the process parameters;

[0081] S23, determining a molten pool size prediction formula;

[0082] S24. Determine the molten pool shape ratio according to the molten pool state and substitute it into the molten pool size prediction formula to obtain a predicted value of the molten pool size.

[0083] like Figure 5 As shown, in step S21, the process parameters for dividing the molten pool state are set to include: the melting degree parameter λ fusion , high melting state critical coefficient μ HM , critical parameter μ of the intermediate melting state MM, critical coefficient of undermelting state Overmelting critical coefficient

[0084] like Figure 5 As shown, in step S22, the molten pool state is divided into five categories according to the process parameters for dividing the molten pool state set in step S21: undermelted state, low melt state, medium melt state, high melt state, and overmelted state; wherein the molten pool morphologies in the low melt state, medium melt state, and high melt state are all morphologies assumed by the analytical shape of the molten pool;

[0085] Specifically, the method for dividing the molten pool state according to the process parameters for dividing the molten pool state set in step S21 is:

[0086] (1) When When , the molten pool state is divided into under-melted state;

[0087] (2) When When , the molten pool state is divided into low melting state;

[0088] (3) When μ MM ≤λ fusion <μ HM When , the molten pool state is divided into the medium melting state;

[0089] (4) When When , the molten pool state is divided into high melting state;

[0090] (5) When When , the molten pool state is divided into the overmelted state;

[0091] Under-melting means that the laser power is insufficient, resulting in a small molten pool with no stable shape and size. Over-melting means that the laser power is too high, resulting in a large molten pool with no stable shape and size. Therefore, in the under-melting and over-melting states, the shape and size of the molten pool are unstable and irregular, unpredictable, and need to be avoided in the actual printing process.

[0092] The morphologies of the melt pools in the low-melting state, medium-melting state, and high-melting state are all based on analytical shape assumptions. They have regular morphologies and predictable dimensions. They are the three states that appear in the actual qualified printing process. The difference between the three lies in the different size ratios, namely the width-to-depth ratio and the height-to-depth ratio.

[0093] In step S23, a melt pool size prediction formula related to the melt pool shape ratio is obtained based on the energy formula and the melt pool morphology assumed by the analytical shape, including: a calculation formula for the melt pool depth d, a calculation formula for the melt pool width w, and a calculation formula for the melt pool height h;

[0094] In step S24, first determine the molten pool shape ratio corresponding to each molten pool state according to the low melting state, medium melting state and high melting state divided in step S22, and then substitute the molten pool shape ratio corresponding to each molten pool state into the molten pool calculation formula determined in step S23 to obtain the molten pool size prediction result.

[0095] Furthermore, the melting degree parameter λ fusion Calculated by the following formula:

[0096] λ fusion =ΔH / C lackfusion ,

[0097] Where ΔH is the specific enthalpy, C lackfusion is the critical specific enthalpy of fusion, which can be calculated by the following two formulas:

[0098]

[0099]

[0100] Where η is the absorption efficiency of solid materials, P is the laser power, π is the circumference, and H sl is the latent heat of melting per unit volume, a is the thermal diffusion coefficient, v is the scanning rate, D is the laser spot diameter, L t is the layer thickness, C is the material specific heat capacity, T m is the melting point of the material, T o is the initial temperature of the material;

[0101] High melting state critical coefficient μ HM Calculated by the following formula:

[0102]

[0103] Where x m is the critical coefficient of melting degree, T b is the boiling temperature of the material;

[0104] Critical parameter μ of the intermediate melting state MM Calculated by the following formula:

[0105]

[0106] Undermelt critical coefficient Calculated by the following formula:

[0107]

[0108] Where, is the critical coefficient of the material undermelting defect state, The value range is

[0109] Overmelting critical coefficient Calculated by the following formula:

[0110]

[0111] Where, is the critical coefficient of the material's overmelting defect state, The value range is

[0112] Among the above physical quantities, the absorption efficiency of solid materials η, the latent heat of melting per unit volume H sl , thermal diffusion coefficient a, material specific heat capacity C, material melting point T m , critical melting coefficient x m , Material boiling temperature T b , critical coefficient of material undermelting defect state Critical coefficient of material overmelting defect state It is a material characteristic parameter, which is determined by the type of material and can be measured by existing material characteristic parameter test methods.

[0113] Among the above physical quantities, laser power P, scanning rate v, laser spot diameter D, layer thickness L t The process parameters need to be set manually. The preferred range is: laser power P: 100-500W, scanning rate v: 0.5-2.5m / s, laser spot diameter D: 30-70μm, layer thickness L t :50~65μm.

[0114] Furthermore, in step S23, the process of determining the melt pool size prediction formula is as follows:

[0115] Considering the energy transfer involved in the molten pool forming process, including: powder melting to form a molten pool, molten pool solidification, conductive heat transfer between the molten pool surface and the substrate, and convection and radiation heat transfer between the molten pool surface and the surrounding environment; according to the law of conservation of energy, the following energy formula is obtained:

[0116]

[0117] Where t is time, V(t) is the volume of the molten pool, ρ is the material density, and E i (t) is the internal energy per unit mass of the molten pool, A(t) is the cross-sectional area of the molten pool, and E s is the specific energy of the solidifying molten pool, Q sc is the heat transfer between the molten pool and the solid substrate surface, Q gc is the convective heat exchange between the molten pool and the surrounding gas environment, Q gr It is the radiation heat exchange between the molten pool and the surrounding environment;

[0118] Based on the energy formula and the molten pool morphology assumed by the analytical shape, the calculation formula for the molten pool size is as follows:

[0119] (1) The calculation formula of the molten pool depth d is:

[0120]

[0121] (2) The calculation formula of the molten pool width w is:

[0122] w=β w / d d;

[0123] (3) The calculation formula of the molten pool height h is:

[0124] h=β h / d d;

[0125] Where, β h / d is the height-to-depth ratio of the molten pool, β w / d is the width-to-depth ratio of the molten pool, β h / d and β w / d Depends on the state of the molten pool, specifically determined in step S5; the heat transfer Q between the molten pool and the solid substrate surface is conducted sc , the convection heat exchange Q between the molten pool and the surrounding gas environment gc , the radiation heat exchange Q between the molten pool and the surrounding environment gc , the specific energy E of the solidifying molten pool s They are determined by the following four formulas:

[0126] Q sc =ξ s α s (λT m -T o ),

[0127] Q gc =ξ g α g (λT m -T o ),

[0128] Q gr =ξ g εσ(λ 4 T m 4 -T o ),

[0129] E s =ρ s vc s (T m -T o ),

[0130] Where, ξ s =25 / 3 β w / h 1 / 3 β l / w 2 / 3 (1+β h / d ) -1 , β w / h is the width-to-height ratio of the molten pool, β l / w is the length-to-width ratio of the molten pool, α s is the equivalent convection coefficient of the solid interface, ξ g =2 5 / 3 β w / d 1 / 3 (β l / w β h / d ) 2 / 3 (1+β h / d ) -2 , α g is the equivalent convection coefficient of the gas interface, ε is the radiation coefficient, σ is the Boltzmann constant, ρ s is the solid density of the material, c s is the solid-state specific heat capacity of the material.

[0131] Furthermore, in step S24, first, according to the low melting state, medium melting state and high melting state divided in step S22, the shape ratio of the molten pool is determined, specifically including:

[0132] (1) When the molten pool state is classified as a low-melting state, the molten pool shape ratio is:

[0133]

[0134]

[0135] Where, is the width-to-depth ratio corresponding to the low-melting state, is the height-to-depth ratio corresponding to the low-melting state, k is the thermal conductivity of the material, ρ p is the powder density of the material, φ=πρCv(T m -T o ), L w / d (τ,ζ)=π,L h / d (τ,ζ)=8;

[0136] (2) When the molten pool state is divided into the medium melting state, the molten pool shape ratio is:

[0137]

[0138]

[0139] Where,

[0140]

[0141]

[0142] (3) When the molten pool state is classified as a high melting state, the molten pool shape ratio is:

[0143]

[0144]

[0145] Where,

[0146]

[0147]

[0148] When the molten pool state is divided into under-melted state or over-melted state, the molten pool morphology is irregular and the size is unpredictable. This state should be avoided in the actual printing process. Therefore, it is unnecessary and impossible to determine the molten pool shape ratio in this state.

[0149] Then, the molten pool shape ratios corresponding to the various molten pool states are substituted into the molten pool calculation formula determined in step S23 to obtain the molten pool size prediction result.

[0150] In order to verify the effectiveness and accuracy of the selective laser melting molten pool size prediction method based on molten pool state division, two groups of experiments were carried out on actual materials, respectively recorded as Experimental Case 1 and Experimental Case 2, and the results are as follows.

[0151] Test Example 1:

[0152] The material selected is 316L stainless steel powder for selective laser melting additive manufacturing. The material characteristic parameters are: solid material absorption efficiency η = 62%, unit volume melting latent heat H sl =2.7×10 5 J / kg, thermal diffusion coefficient a=6.37×10 -6 m 2 / s, material specific heat capacity C = 725J / (kg·K), material melting point T m =1700K, critical melting coefficient x m =2, material boiling temperature T b =3273K, critical coefficient of material undermelting defect state Critical coefficient of material overmelting defect state Solid interface equivalent convection coefficient α s =300W·(m 2 ·K), gas interface equivalent convection coefficient αg =100W·(m 2 ·K), radiation coefficient ε=0.35, Boltzmann constant σ=5.67×10 -8 W / (m 2 ·K 4 ), material solid density ρ s =7800kg / m 3 , the solid-state specific heat capacity of the material c s =725J / (kg·K), thermal conductivity of the material k=36W / mK, powder density of the material ρ p =4680kg / m 3 ;

[0153] In the selective laser melting additive manufacturing, the selected process parameters are: laser power P = 300W, scanning rate v = 1.5m / s, laser spot diameter D = 54μm, layer thickness L t =30μm;

[0154] Substitute the material characteristic parameters and process parameter settings in the first test example into the method proposed in the present invention, first divide the molten pool state, and calculate μ MM =1.3,μ HM =5.7,λ fusion =4.3, so μ is satisfied MM ≤λ fusion <μ HM The molten pool state is divided into the medium melting state. The molten pool size ratio is calculated based on the divided state and substituted into the molten pool size calculation formula. Figure 6 The predicted results are: height h = 39 μm, width w = 90 μm, depth d = 86 μm; At the same time, according to the set process parameters, the actual selective laser melting test of 316L stainless steel powder was carried out, see Figure 6 The experimental results obtained are: height h = 35 μm, width w = 85 μm, and depth d = 92 μm; therefore, the maximum error between the predicted value of the molten pool size of Experimental Example 1 obtained by the selective laser melting molten pool size prediction method based on molten pool state division and the experimental result is 6 μm.

[0155] Test Example 2:

[0156] The material selected is 316L stainless steel powder for selective laser melting additive manufacturing. The material characteristic parameters are: solid material absorption efficiency η = 62%, unit volume melting latent heat H sl =2.7×10 5 J / kg, thermal diffusion coefficient a=6.37×10 -6 m 2 / s, material specific heat capacity C = 725J / (kg·K), material melting point T m =1700K, critical melting coefficient x m =2, material boiling temperature T b =3273K, critical coefficient of material undermelting defect state Critical coefficient of material overmelting defect state Solid interface equivalent convection coefficient α s =300W·(m 2 ·K), gas interface equivalent convection coefficient α g =100W·(m 2 ·K), radiation coefficient ε=0.35, Boltzmann constant σ=5.67×10 -8 W / (m 2 ·K 4 ), material solid density ρ s =7800kg / m 3 , the solid-state specific heat capacity of the material c s =725J / (kg·K), thermal conductivity of the material k=36W / mK, powder density of the material ρ p =4680kg / m 3 ;

[0157] In the selective laser melting additive manufacturing, the selected process parameters are: laser power P = 300W, scanning rate v = 1.8m / s, laser spot diameter D = 54μm, layer thickness L t =30μm;

[0158] Substitute the material characteristic parameters and process parameter settings in Experimental Example 2 into the method proposed by the present invention, first divide the molten pool state, and calculate μ MM =1.3,μ HM =5.7,λ fusion =3.6, so μ is satisfied MM ≤λ fusion <μ HM The molten pool state is divided into the medium melting state. The molten pool size ratio is calculated based on the divided state and substituted into the molten pool size calculation formula. Figure 7 The predicted results are: height h = 49 μm, width w = 102 μm, depth d = 67 μm; At the same time, according to the set process parameters, the actual selective laser melting test of 316L stainless steel powder was carried out, see Figure 7 The experimental results obtained are: height h = 47 μm, width w = 97 μm, and depth d = 65 μm; therefore, the maximum error between the predicted value of the molten pool size in Experimental Example 2 obtained by the selective laser melting molten pool size prediction method based on molten pool state division and the experimental result is 5 μm.

[0159] From Experimental Examples 1 and 2, it can be seen that the maximum error between the predicted value of the molten pool size obtained by the selective laser melting molten pool size prediction method based on molten pool state division and the experimental result is 5 μm, which verifies the effectiveness and accuracy of the selective laser melting molten pool size prediction method based on molten pool state division.

[0160] Specifically, in step S30, the quasi-static thermal model used to calculate the thermal field during the printing process is:

[0161]

[0162] Where T(x, y, z) is the thermal field during printing, (x, y, z) represents the coordinates of the scanning unit point relative to the current heat source position, and the current heat source position is the irradiation position of the laser; T r (x, y, z) represents the residual temperature, which is introduced to consider the impact of different scanning trajectories in the scanning layer on printing; P, η, v, λ, and a represent the laser beam power, energy absorption rate, scanning speed, thermal conductivity, and thermal diffusivity, respectively; a is calculated by a = λ / ρc, where ρ represents density and c represents specific heat; R represents the distance from the scanning unit point to the heat source;

[0163] Among them, the x direction is the scanning direction, the z direction is the vertical direction of the substrate, and the y direction is perpendicular to the xz plane according to the right-hand coordinate system;

[0164] Among them, the residual temperature T r (x,y,z) is calculated as follows:

[0165]

[0166] Where, T a represents the ambient temperature and the virtual heat source laser power, w t It represents the distance between the scanning unit point and the current heat source position in the scanning direction, and t represents the scanning track number.

[0167] Specifically, in step S40, the total strain model used to calculate the total strain of the printing process is:

[0168]

[0169]

[0170]

[0171] Where, are the total strains in the x-, y-, and z-directions, respectively; E is the elastic modulus of the material; σ xx , σ yy , σzz are the total stress in the x, y, and z directions, respectively, and v e is the Poisson's ratio of the material in elastic state, E p is the plastic modulus of the material;

[0172] Among them, σ xx , σ yy , σ zz Calculated by the following three formulas:

[0173]

[0174]

[0175]

[0176] Where α is the thermal expansion coefficient of the material;

[0177] In step S40, the thermoelastic model used to calculate the thermoelastic strain during the printing process is:

[0178]

[0179]

[0180]

[0181] Where, are the thermoelastic strains in the x, y, and z directions, respectively.

[0182] Specifically, in step S50, the inherent strain model used to calculate the inherent strain of the printing process is:

[0183]

[0184]

[0185]

[0186] Where, are the inherent strains in the x, y, and z directions, respectively.

[0187] Specifically, in step S60, the formula for obtaining the predicted surface result is:

[0188]

[0189]

[0190]

[0191]

[0192] According to step S10, the printing layers are sequentially set from 1 to I; when the printing layer is the i-th layer, the printing paths are sequentially set from 1 to J i The molten pool surface prediction results of all discrete points are obtained, and the set of molten pool surface prediction results of all discrete points is the final predicted SLM molded part surface prediction result.

[0193] Test example:

[0194] In order to verify the effectiveness and accuracy of the method proposed in this invention, the theoretical surface prediction results and the actual surface measurement results of the molded parts were compared using TC4 material. Figure 8 The theoretical surface prediction results of rectangular formed parts obtained by the method proposed in this invention are: Figure 9 The schematic diagram of the actual molded part corresponding to the theoretical surface prediction results is shown in Figure 2. Figure 8 Theoretical surface prediction results and Figure 9 The surface measurement results of the actual molded parts were compared, and the maximum deviation between the theoretical results and the actual results was 6.2μm, and the relative error was 2.4%, which proved the effectiveness and accuracy of the method proposed in the present invention.

[0195] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification, equalization change and modification made to the above embodiment by any technician familiar with the field without departing from the content of the technical solution of the present invention based on the technical essence of the present invention shall fall within the scope of the present invention.

Claims

1. A surface prediction method for selective laser melting parts based on the inherent strain method, characterized in that: The following steps are involved: S10, set the printing layer from 1 to I in sequence; when the printing layer is the i-th layer, set the printing path from 1 to J in sequence i Where, I is the total number of printed layers, J i is the total number of printing paths for the i-th printing layer; S20, print the Jth layer of the i-th layer i The printing paths are discretized, and the ideal analytical prediction result of the upper surface of each discrete point is obtained by using the analytical shape hypothesis at each discrete point; The spacing Δc between the discrete points is 10 μm. At each discrete point, the surface is a raised molten pool. The key dimensions of the molten pool include: molten pool height h, molten pool depth d, molten pool width w, and molten pool length l. The analytical shape of the melt pool is assumed to be a combination of two upper and lower semi-ovals, with the upper semi-oval opening facing downward and the lower semi-oval opening facing upward. The openings of the two semi-ovals are equal in length, and the two semi-ovals are combined at the openings. The melt pool height h is the height of the semi-oval in the upper half of the melt pool, the melt pool depth d is the height of the semi-oval in the lower half, and the melt pool width w is the length of the opening of the semi-oval in the upper half of the melt pool. The critical size of the molten pool is determined by the selective laser melting molten pool size prediction method based on the molten pool state division; S30, calculating the thermal field during the printing process using a quasi-static thermal model; S40, calculating the total strain and thermoelastic strain of the printing process respectively using the total strain model and the thermoelastic model; S50, based on the total strain and thermoelastic strain obtained in step S40, using an inherent strain model to obtain the inherent strain of the printing process; S60 , using the inherent strain obtained in step S50 to correct the surface ideal analytical expression prediction result obtained in step S20 , to obtain a surface prediction result.

2. The surface prediction method for selective laser melting parts based on the inherent strain method according to claim 1 is characterized in that: In step S10, I and J i All of them are determined when planning the printing process parameters before actual printing. The determination principles are: I=H / L t ; J i =W i / D l ; In the above two formulas, H is the total design height of the part, W i Design the width of the part at layer i, L t D is the set printing layer height. l The spacing of the printing path, H and W i Determined by the design size of the part.

3. The surface prediction method for selective laser melting parts based on the inherent strain method according to claim 2 is characterized in that: L t The value of D is 50~65μm, l The value is 40~60μm.

4. The surface prediction method for selective laser melting parts based on the inherent strain method according to claim 1 is characterized in that: In step S30, the quasi-static thermal model used to calculate the thermal field during the printing process is: Where T(x, y, z) is the thermal field during printing, (x, y, z) represents the coordinates of the scanning unit point relative to the current heat source position, and the current heat source position is the irradiation position of the laser; T r (x, y, z) represents the residual temperature; P, η, v, λ, and a represent the laser beam power, energy absorption rate, scanning speed, thermal conductivity, and thermal diffusivity, respectively; a is calculated by a = λ / ρc, where ρ represents density and c represents specific heat; R represents the distance from the scanning unit point to the heat source; Among them, the x direction is the scanning direction, the z direction is the vertical direction of the substrate, and the y direction is perpendicular to the xz plane according to the right-hand coordinate system; Among them, the residual temperature T r (x,y,z) is calculated as follows: Where, T a represents the ambient temperature and the virtual heat source laser power, w t It represents the distance between the scanning unit point and the current heat source position in the scanning direction, and t represents the scanning track number.

5. The surface prediction method for selective laser melting parts based on the inherent strain method according to claim 4 is characterized in that: In step S40, the total strain model used to calculate the total strain of the printing process is: Where, are the total strains in the x-, y-, and z-directions, respectively; E is the elastic modulus of the material; σ xx , σ yy , σ zz are the total stress in the x, y, and z directions, respectively, and v e is the Poisson's ratio of the material in elastic state, E p is the plastic modulus of the material; Among them, σ xx , σ yy , σ zz Calculated by the following three formulas: Where α is the thermal expansion coefficient of the material; In step S40, the thermoelastic model used to calculate the thermoelastic strain during the printing process is: Where, are the thermoelastic strains in the x, y, and z directions, respectively.

6. The surface prediction method for selective laser melting parts based on the inherent strain method according to claim 5 is characterized in that: In step S50, the inherent strain model used to calculate the inherent strain of the printing process is: Where, are the inherent strains in the x, y, and z directions, respectively.

7. The surface prediction method for selective laser melting parts based on the inherent strain method according to claim 6, characterized in that: In step S60, the formula for obtaining the predicted surface result is: According to step S10, the printing layers are sequentially set from 1 to I; when the printing layer is the i-th layer, the printing paths are sequentially set from 1 to J i The molten pool surface prediction results of all discrete points are obtained, and the set of molten pool surface prediction results of all discrete points is the final predicted SLM molded part surface prediction result.

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