A method for calculating the cross-sectional morphology of a cladding layer by laser cladding

Abstract

The present invention discloses a method for calculating the cross-sectional morphology of a clad layer by laser cladding. Laser cladding is carried out; the processing area of the laser cladding is discretized, and each discrete unit is used as a cell; a powder beam model expressing the powder beam concentration distribution on different-shaped substrates is constructed; a laser heat source model is constructed based on the physical processes existing during laser cladding; the state of each cell is obtained according to the powder beam model and the laser heat source model, and the cell state includes the phase state and temperature; based on the cellular automaton, the cell state at the next moment is calculated according to the temperature transfer rule of the clad layer and the instantaneous cell state, realizing the update of the cell state; the droplet forming method is adopted to calculate the cell distribution of the clad layer, and the cross-sectional morphology of the clad layer is obtained. By combining the cellular automaton method and the droplet forming theory, a more perfect calculation model for the cross-sectional profile of the clad layer is established, realizing the accurate calculation of the cross-sectional morphology of the clad layer.

Description

Technical Field

[0001] The present invention relates to laser cladding, and particularly to a method for calculating the cross-sectional morphology of a cladding layer in laser cladding. Background Art

[0002] With the development of laser cladding products towards large size and high precision, the manufacturing accuracy of coaxial powder-fed laser cladding needs to be improved urgently. At present, the research on the morphology of the cladding layer in coaxial powder-fed laser cladding is still lacking, and most of the morphology calculations are about powder-laying laser cladding. However, due to the complexity of the temperature field and the molten pool flow field, the cladding layer contour is usually approximated as a spherical crown shape or simplified into a square, resulting in inaccurate calculation of the cladding layer morphology. The related research on the geometric accuracy of laser cladding technology mainly focuses on the calculation and simulation of the width and height of the cladding layer, and the research on the contact angle and cross-sectional area of the cladding layer is relatively less.

[0003] At present, most of the research on the morphology of laser cladding is carried out on the premise of a flat substrate, and the conclusions obtained are difficult to be directly applied to laser cladding on other-shaped substrates. In the actual laser cladding process, the situation where the substrate surface is not completely flat is very common, and the contour of the cladding layer on different-shaped substrates affects the control of the manufacturing accuracy of laser cladding technology. Summary of the Invention

[0004] Objective of the Invention: Aiming at the above disadvantages, the present invention provides a calculation method for accurately calculating the cross-sectional morphology of the cladding layer in laser cladding.

[0005] Technical Solution: To solve the above problems, the present invention adopts a method for calculating the cross-sectional morphology of a cladding layer in laser cladding, including the following steps:

[0006] (1) The laser beam and the powder beam are sprayed onto the substrate surface through a powder feeding nozzle to form a cladding layer, and laser cladding is carried out; the processing area of the laser cladding is discretized, and each discrete unit is used as a cell.

[0007] (2) A powder beam flow model is constructed, and the powder beam flow model expresses the powder beam flow concentration distribution on different-shaped substrates.

[0008] (3) A laser heat source model is constructed based on the physical processes existing during laser cladding.

[0009] (4) The state of each cell is obtained according to the powder beam flow model and the laser heat source model, and the cell state includes the phase state and the temperature.

[0010] (5) Based on the cellular automaton, the cell state at the next moment is calculated according to the temperature transfer rule of the cladding layer and the instantaneous cell state, and the cell state update is realized.

[0011] (6) Adopt the droplet forming method, calculate the distribution of the cells in the cladding layer according to the spreading process of the liquid cells, and obtain the cross-sectional morphology of the cladding layer.

[0012] Further, in the step (2), the powder beam model adopts a modified Gaussian model, and the expression of the powder beam concentration Pcon distribution of the modified Gaussian model is:

[0013]

[0014] where pcon = F / V is the powder amount ejected per unit length of the powder beam (F is the powder feeding rate, V is the scanning speed), z is the center line of the powder beam, h is the distance from the laser head to the center point of the laser spot on the substrate, θ is half of the divergence angle of the powder beam, x is the axis on the inclined substrate surface, is the inclination angle of the substrate.

[0015] Further, in the step (3), the physical processes existing during laser cladding include the shielding effect of the powder material on the laser energy; the heat input of the laser loaded on the powder and the substrate surface; the heat convection and heat radiation between the cladding layer and the air, and the internal heat conduction between the cladding layer and the substrate.

[0016] Further, in the case where the powder material shields the laser energy, the laser is used as a heat source to input heat to the powder, and the power density q(t) of the laser heat source moving with time s is expressed as:

[0017]

[0018] where P is the laser power, β is the attenuation rate of the powder to the laser energy, x and y respectively represent the position of the current cell in the cell space, r is the laser spot radius, V x is the moving speed of the laser along the X-axis direction, V y is the moving speed of the laser along the Y-axis direction, t is the running time of the laser, and a is the cell size.

[0019] Further, for the heat convection between the cladding layer and the air, the power density of the convective heat transfer is expressed by Newton's cooling law as follows:

[0020] q(i,j,k) conv = h(T (i,j,k) - T f )

[0021] where q(i,j,k) conv is the convective heat transfer power density, h is the convective heat transfer coefficient; T (i,j,k) is the convective heat transfer cell temperature at the position (i,j,k); T f is the ambient temperature;

[0022] Thermal radiation occurs between the cladding layer and the air, and the power density of the thermal radiation energy can be expressed by the Stefan-Boltzmann law;

[0023] q(i,j,k) rad =σ b ε(T (i,j,k) 4 -T f 4 )

[0024] where q(i,j,k) rad is the thermal radiation rate; σ b is the Stefan-Boltzmann coefficient; ε is the emissivity;

[0025] Internal heat conduction occurs between the cladding layer and the substrate, and the power density of the heat conduction can be expressed by Fourier's law of heat conduction as follows:

[0026]

[0027] where q(i,j,k) cond is the heat conduction rate, K is the thermal conductivity; is the temperature gradient in the direction ; A is the contact area of heat transfer.

[0028] Furthermore, the cell phase states include liquid cells, solid cells, gas cells, and boundary cells.

[0029] Furthermore, in the step (5), the temperature transfer rules of the cladding layer include the heat input of the laser loading on the powder and the substrate surface; the heat conduction between the solid cells; the heat convection and heat conduction between the liquid cells; and the heat convection and heat convection between the boundary cells on the substrate and cladding layer surfaces and the gas cells.

[0030] Furthermore, in the step (6), the droplet forming method describes the total energy E of the solid-liquid, solid-gas, and liquid-gas interfacial free energies and the gravitational potential energy of the molten droplets, and the expression is:

[0031]

[0032] where cosδ=(γ SV -γ SL ) / γ LV , δ is the contact angle, γ SV represents the solid-gas surface free energy, γ SL represents the solid-liquid surface free energy, γ LV represents the liquid-gas surface free energy; A LV represents the boundary area of each cell at the liquid-gas interface, A SVrepresents the boundary area of each cell at the solid-liquid interface, ρ is the density of the liquid, g is the gravitational acceleration constant, and v k is the volume of the liquid cell, and z k is the height of the centroid of the liquid cell. When E is minimized, the final distribution of the cells in the clad layer is obtained. Based on the distribution of the cells in the clad layer, the cross-sectional morphology of the clad layer is obtained.

[0033] Advantageous effects: Compared with the prior art, the significant advantage of the present invention is that by combining the cellular automaton method and the droplet forming theory, a more perfect calculation model for the cross-sectional profile of the clad layer is established, and the accurate calculation of the cross-sectional morphology of the clad layer is realized. The established profile calculation model of the clad layer on different-shaped substrates is applicable to the calculation of the morphology of the clad layer of different materials on different-shaped substrates. Description of the Drawings

[0034] Figure 1 is a schematic flow chart of the cross-sectional morphology calculation method of the present invention;

[0035] Figure 2 is a schematic diagram of the powder beam concentration distribution in the present invention;

[0036] Figure 3 is a schematic diagram of the cell type and the droplet forming method (DFM) in the present invention;

[0037] Figure 4 is a schematic diagram of the cellular automaton model in the present invention;

[0038] Figure 5 is a comparison chart of the calculation results and the experimental results in the present invention. Detailed Embodiments

[0039] As Figure 1 shown, in this embodiment, a method for calculating the cross-sectional morphology of a clad layer by laser cladding includes the following steps:

[0040] (1) The laser beam and the powder beam are sprayed onto the surface of the substrate through a powder feeding nozzle to form a clad layer, and laser cladding is carried out; the processing area of the laser cladding is discretized, and each discrete unit is used as a cell;

[0041] (2) A powder beam model is constructed, and the powder beam model expresses the powder beam concentration distribution on different-shaped substrates; the powder beam model uses a modified Gaussian model to express the powder beam concentration distribution on different-shaped substrates, and the powder rebound effect of the substrate is increased based on the powder utilization rate of different substrates;

[0042] The expression of the modified Gaussian model for the powder beam concentration distribution is:

[0043]

[0044] Wherein, is the powder amount ejected from a powder beam per unit length (F is the powder feeding rate, which is 1.5 r / min in this embodiment, V is the scanning speed, and 300 mm / min is adopted); z is the center line; h is the distance from the laser head to the center point of the light spot on the substrate, and 10 mm is adopted; θ is half of the powder beam divergence angle, and 3° is adopted; x is the axis on the inclined substrate surface; is the inclination angle of the substrate, which is set to 20 degrees in this embodiment.

[0045] (3) Construct a laser heat source model based on the physical processes existing during laser cladding; the physical processes include: the shielding effect of the alloy powder material on the laser energy; the heat input of the laser loaded on the alloy powder and the substrate surface; the internal heat conduction between the cladding layer and the substrate and the heat convection and heat radiation between them and the air. Then the heat sources acting on the powder include the laser energy received after powder shielding, the heat conduction provided by the substrate that also absorbs the laser energy, the heat convection and heat radiation between the cladding layer and the air.

[0046] In the case where the powder material shields the laser energy, the laser is used as a heat source to input heat to the powder. By setting the center position of the laser heat source to (V x ·t, V y ·t), the light spot position of the laser beam changes continuously with time. In the cell space, the power density of the laser heat source with a Gaussian distribution of energy on the inclined substrate moving with time is expressed as:

[0047]

[0048] In the formula, P is the laser power, which is set to 2000 W, β is the attenuation rate of the powder to the laser energy, x

[0049] and y respectively represent the position of the current cell in the cell space, r is the laser spot radius, V x is the moving speed of the laser along the X-axis direction, V y is the moving speed of the laser along the Y-axis direction, t is the running time of the laser, and a is the cell size.

[0050] The power density of convective heat transfer is expressed by Newton's cooling law as follows:

[0051] q(i,j,k) conv = h(T (i,j,k) - T f )

[0052] Among them, q(i,j,k) conv is the convective heat transfer power density; h is the convective heat transfer coefficient; T (i,j,k) is the convective heat transfer cell temperature at the position (i,j,k); T f is the ambient temperature; a is the cell size.

[0053] The power density of the thermal radiation energy can be expressed by the Stefan-Boltzmann law:

[0054] q(i,j,k) rad =σ b ε(T (i,j,k) 4 -T f 4 )

[0055] where q(i,j,k) rad is the thermal radiation rate; σ b is the Stefan-Boltzmann coefficient, set to 5.67×10-8 W / (m2·K4); ε is the emissivity (blackness), depending on the material and temperature, and this value ranges from 0 to 1; a is the cell size; T (i,j,k) is the convective heat transfer cell temperature at the (i,j,k) position; T f is the ambient temperature.

[0056] The power density of heat conduction can be expressed by Fourier's law of heat conduction as follows:

[0057]

[0058] where K is the thermal conductivity; is the temperature gradient in the direction ; A is the contact area of heat transfer.

[0059] (4) Set the material phase transition rule for the laser cladding process: when the temperature of the metal material exceeds its melting point, melting will occur; conversely, when the temperature of the metal material drops to the corresponding temperature range, solidification will occur. According to the powder beam model and the laser heat source model, the state of each cell is obtained, and each cell is set with two states: the phase state S and the temperature state T. The S state represents that the current cell is a liquid cell, a solid cell, a boundary cell, or a gas cell, and the T state represents the temperature of the current cell.

[0060] (5) Based on the cellular automaton, calculate the cell state at the next moment according to the temperature transfer rule of the cladding layer and the instantaneous cell state to realize the update of the cell state; the temperature transfer rule of the cladding layer: the heat input of the laser loading on the alloy powder and the substrate surface; the heat conduction inside the solid material; the heat convection and heat conduction of the molten liquid in the molten pool; the convective heat transfer and radiative heat transfer between the substrate and the cladding layer surface and the air.

[0061] (6) According to the change of the interfacial free energy and gravitational potential energy of the molten pool, adopt the droplet forming method, and calculate the cell distribution of the cladding layer according to the spreading process of the liquid cells to obtain the cross-sectional morphology of the cladding layer.

[0062] The droplet forming method describes the solid-liquid (γ SL ), solid-gas (γ SV ), liquid-gas (γ LV ) interfacial free energies and the gravitational potential energy. Using Young's equation: cosδ = (γ SV - γ SL ) / γ LV , the droplet forming method can be expressed as:

[0063]

[0064] where A LV , A SV respectively represent the boundary areas of each cell at the liquid-gas and solid-liquid interfaces, ρ is the density of the liquid, g is the gravitational acceleration constant, v k , z k are respectively the volume and the centroid height of the liquid cell. When E is the smallest, the cell distribution of the cladding layer is the final morphology of the cladding layer.

[0065] As shown in (a) of Figure 5 , the laser power is set to 2000W, and the cladding layer material used is a nickel-based alloy. The material density is set to 7528 kg / m3, the melting point is set to 1163K, the thermal conductivity is set to 24 W / (m*K), and the specific heat capacity is set to 640 J / (kg*K). The relative error (%) between the calculation results and the experimental results is shown in Table 1:

[0066] Table 1

[0067]

[0068] where W is the cladding layer width error, H is the cladding layer height error, P-S is the cladding layer peak offset error, and R-A is the cladding layer relative cross-sectional area error.

[0069] As shown in (b) of Figure 5 , the laser power is set to 2000W, F is the powder feeding rate of 2.0 r / min, V is the scanning speed of 300 mm / min, is the tilt angle of the substrate of 30°, and the cladding layer material used is a nickel-based alloy. The material density is set to 7528 kg / m3, the melting point is set to 1163K, the thermal conductivity is set to 24 W / (m*K), and the specific heat capacity is set to 640 J / (kg*K). The relative error (%) between the calculation results and the experimental results is shown in Table 2:

[0070] Table 2

[0071]

[0072] As shown in Figure 5As shown in (c), the laser power is set to 2000 W, F is the powder feeding rate of 1.5 r / min, V is the scanning speed of 300 mm / min, is the tilt angle of the substrate of 30°, and the clad layer material used is cobalt-based alloy. The material density is set to 8450 kg / m3, the melting point is set to 1523 K, the thermal conductivity is set to 27 W / (m*K), and the specific heat capacity is set to 618 J / (kg*K). The relative error (%) between the calculation results and the experimental results is shown in Table 3:

[0073] Table 3

[0074]

[0075] It can be seen that the relative errors between the calculation results and the experimental results are all less than 10%, and the calculation error of this morphology calculation method is small and the accuracy is high.

Claims

1. A method for calculating the cross-sectional morphology of a laser cladding layer, characterized in that: It includes the following steps: (1) The laser beam and powder beam are sprayed onto the substrate surface through a powder feeding nozzle to form a cladding layer, and laser cladding is carried out; the processing area of the laser cladding is discretized, and each discrete unit is used as a cell. (2) Construct a powder beam model, and the powder beam model expresses the powder beam concentration distribution on different-shaped substrates; the powder beam model adopts a modified Gaussian model, and the expression of the modified Gaussian model for the powder beam concentration Pcon distribution is: where pcon = F / V is the powder amount ejected from the powder beam per unit length; F is the powder feeding rate, V is the scanning speed, z is the center line of the powder beam, h is the distance from the laser head to the center point of the laser spot on the substrate, θ is half of the powder beam divergence angle, and x is the axis on the inclined substrate surface, is the tilt angle of the substrate; (3) Construct a laser heat source model based on the physical processes existing during laser cladding; the physical processes existing during laser cladding include the shielding effect of the powder material on the laser energy; the heat input of the laser loaded on the powder and substrate surface; the heat convection and heat radiation between the cladding layer and the air, and the internal heat conduction between the cladding layer and the substrate. When the powder material blocks the laser energy, the laser is used as a heat source to input heat to the powder, and the power density q(t) of the laser heat source moving with time s The expression is as follows: Among them, P is the laser power, β is the attenuation rate of the powder to the laser energy, i and j respectively represent the positions of the current cell in the cellular space, r is the laser spot radius, V x is the moving speed of the laser along the X-axis direction, V y is the moving speed of the laser along the Y-axis direction, t is the running time of the laser, and a is the cell size; (4) Obtain the state of each cell according to the powder beam model and the laser heat source model, and the cell state includes the phase state and temperature. (5) Based on the cellular automaton, calculate the cell state at the next moment according to the temperature transfer rule of the cladding layer and the instantaneous cell state, and realize the update of the cell state. (6) Adopt a droplet forming method, and calculate the cell distribution of the cladding layer according to the spreading process of the liquid cells to obtain the cross-sectional morphology of the cladding layer.

2. The calculation method of the clad layer cross-sectional morphology according to claim 1, wherein Heat convection occurs between the cladding layer and the air, and the power density of convective heat transfer is expressed by Newton's cooling law as follows: q(i,j,k) conv = h(T (i,j,k) - T f ) where q(i,j,k) conv is the convective heat transfer power density, h is the convective heat transfer coefficient; T (i,j,k) is the temperature of the convective heat transfer cell at the position (i,j,k); T f is the ambient temperature; Heat radiation occurs between the cladding layer and the air, and the power density of the heat radiation energy can be expressed by the Stefan-Boltzmann law. q(i,j,k) rad = σ b ε(T (i,j,k) 4 - T f 4 ) where q(i, j, k) rad is the thermal emissivity; σ b is the Stefan-Boltzmann coefficient; ε is the emissivity; Internal heat conduction occurs between the cladding layer and the substrate, and the power density of heat conduction can be expressed by Fourier's heat transfer law as follows: where q(i,j,k) cond is the thermal conductivity, and K is the heat transfer coefficient; is the temperature gradient in the direction ; A is the contact area for heat transfer.

3. The method for calculating the cross-sectional morphology of the cladding layer according to claim 1, wherein, The cell phase states include liquid cells, solid cells, gaseous cells, and boundary cells.

4. The method for calculating the cross-sectional morphology of the cladding layer according to claim 3, characterized in that In the step (5), the temperature transfer rule of the cladding layer includes the heat input of the laser loaded on the powder and substrate surface; the heat conduction between the solid cells; the heat convection and heat conduction between the liquid cells; the heat convection and heat convection between the boundary cells on the substrate and cladding layer surfaces and the gaseous cells.

5. The method for calculating the cross-sectional morphology of the cladding layer according to claim 1, wherein In the step (6), the droplet forming method describes the total energy E of the solid-liquid, solid-gas, and liquid-gas interfacial free energies and gravitational potential energies of the molten droplets, and the expression is: where, cosδ = (γ SV - γ SL ) / γ LV , δ is the contact angle, γ SV represents the solid-gas surface free energy, γ SL represents the solid-liquid surface free energy, γ LV represents the liquid-gas surface free energy; A LV represents the boundary area of each cell of the liquid-gas interface, A SV represents the boundary area of each cell of the solid-liquid interface, ρ is the density of the liquid, g is the gravitational acceleration constant, v k is the volume of the liquid cell, z k is the height of the centroid of the liquid cell.

6. The method for calculating the cross-sectional morphology of the cladding layer according to claim 5, wherein When E is the smallest, the final distribution of the cladding layer cells is obtained, and according to the cladding layer cell distribution, the cross-sectional morphology of the cladding layer is obtained.

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