US 2025/0276397 A1 · METHOD FOR DETERMINING MAGNETIC FIELD PARAMETER THRESHOLD OF NEGATIVE-PRESSURE ARC WELDING

Abstract

The present disclosure provides a method for determining a magnetic field parameter threshold of negative-pressure arc (NPA) welding including the following steps: forming a control equation using the Navier-Stokes equation, heat transfer equation, and Maxwell's electromagnetic equation; establishing a geometric model and meshing; setting material parameters; setting initial conditions and boundary conditions; conducting parameterized scanning, setting solver, collecting NPA data, and fitting NPA function; afterwards, performing numerical simulation calculation of NPA under different conditions, and then fitting the calculated NPA threshold data, such that the equation for determining the magnetic field parameter threshold of NPA welding can be obtained. The method may more accurately predict the threshold condition of NPA welding and provide guidance for NPA welding technology; and solving the instability of the molten pool caused by gravity and arc positive pressure during conventional positive pressure arc thin-wall surfacing, additive manufacturing, and inclined welding process.

A method for determining a magnetic field parameter threshold of negative-pressure arc welding, comprising firstly, establishing a mathematical model of a negative-pressure arc, calculating the negative-pressure threshold under different conditions, and then fitting the calculated negative-pressure threshold to obtain an equation for determining the magnetic field parameter threshold of negative-pressure arc welding;

specifically comprise the following step:
step 1, establishing a control equation, which consists of a Navier-Stokes equation, a heat transfer equation, and a Maxwell's electromagnetic equation, specifically comprising;
determining velocity and pressure distribution of arc plasma based on mass conservation equation and momentum conservation equation;
∂
ρ
∂
t
+
∇
·
(
ρυ
)
=
0
(
1
)
ρ
⁢
∂
υ
∂
t
+
ρ
⁡
(
υ
·
∇
)
⁢
υ
=
∇
·
[
-
pI
+
μ
⁡
(
∇
υ
+
(
∇
υ
)
T
)
-
2
3
⁢
μ
⁡
(
∇
·
υ
)
⁢
I
]
+
F
(
2
)
wherein ρ is density, V is velocity vector, P is pressure, μ is viscosity, I is identity matrix, and F is momentum source;
solving arc temperature T according to energy conservation equation;
ρ
⁢
C
p
(
∂
T
∂
t
+
υ
·
∇
T
)
=
∇
·
(
k
⁢
∇
T
)
+
Q
(
3
)
wherein k is coefficient of heat conduction, T is temperature, Cp is specific heat capacity, and Q is a source term of the energy conservation equation;
calculating potential and magnetic vector potential distribution according to current continuity equation and Ohm's law;
∇
·
(
σ
⁢
∇
V
+
σ
⁢
∂
A
∂
t
)
=
0
(
4
)
∇
×
(
1
μ
0
⁢
∇
×
A
)
+
σ
⁢
∇
V
=
0
(
5
)
wherein V is potential, A is magnetic vector potential, and σ is conductivity;
solving current density J and magnetic flux density B of electric field E based on V and A according to equations:
J
=
-
σ
(
∇
V
+
∂
A
∂
t
)
(
6
)
E
=
-
(
∇
V
+
∂
A
∂
t
)
(
7
)
B
=
∇
×
A
(
8
)
wherein J is current density, E is electric field and B is magnetic flux density;
solving the arc energy source term consisting of Joule heat, electron enthalpy transfer, and arc radiation loss according to:
Q
=
J
·
E
+
∂
∂
T
(
5
⁢
k
b
⁢
T
2
⁢
q
)
⁢
(
∇
T
·
J
)
-
Q
r
⁢
a
⁢
d
(
9
)
wherein KB is Boltzmann constant;
e is electron charge;
T is temperature field of arc shape;
Q is heat source term;
Qrad is arc radiation loss;
solving a momentum source term in the momentum conservation equation based on the arc self-induced magnetic flux density B, the current density J, and the momentum conservation equation according to:
F
=
J
×
B
(
10
)
step 2, establishing geometric models and meshing:
establishing geometric models of a hollow tungsten electrode arc and a solid tungsten electrode arc and then selectively meshing the models;
step 3, setting material parameters:
selectively setting material parameters for each part of the geometric models;
step 4, setting initial conditions and boundary conditions comprising boundary heat flux, cathode boundary, anode boundary, pressure, current density and potential, and loading volume force J*(B+B0);
the boundary conditions comprise:
(1) solid current density input given by:
J
=
I
π
⁢
R
w
2
(
11
)
(2) current density of hollow tungsten electrode given by:
J
=
I
R
w
2
-
R
i
2
(
12
)
(3) shielding gas flow rate given by:
v
i
⁢
n
(
r
)
=
2
⁢
Q
R
n
2
-
r
2
+
(
R
n
2
-
R
w
2
)
⁢
(
ln
(
r
R
n
)
/
ln
(
R
n
R
w
)
)
)
π
⁢
R
n
4
-
R
w
4
+
(
(
R
n
2
-
R
w
2
)
2
/
ln
⁡
(
R
n
R
w
)
)
(
13
)
I is the welding current, Q is the shielding gas flow, Rn is the shielding gas inlet radius, Rw is the tungsten electrode radius, Ri is the inner diameter of hollow cavity, and r is the distance from shielding gas inlet to center;
(4) the cathode boundary given by:
-
n
·
(
-
k
⁢
∇
T
)
=
❘
"\[LeftBracketingBar]"
J
i
❘
"\[RightBracketingBar]"
⁢
V
i
-
❘
"\[LeftBracketingBar]"
J
e
❘
"\[RightBracketingBar]"
⁢
ϕ
e
-
α
⁢
ε
⁢
T
4
(
14
)
J
e
=
J
r
[
(
❘
"\[LeftBracketingBar]"
J
·
n
❘
"\[RightBracketingBar]"
-
J
r
)
>
0
]
+
❘
"\[LeftBracketingBar]"
J
·
n
❘
"\[RightBracketingBar]"
[
(
❘
"\[LeftBracketingBar]"
J
·
n
❘
"\[RightBracketingBar]"
-
J
r
)
<
0
]
(
15
)
J
i
=
❘
"\[LeftBracketingBar]"
J
·
n
❘
"\[RightBracketingBar]"
-
J
e
(
16
)
J
r
=
A
r
⁢
T
2
⁢
exp
⁢
(
-
ϕ
e
k
b
⁢
T
)
(
17
)
(5) the anode boundary given by:
-
n
·
(
-
k
⁢
∇
T
)
=
❘
"\[LeftBracketingBar]"
J
·
n
❘
"\[RightBracketingBar]"
⁢
ϕ
a
-
α
⁢
ε
⁢
T
4
(
18
)
wherein |Ji|Vi is cathode ion heat, |Je|φc is electron heat that plays a cooling role;
and φa, φc is surface work function;
Vi is ionization potential of argon;
Ar is Richardson constant, φe is effective work function of cathode, e is elementary charge and kb is Boltzmann constant;
and wherein
(6) an external electromagnetic force is added by changing the momentum source term:
F
=
J
×
(
B
+
B
0
)
(
19
)
wherein B0 is magnetic flux density of an external longitudinal magnetic field;
step 5, performing parameterized scanning, and setting a solver:
performing calculation and solving according to the above steps and verifying whether the calculated results are consistent with experimental results under same conditions;
when the calculated results are consistent with the experimental results, proceeding to the next step;
otherwise, returning to step 2, adjusting the model or the boundary conditions, and repeating a cycle process of modeling and numerical simulation calculation until the calculated results are consistent with the experimental results under the same conditions so that a model accuracy verification is achieved;
step 6:
fixing the model, parameterizing a batch calculation to obtain the parameter threshold of negative-pressure welding under other conditions, processing the parameter threshold of negative-pressure welding, and determining a threshold function of negative-pressure welding:
fitting multiple groups of threshold data of negative-pressure welding under different conditions to obtain a functional equation of a threshold of longitudinal magnetic field parameters of negative-pressure arc welding, to predict an occurrence of negative-pressure.

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Method for determining magnetic field parameter threshold of negative-pressure arc welding

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Method for determining magnetic field parameter threshold of negative-pressure arc welding

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Abstract

Claims6