- Email: [email protected]
Numerical and experimental investigation of keyholing process in ultrasonic vibration assisted plasma arc welding
Journal of Manufacturing Processes 50 (2020) 603–613
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Numerical and experimental investigation of keyholing process in ultrasonic vibration assisted plasma arc welding
T
Junnan Qiao, ChuanSong Wu*, Yongfeng Li MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, Institute of Materials Joining, Shandong University, Jinan, 250061, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Ultrasonic vibration Plasma arc welding Keyholing capability Plasma arc pressure Weld pool
To improve the keyholing capability and welding efficiency, ultrasonic vibration assisted plasma arc welding (UPAW) is developed by connecting the specially manufactured ultrasonic horn with the tungsten electrode. The ultrasound pressure in the plasma arc is considered to derive a formula for calculating the plasma arc pressure on anode in U-PAW. A transient model of U-PAW process is developed with accounting for the dynamic variation of both heat flux and arc pressure distribution on the curved keyhole wall. The weld pool and keyhole behaviors are numerically simulated to predict the fluid flow and heat transfer as well as the dynamic keyhole evolution in UPAW. It is found that the exerted ultrasonic vibration increases the plasma arc pressure so that open keyhole can be established at lower welding current and higher welding speed in U-PAW. The experimental observation validates the numerical simulation results.
1. Introduction
industrial applications [7], especially into gas tungsten arc and gas metal arc welding processes to increase the weld penetration [8] and improve the droplet transfer [9], Wu’s group developed the ultrasonicassisted PAW [10], and found that open keyhole can be established with lower welding current or higher welding speed, which means the increasing of keyholing capability and welding efficiency. It is found that when ultrasonic vibration is exerted into gas tungsten arc or gas metal arc or plasma arc, the arc is constricted and the arc pressure is increased [8–10]. However, the underlying interaction mechanism between the ultrasonic vibration and the arc has not been fully elucidated. The previous studies just correlate the arc pressure with the square of the welding current [11,12]. Though Li et al. proposed an analytic formula for calculating the plasma arc pressure and took the main process parameters (welding current, arc voltage, plasma gas flow rate and density, nozzle radius) into consideration [13], but it did not include the effect of ultrasonic vibration on the plasma arc pressure. In this study, the influence of ultrasound on the plasma arc pressure is firstly analyzed, and a new arc pressure model for the U-PAW process is developed. Then the weld pool behavior and keyhole dynamics in UPAW process are numerically simulated. The experiments of the ultrasonic-assisted PAW are conducted to validate the developed model.
Plasma arc welding (PAW) can produce full penetration welds with only one pass for the mid-thickness workpieces because a keyhole channel (open keyhole) is formed inside the weld pool and both the arc heat and pressure can act along the plate thickness. The stability of the weld pool and keyhole is critical to obtain good weld quality. But in conventional PAW process, the dynamic stability of keyhole and weld pool is poor, and the welding process-parameter window for sustaining an open keyhole is narrow, which restricts the applications of plasma arc welding process in manufacturing industry [1–3]. To improve the keyholing capability and the dynamic stability of an open keyhole, some researchers have tried to modify the conventional PAW process. The torch was redesigned to add radial gas so that the plasma arc near the nozzle exit is further constricted and the heat intensity of plasma arc is increased [4]. Low power laser was used to interact with the plasma arc to increase the keyholing/penetration capability [5]. The controlled pulse waveform of welding current was employed to ensure establishment and sustainment of open keyhole status [6]. However, all the above-mentioned modifications require special design of the plasma torch or addition of laser beam or employment of special current waveform, which increases not only the investment and equipment cost but also the complexity and difficulty of the process-parameter matching and optimization. Since ultrasonic vibration has been successfully integrated into
⁎
2. Plasma arc pressure in U-PAW As is shown in the Fig. 1, the ultrasonic-assisted PAW (U-PAW),
Corresponding author. E-mail address: [email protected] (C. Wu).
https://doi.org/10.1016/j.jmapro.2020.01.019 Received 30 October 2019; Received in revised form 10 January 2020; Accepted 11 January 2020 1526-6125/ © 2020 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 1. Schematic diagram of U-PAW process.
According to kinetic energy theorem, electric field force and acoustic energy drive plasma to move. The accelerating process in the plasma arc can be described by following equation,
tungsten electrode is connected with ultrasonic horn so that ultrasonic vibration is applied to the plasma arc directly [10]. The ultrasonic wave interacts with the plasma arc so that both the arc heat and pressure are varied, and part of ultrasonic energy is also delivered into the weld pool through the plasma arc. Therefore, ultrasound certainly affects the fluid flow and heat transfer in the weld pool, and the keyhole dynamics is changed correspondingly. During the U-PAW process the interaction of ultrasonic vibration with the plasma arc will vary the distribution and magnitude of the arc pressure. First, the influence of ultrasound on the plasma arc pressure is taken into consideration, and a modified formula is derived to calculate the plasma arc pressure in U-PAW. In PAW, the average arc pressure on anode is related to the velocity of plasma jet striking on the workpiece surface [13],
Pave =
ρAr Qplas Snoz
E + Qe U =
m = ρAr Qplas Δt v1 =
1 2 mvm 2
(4)
Qplas Snoz
Qe = IΔt v2
(3)
where Qe is the number of charges carried by the plasma, U is the arc voltage, v2 is the velocity of plasma near the workpiece surface, v1 is the velocity of plasma gas at the nozzle exit.
(5) (6)
where I is the electric current, and Δt is the time interval. In fact, most of the electric energy of the plasma arc is converted into the arc heat, and only a small part is used to accelerate the plasma [15]. Therefore, ηv is introduced to characterize the conversion efficiency of electric energy to plasma kinetic energy. ηv is relatively small, generally on the order of 10−3-10-2. Based on Eqs. (3)–(6), we obtain
(1)
where Pave is the average value of arc pressure on anode, ρAr is the argon density, Qplas is the plasma gas flow rate, Snoz is the area of nozzle exit, and v2 is the velocity of plasma near the workpiece surface. In U-PAW, when ultrasonic vibration interacts with the plasma arc, it is easy to produce additional high-frequency vibration, which increases the velocity of charged particles in the plasma arc along the vibration direction. Therefore, the effect of the acoustic energy on the plasma jet velocity must be considered. The total vibration energy E is the sum of the potential energy and the kinetic energy, and E is simply equal to the maximum potential or kenetic energy during a cycle [14],
E=
1 1 mv22 − mv12 2 2
1 2 1 mvm + ηv IΔtU = ρAr Qplas Δt (v22 − v12) 2 2
(7)
Since the phase angle of the sound pressure and the vibration speed are the same, the vibration speed vm in Eq. (7) is determined by the sound pressure amplitude [16].
(2)
vm =
where m is the mass of the plasma gas ejected from the nozzle within the time interval Δt , and vm is the maximum value of vibration velocity.
pm ρAr cAr
(8)
where pm is the sound pressure amplitude at the tungsten tip, which is 604
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
plasma arc pressure: (1) the process parameters like welding current I, arc voltage U, plasma gas flow rate Qplas and argon density ρAr ; (2) torch geometry like the nozzle exit area Snoz , and the radius rP of action area of plasma arc pressure; (3) acoustic parameters like ultrasonic pressure Pm and sound velocity in argon cAr . Our previous study has shown that in U-PAW the enhancement of plasma arc pressure by ultrasonic vibration becomes weaker as the welding current increases [10]. To describe this issue, we introduce another correction coefficient ηi by comparison of the measured and calculated peak values of plasma arc pressure,
calculated by a method introduced in our previous work [17], ρAr is the argon density, cAr is the sound velocity in argon. And substitute Eq. (8) into (7), we can obtain
pm2
v2 =
+
2 2 ρAr cAr
Qplas ⎞2 2ηv IU +⎛ ρAr Qplas ⎝ Snoz ⎠ ⎜
⎟
(9)
Combining Eqs. (1) and (9), we may write
Pave =
ρAr Qplas
pm2
Snoz
2 2 ρAr cAr
+
Qplas ⎞2 2ηv IU +⎛ ρAr Qplas ⎝ Snoz ⎠ ⎜
⎟
(10)
ηi = 1 + e−0.02I
Therefore, the plasma arc force at anode can be described by following formula: 2 Fplas = Snoz Pave = πrnoz ρAr
2 Qplas pm2 2 2 2 ρAr cAr Snoz
+
2ηv IUQplas 2 ρAr Snoz
Qplas ⎞ +⎛ ⎝ Snoz ⎠ ⎜
(19)
Finally, we get,
4
P (x , y, z ) =
⎟
(11)
where rnoz is the nozzle exit radius. During plasma arc welding, the plasma arc pressure distribution is assumed to follow Gaussian function [18],
2 ηi 3rnoz ρAr QPlas AI S noz
−3
2ηv IU 2Pe2 Q 2 μ0 I 2 + + Plas exp ⎜⎛ 2 2 2 ρAr QPlas ρAr c Snoz 4π 2rp2 ⎝
x 2 + y2 ⎞ ⎟ rp2 ⎠
(20)
where Pe is the effective sound pressure which is determined by,
⎛ 3r 2 ⎞ exp ⎜− 2 ⎟ ⎝ rp ⎠
Parc = Pmax
Pe =
(12)
where Pmax is the maximum plasma arc pressure at the center of the plasma arc, r is the radial distance away from the arc axis, and rP is the radius of action area of plasma arc pressure. Therefore,
∫0
Fplas =
Pmax =
∞
Parc⋅2πr dr =
∫0
∞
Pmax πrp2 3r 2 Pmax exp ⎜⎛− 2 ⎟⎞⋅2πr dr = 3 ⎝ rp ⎠
(13)
(14)
Substituting Eqs. (11) and (14) into (12), a specific expression of plasma arc pressure is obtained:
P (x , y ) = 3
2 rnoz ρ rp2 Ar
−
2 Qplas pm2 2 2 2 ρAr cAr Snoz
+
2ηv IUQplas 2 ρAr Snoz
4
Qplas ⎞ ⎛ +⎛ exp ⎜ ⎝ Snoz ⎠ ⎝ ⎜
⎟
3(x 2 + y 2 ) ⎞ ⎟ rp2 ⎠
3. Modeling of keyhole and weld pool behavior in U-PAW (15)
The U-PAW process involves complicated physical phenomena. To study the dynamic behaviors and keyhole and weld pool, some simplifications and assumptions have to be made: (1) the fluid flow in weld pool is incompressible and laminar; (2) the influence of the gas shear force on the molten pool flow and the keyholing process is not considered, because of its little influence on the keyholing process [20]; (3) the sound pressure delivered into molten pool is temporarily neglected as it is much lower than arc pressure; (4) the effect of ultrasonic vibration on plasma arc shape is temporarily not considered. Fig. 3 shows the selected calculation domain. In fact, it is less than the size of real test workpiece but with the same thickness (stainless steel plates of thickness 4 mm) in order to save the calculation cost. As shown in Fig. 3, due to the symmetry of the workpiece, half of the calculation domain is used in the calculation. The calculation domain includes three layers: air, workpiece, and air. The coordinate origin
Eq. (16) is derived by using the continuous plasma impact theory, and only the electric field force and the acoustic driving force are considered to accelerate the plasma. In order to comprehensively consider the effect of electromagnetic field, Eq. (15) needs to be modified to reflect the effect of magnetic field on plasma. Arc plasma is essentially an electric conductor. Under the action of its own magnetic field, the plasma is subjected to the following magnetic field force [19],
FM =
μ0 I 2 4π 2
(16)
Since the dimension of magnetic force is Newton, a dimensionless magnetic force coefficient βM is introduced to correct the plasma arc pressure,
βM =
μ0 I 2 1 ⋅ 4π 2 AI
(17)
Table 1 Welding process parameters.
where AI is a constant, and μ0 is the permeability in vacuum. Put this correction factor into Eq. (15), we have
P (x , y ) =
1 2 ⋅3rnoz ρAr AI −3
x 2 + y2 ⎞ ⎟ rp2 ⎠
(21)
The plasma arc pressure in both PAW and U-PAW were measured under the welding process parameters in Tables 1 and 2. The detailed measurement method and description may be referred to [10]. With the torch design and acoustic parameters listed in Table 2, Pm = 732 Pa. If Pm = 0 , ηi = 1, Eqs. (20) and (21) can be used to calculate the plasma arc pressure in PAW. Eqs. (20) and (21) were employed to calculate the plasma arc pressure at the workpiece surface under the welding process parameters in Tables 1 and 2. Fig. 2 shows the comparison of predicted plasma arc pressure in PAW and U-PAW with the experimentally measured ones. It is clear that both are in good agreement, especially for U-PAW. Thus, Eq. (20) is verified and can be used to predict the plasma arc pressure in U-PAW.
3Fplas πrp2
Pm 2
2 2η IUQPlas QPlas Pm2 Q 4 μ0 I 2 ⎛ + v 2 + Plas exp ⎜ 2 2 2 4 ρAr cAr Snoz ρAr Snoz Snoz 4π 2rp2 ⎝
(18)
Eq. (18) contains following groups of parameters influencing the 605
Case
Welding current (A)
Arc voltage (V)
Welding speed (mm/min)
Welding process
A1 B1 A2 B2 A3 B3
80 80 100 90 95 95
19.5 19.8 20.6 20.2 20.5 20.7
100 100 110 110 100 115
PAW U-PAW PAW U-PAW PAW U-PAW
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
∂ρ v)=0 + ∇⋅(ρ→ ∂t
Table 2 Other parameters used in calculation of plasma arc pressure. Parameters
Value
Plasma gas flow rate (L/min) Nozzle diameter (m) Distance from nozzle exit to workpiece (m) Shielding gas flow rate (L/min) Effective radius of plasma arc pressure (m) Density of Ar (kg/m3) Sound velocity in Ar (m/s) Space permeability (H/m)
2.8 0.003 0.005 20 0.0036 1.784 341 1.256 × 10−6
(22)
where ρ is the density of molten metal, t is the time, and → v is the fluid velocity vector. Energy equation
∂ (ρH ) + ∇⋅(→ v ρH ) = ∇⋅(k∇T ) + Q v ∂t
(23)
where H is the enthalpy, k is the thermal conductivity, T is the temperature, and Q v is the source term of energy equation. Momentum equation
locates at the top surface of workpiece, the x axis is along the welding direction, and z axis is along the thickness direction of the workpiece.
3.1. Governing equations The governing equations describe the behaviors of weld pool and keyhole are as follows. Continuity equation
∂p ∂ (ρu) + ∇⋅(ρu→ v)=− + ∇⋅∇ (μ u) + Fx ∂t ∂x
(24)
∂p ∂ (ρv ) + ∇⋅(ρv→ v)=− + ∇⋅∇ (μ v ) + Fy ∂y ∂t
(25)
∂p ∂ (ρw ) + ∇⋅(ρw→ v)=− + ∇⋅∇ (μ w ) + Fz ∂z ∂t
(26)
where (u , v , w ) are the velocity components in x, y and z directions, p is the pressure in fluid, μ is viscosity, Fx , Fy and Fz are the momentum
Fig. 2. The calculated and measured plasma arc pressure. 606
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 3. Calculation domain.
action area of plasma arc transforms into a curved surface (keyhole wall). Thereby, the distribution mode of heat flux on the keyhole wall should be further modified by accounting for this dynamic variation of the action area of plasma heat flux. According to the experimentally measured results of plasma arc heat flux [22], a coefficient χp is introduced to characterize the dynamic change process of plasma arc heat flux with the depth of keyhole.
⎛ q (x , y, z ) = χp qmax exp ⎜− ⎝
3(x 2 + y 2 ) ⎞ ⎟ rq2 ⎠
(28)
2
Γ (x , y ) ⎞ χp = 1 − ⎛ ZL + Hnw ⎠ ⎝ ⎜
ηUI =
qmax exp ⎛⎜− Γ (x , y ) ⎝
∫
(29)
3(x 2 + y 2 ) ⎞ ⇀ ⇀ ⎟d s ⋅ k rq2 ⎠
(30)
where qmax is the maximum heat flux, Γ (x , y ) is the function of keyhole wall, ZL is the thickness of the workpiece, and Hnw is the distance from the nozzle to the workpiece surface, U is the arc voltage, I is the ⇀ welding current, d⇀ s is the area element, k is the unit vector from nozzle to workpiece along z direction. The source term QV in Eq. (23) is mainly related to the element cells on the keyhole wall, which include two parts, the deposited plasma arc heat QV 1 and heat loss QV 2 . The grid sizes in x , y , z directions are defined as x g , yg , z g , as shown in Fig. 4. The energy in the control volume is QV 1⋅x g⋅yg ⋅z g , and the plasma arc heat flux acting on the control volume is q (x , y, z )⋅x g⋅yg . Due to energy conservation, we have
Fig. 4. Heat flux on the control volume at keyhole wall.
source terms in x, y, and z directions, respectively. VOF equation
∂ (ϕ) + ∇⋅(ϕ→ vs ) = 0 ∂t
⎟
(27)
where vs is the fluid velocity at the interface, and the function ϕ is defined as follows. If ϕ = 0 , the cell is full with the plasma arc; if ϕ = 1, the cell is full with the molten metal; if 0 < ϕ < 1, the cell is occupied by both the plasma arc and the molten metal. Solving Eq. (27), we get the volume fraction ϕ to track the gas-liquid free surface, i.e., the keyhole wall.
QV 1⋅x g⋅yg ⋅z g = q (x , y, z )⋅x g⋅yg
(31)
QV 1 = q (x , y, z ) z g
(32)
For heat loss from the control volume,
QV 2 = −ah (T − T0) z gs
3.2. Boundary conditions
(33)
where ah is combined heat loss coefficient, T is the weld pool temperature, T0 is the ambient temperature. Therefore, the energy source term in Eqs. (23) is as follows:
The heat flux deposited on the weld pool surface is taking the Gaussian distribution mode [21]. As the weld pool surface gets depressed, the specific distribution changes subsequently. Initially the depression of weld pool surface is the depth of blind keyhole. Then the keyhole depth becomes larger and larger until open keyhole is established. During this fast evolution of weld pool surface, the initial planar
QV = QV 1 + QV 2
(34)
The top surface of any element cell (control volume) is flat. When keyhole is formed, the top surface of control volume along the keyhole 607
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
cos α =
nz n x2 + n y2 + nz2
(36)
where n x , n y , n z is the component of the normal vector of the keyhole interface. The function ϕ is used to determine the normal vector of the keyhole wall (⇀ n ).
⇀ ⇀ ⇀ ϕx i + ϕy j + ϕx k ∇ϕ ⇀ ⇀ ⇀ ⇀ n = = nx i + n y j + nz k = |∇ϕ| ϕx2 + ϕy2 + ϕz2
(37)
The source term QV is just available at the physical boundary, i.e., keyhole wall and gas-liquid interface of the molten pool. To limit this source term within the grid nodes along the physical boundary, following functions are defined as follows [21], Fig. 5. The relation between the curved and flat surface of control volume. Table 3 Physical parameters in numerical simulation. Parameters
Value
Thermal conductivity of 304 stainless steel (W/K m) Density of 304 stainless steel (Kg/m3) Viscosity (liquid) of 304 stainless steel (Pa∙s) Specific heat (J/Kg∙K) Liquid temperature (K) Solidus temperature (K) Surface tension (N m−1) Surface tension gradient (N (m K)−1)
28.4 6800 0.005 760 1727 1672 1.9993 0.00057
(38)
1ifϕ ≥ ε1 and |∇ϕ| ≥ ε2 δ2 = ⎧ ⎨ ⎩ 0else
(39)
where ε1, ε2 , ε3 are very small constants corresponding to the position and curvature of the nodes in the grid system. If δ1 = 1, the nodes are on the keyhole wall. If δ2 = 1, the nodes locate on the physical boundary including top and bottom surfaces of the molten pool. Thereby, the final energy source term may be written as
Q v = δ1 q (x , y, z ) cosα / z g − δ2 ah (T − T0)/ z g
(40)
Eq. (20) just defines the distribution of the plasma arc pressure on a flat anode surface. When the weld pool surface gets depressed and keyhole depth gets larger, the distribution of the plasma arc pressure on a curved surface (keyhole wall) changes subsequently. A keyhole geometry dependent variable χp defined by Eq. (29) is introduced into Eq. (20) to describe the distribution of the plasma arc pressure on keyhole wall, i.e.,
wall is curved. As demonstrated in Fig. 5, the curved and flat surface areas are written as ds1 and ds2 , and the heat flux on the curved and flat surface areas are written as q1 and q2 . Since the angle between the normal direction → n of the curved surface and the Z axis is α , thus,
q1 = q2 cos α
1ifϕ ≥ ε1 and |∇ϕ| ≥ ε2 andϕz ≥ ε3 δ1 = ⎧ ⎨ ⎩ 0else
(35)
Fig. 6. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case A1(PAW). 608
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 7. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case B1 (U-PAW).
the energy source term. In Eqs. (24)–(26), the momentum source terms are expressed as
Fx = Fex + Fm x + δ2 Fstx / x gs + δ1 Px / x gs
(45)
Fy = Fe y + Fm y + δ2 Fsty / ygs + δ1 Py / ygs
(46)
Fz = Fez + Fmz + ρg + δ2 Fstz / z gs + δ1 Pz / z gs
(47)
where (Fex , Fe y , Fez ) are the electromagnetic force components, (Fm x , Fm y , Fmz ) are the components of the resistance force in mushy zone, (Fstx , Fsty , Fstz ) are the surface tension components, (Px , Py , Pz ) are the plasma arc force components. The equations to determine the surface tension, the electromagnetic force and the resistance force in mushy zone have been introduced in detail in literatures [23,24], and will not be described again here. 4. Results and discussions The governing equations and boundary conditions were numerically solved by ANSYS Fluent 14.5. The welding process parameters are list in Tables 1 and 2. The thermophysical properties of SUS304 stainless steel are list in Table 3. In U-PAW, the ultrasonic output power is 500 W, the vibration frequency is 25 kHz, and the amplitude is 20 μm. Figs. 6 and 7 present the transient development of the keyhole geometry, temperature field and fluid flow at longitudinal cross-section. Different colors represent the temperature scale, and the arrows in the pictures demonstrate the fluid velocity vector inside the weld pool. In both PAW and U-PAW processes, as soon as the plasma arc deposits heat and pressure on the workpiece, it melts immediately, and the weld pool is formed, as shown in Figs. 6(a) and 7 (a). Then, a depression of the weld pool surface is caused by the plasma arc pressure, and a blind keyhole (cavity) is produced, as demonstrated in Figs. 6(b) and 7 (b). For Case A1, it is PAW without ultrasound, and its plasma arc pressure is insufficient to establish an open keyhole. As shown in Fig. 6(d), just a blind keyhole is formed inside the weld pool under the condition of Case A1. For Case B1, although all other welding conditions are the same as those in Case A1, an open keyhole is established, as shown in
Fig. 8. The variation of the keyhole depth with time in Cases A1 and B1.
P (x , y, z ) =
2 χp ηi 3rnoz ρAr QPlas
AI Snoz −3
x2
+ y2 ⎞ ⎟ rp2 ⎠
2ηv IU 2Pe2 Q 2 μ0 I 2 ⎛ + + Plas exp ⎜ 2 2 2 ρAr QPlas ρAr c Snoz 4π 2rp2 ⎝ (41)
The plasma arc pressure acts on the keyhole wall includes the tangential and normal components. Only considered the normal components are taken into consideration,
Px = P (x , y, z ) cos α⋅n x
(42)
Py = P (x , y, z ) cos α⋅n y
(43)
Pz = P (x , y, z ) cos α⋅n z
(44)
The treatment method of the momentum source term is the same as 609
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 9. Schematic diagram of U-PAW welding experiment.
Fig. 10. The captured image of the keyhole exit in PAW and U-PAW.
is established at t = 5.60 s. At initial stage (before t = 2.0 s), the variation of blind keyhole depth in PAW and U-PAW looks similar. But after this moment, keyholing speed in U-PAW increases quickly because ultrasound enhances the arc pressure. PAW and U-PAW experiments were conducted on stainless steel plates of thickness 4 mm. The test system is schematically illustrated in Fig. 9. A vision system was used to capture the images of keyhole exit at bottom side of workpieces. The specific details of experiments may refer to [29]. As is shown in Fig. 10, no images of keyhole exit were observed, which means that no open keyhole was established in PAW (case A1). In U-PAW (case B1), clear images of keyhole exit were captured after t = 4.6 s, which means that open keyhole was formed in this test case. These experimental observation results validate the predicted ones in Figs. 6–8. In Case A2, the welding current is increased to 100 A. Thus, open keyhole is established even in PAW at instant t = 4.671 s, as shown in Fig. 11. For Case B2 with a lower level of welding current (90 A), open keyhole is still formed at an earlier instant (t = 3.811 s) due to action of ultrasound, as shown in Fig. 12. U-PAW can produce open keyhole at faster welding speed. With the same welding current (95 A), in case B3 (U-PAW, welding speed is 115 mm/min) open keyhole is established at instant t = 3.33 s, while in case A3 (PAW, welding speed is 100 mm/min) open keyhole is formed at instant t = 4.403 s, as shown in Figs. 13 and 14. This implies that exerted ultrasound can increase the welding speed by 15 % under the
Fig. 7(d). This is because the interaction of ultrasound with plasma arc increases the arc pressure (peak value) from about 1201 Pa–1450 Pa under the current level of 80 A, as demonstrated in Fig. 2. As shown in Fig. 6(c), there are two flow circulations in the molten pool. The anticlockwise circulation in the lower part of the molten pool is caused by arc pressure and electromagnetic force in PAW. The anticlockwise circulation gradually increases with the volume of the molten pool. The clockwise circulation on the upper surface of the molten pool is caused by Marangoni force. This is consistent with the results described in the literature [25–28]. At t = 6.707 s, the depth of the keyhole does not change any more. As shown in Fig. 6(d), under the action of arc pressure, the liquid metal at the bottom of the molten pool flows to the rear of the molten pool. When the liquid metal meets the solid-liquid interface, it flows to the upper part of the molten pool. In U-PAW, at initial stage the fluid flow trend seems like that in PAW. But as keyhole depth reaches a certain extent, as shown in Fig. 7(c), the counterclockwise circulation in the molten pool is not obvious in U-PAW. After the ultrasonic vibration is applied, open keyhole is rapidly formed while the maximum flow velocity in the molten pool gets larger. Fig. 8 compares the variation of keyhole depth in Case A1 (PAW) and Case B1 (U-PAW). The stainless steel workpieces were 4 mm in thickness. In PAW there is no open keyhole. At t = 6.12 s, the keyhole reaches the thermodynamic equilibrium state, the keyhole depth is around 2.8 mm and does not change with time. In U-PAW open keyhole 610
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 11. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case A2 (PAW,100 A,110 mm/min).
Fig. 12. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case B2 (U-PAW, 90 A, 110 mm/min).
pressure in U-PAW makes the anti-clockwise eddy be dominant in the weld pool, but the clockwise eddy is not obvious. Fan et al. thought that plasma arc shear force had little effect on keyholing process [20]. However, Wu et al. shown that the plasma arc shear stress affected weld pool flow, and resulted in a clockwise eddy at the rear part of the weld pool [26–28]. In this study the influence of plasma arc shear stress on weld pool flow is not considered, and the size
same welding conditions. From the above simulation results, it can be seen that there are clockwise and anti-clockwise eddy in the weld pool. The clockwise eddy depends on Marangoni force. The anti-clockwise eddy depends on plasma arc pressure. Wu et al. found that the Marangoni force has little influence on the weld pool flow [27]. Comparing the PAW case (Fig. 13) and the U-PAW case (Fig.14), the increased plasma arc 611
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 13. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case A3 (PAW, 95 A,100 mm/min).
Fig. 14. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case B3 (U-PAW, 95 A,115 mm/min).
experimental results. Thus, it still needs further investigation.
of the clockwise eddy is smaller than that in literatures. In next step, we will consider the effect of plasma shear force on the weld pool flow. Fig. 15 compares the calculated and measured weld geometry in UPAW (Case B1). Generally, both are in agreement with each other. Since the mathematical model simplifies the effect of ultrasonic vibration on the flow of weld pool and does not consider the plasma arc shear force, there is still some unmatched errors between the simulation and the
5. Conclusions (1) The ultrasonic vibration interacts with the plasma arc, and increases the velocity of charged particles in the plasma arc along the vibration direction. This additional driving force is considered, and 612
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
[3] Jia CB, Liu XF, Wu CS, Lin SB. Stereo analysis on the keyhole and weld pool behaviorsin K-PAW with triple CCD cameras. J Manuf Processes 2018;32:754–62. [4] Vredeveldt HL. Increased power density plasma arc welding: the effect of an added radial gas flow around the arc root. Delft: Technische Universiteit Delft; 2014. [5] Mahrle A, Rose S, Schnick M, et al. Stabilisation of plasma welding arcs by low power laser beams. Sci Technol Weld Joining 2013;18(4):323–8. [6] Wu CS, Jia CB, Chen MA. A control system for keyhole plasma arc welding of stainless steel plates with medium thickness. Weld J 2010;89(11):225s–31s. [7] Sachin K, Wu CS, Padhy GK, Ding W. Application of ultrasonic vibrations in welding and metal processing: a status review. J Manuf Process 2017;263:295–322. [8] Sun QJ, Lin SB, Yang CL, et al. Penetration increase of AISI 304 using ultrasonic assisted tungsten inert gas welding. Sci Technol Weld Joining 2009;14(8):765–7. [9] Fan YY, Yang CL, Lin SB, et al. Ultrasonic wave assisted GMAW. Weld J 2012;91(3):91s–9s. [10] Wu CS, Zhao CY, Zhang C, et al. Ultrasonic vibration assisted keyholing plasma arc welding. Weld J 2017;96(8):279s–86s. [11] Allum CJ. Gas flow in the column of a TIG welding arc. J Phys D Appl Phys 1981;14(6):1041–59. [12] Lin ML, Eagar TW. Pressures produced by gas tungsten arcs. Metall Mater Trans B 1986;17(3):601–7. [13] Li TQ, Wu CS. An analytic formula describing the plasma arc pressure distribution. China Welding 2014;23(2):7–11. [14] David C. Fundamentals and applications of ultrasonic waves. CRC Press; 2002. [15] Cobine JD. Gaseous conductors: theory and engineering applications. Dover; 1958. [16] Georgy IE, Dmitry GE. Ultrasonic treatment of light alloy melts. CRC Press; 2015. [17] Li YF, Wu CS, Chen MA. Numerical analysis of the ultrasound induced arc pressure increment in plasma arc welding. J Phys D Appl Phys 2019;52:1–14. [18] Lin ML, Eagar TW. Influence of arc pressure on weld pool geometry. Weld J 1985;64:163s–9s. [19] Griffith DJ, Ruppeiner G. Introduction to electrodynamics. Am J Phys 1981;49(12):1188–9. [20] Fan HG, Kovacevic R. Keyhole formation and collapse in plasma arc welding. J Phys D Appl Phys 1999;32(22):2902–9. [21] Li TQ, Wu CS. Numerical simulation of plasma arc welding with keyhole-dependent heat source and arc pressure distribution. Int J Adv Manuf Technol 2015;78(1–4):593–602. [22] Chen SJ, Jiang F, Lu ZY, et al. Measurement and analysis of the welding arc current density and pressure distribution based on split anode method. Proceedings of International Conference on Mechatronics and Automation 2011:1544–9. [23] Chen SJ, Xu B, Jiang F. Blasting type penetrating characteristic in variable polarity plasma arc welding of aluminum alloy of type 5A06. Int J Heat Mass Transf 2018;118:1293–306. [24] Gao XS, Wu CS, Goecke SF, et al. Numerical simulation of temperature field, fluid flow and weld bead formation in oscillating single mode laser-GMA hybrid welding. J Mater Process Technol 2017;242:147–59. [25] Li Y, Wang L, Wu CS. A novel unified model of keyhole plasma arc welding. Int J Heat Mass Transf 2019;133:885–94. [26] Anh NV, Tashiro S, Hanh BV, et al. Experimental investigation on weld pool formation process in plasma keyhole arc welding. J Phys D Appl Phys 2018;51:1–14. [27] Wu DS, Nguyen AV, Tashiro S. Elucidation of the weld pool convection and keyhole formation mechanism in the keyhole plasma arc welding. Int J Heat Mass Transf 2019;131:920–31. [28] Wu DS, Tashiro S, Hua XM, et al. A novel electrode-arc-weld pool model for studying the keyhole formation in the keyhole plasma arc welding process. J Phys D Appl Phys 2019;52:1–15. [29] Zhang GK, Wu CS, Liu XF. Single vision system for simultaneous observation of keyhole and weld pool in plasma arc welding. J Mater Process Technol 2015;215:71–8.
Fig. 15. Comparison of the measured and calculated weld cross section of Case B1.
a formula is derived to calculate the plasma arc pressure on anode in U-PAW. (2) As the weld pool surface gets depressed and keyhole evolves from blind to open status, the distribution modes of plasma arc heat and pressure on keyhole boundary are varied at each time step, and the keyhole geometry and heat transfer and fluid flow in weld pool are numerically simulated. (3) Both numerical simulation and experimental observation show that the exerted ultrasonic vibration improve the keyholing capability. Open keyhole status can be achieved at lower welding current and higher welding speed in U-PAW. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The research was financially supported by the National Natural Science Foundation of China under Grant No. 51775312. References [1] Wu CS, Wang L, Ren WJ, Zhang XY. Plasma arc welding: process, sensing, control and modeling. J Manuf Processes 2014;16:74–85. [2] Liu ZM, Cui SL, Luo Z, Zhang CZ, Wang ZM, Zhang YC. Plasma arc welding: process variants and its recent developments of sensing, controlling and modeling. J Manuf Processes 2016;23:315–27.
613
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Numerical and experimental investigation of keyholing process in ultrasonic vibration assisted plasma arc welding
T
Junnan Qiao, ChuanSong Wu*, Yongfeng Li MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, Institute of Materials Joining, Shandong University, Jinan, 250061, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Ultrasonic vibration Plasma arc welding Keyholing capability Plasma arc pressure Weld pool
To improve the keyholing capability and welding efficiency, ultrasonic vibration assisted plasma arc welding (UPAW) is developed by connecting the specially manufactured ultrasonic horn with the tungsten electrode. The ultrasound pressure in the plasma arc is considered to derive a formula for calculating the plasma arc pressure on anode in U-PAW. A transient model of U-PAW process is developed with accounting for the dynamic variation of both heat flux and arc pressure distribution on the curved keyhole wall. The weld pool and keyhole behaviors are numerically simulated to predict the fluid flow and heat transfer as well as the dynamic keyhole evolution in UPAW. It is found that the exerted ultrasonic vibration increases the plasma arc pressure so that open keyhole can be established at lower welding current and higher welding speed in U-PAW. The experimental observation validates the numerical simulation results.
1. Introduction
industrial applications [7], especially into gas tungsten arc and gas metal arc welding processes to increase the weld penetration [8] and improve the droplet transfer [9], Wu’s group developed the ultrasonicassisted PAW [10], and found that open keyhole can be established with lower welding current or higher welding speed, which means the increasing of keyholing capability and welding efficiency. It is found that when ultrasonic vibration is exerted into gas tungsten arc or gas metal arc or plasma arc, the arc is constricted and the arc pressure is increased [8–10]. However, the underlying interaction mechanism between the ultrasonic vibration and the arc has not been fully elucidated. The previous studies just correlate the arc pressure with the square of the welding current [11,12]. Though Li et al. proposed an analytic formula for calculating the plasma arc pressure and took the main process parameters (welding current, arc voltage, plasma gas flow rate and density, nozzle radius) into consideration [13], but it did not include the effect of ultrasonic vibration on the plasma arc pressure. In this study, the influence of ultrasound on the plasma arc pressure is firstly analyzed, and a new arc pressure model for the U-PAW process is developed. Then the weld pool behavior and keyhole dynamics in UPAW process are numerically simulated. The experiments of the ultrasonic-assisted PAW are conducted to validate the developed model.
Plasma arc welding (PAW) can produce full penetration welds with only one pass for the mid-thickness workpieces because a keyhole channel (open keyhole) is formed inside the weld pool and both the arc heat and pressure can act along the plate thickness. The stability of the weld pool and keyhole is critical to obtain good weld quality. But in conventional PAW process, the dynamic stability of keyhole and weld pool is poor, and the welding process-parameter window for sustaining an open keyhole is narrow, which restricts the applications of plasma arc welding process in manufacturing industry [1–3]. To improve the keyholing capability and the dynamic stability of an open keyhole, some researchers have tried to modify the conventional PAW process. The torch was redesigned to add radial gas so that the plasma arc near the nozzle exit is further constricted and the heat intensity of plasma arc is increased [4]. Low power laser was used to interact with the plasma arc to increase the keyholing/penetration capability [5]. The controlled pulse waveform of welding current was employed to ensure establishment and sustainment of open keyhole status [6]. However, all the above-mentioned modifications require special design of the plasma torch or addition of laser beam or employment of special current waveform, which increases not only the investment and equipment cost but also the complexity and difficulty of the process-parameter matching and optimization. Since ultrasonic vibration has been successfully integrated into
⁎
2. Plasma arc pressure in U-PAW As is shown in the Fig. 1, the ultrasonic-assisted PAW (U-PAW),
Corresponding author. E-mail address: [email protected] (C. Wu).
https://doi.org/10.1016/j.jmapro.2020.01.019 Received 30 October 2019; Received in revised form 10 January 2020; Accepted 11 January 2020 1526-6125/ © 2020 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 1. Schematic diagram of U-PAW process.
According to kinetic energy theorem, electric field force and acoustic energy drive plasma to move. The accelerating process in the plasma arc can be described by following equation,
tungsten electrode is connected with ultrasonic horn so that ultrasonic vibration is applied to the plasma arc directly [10]. The ultrasonic wave interacts with the plasma arc so that both the arc heat and pressure are varied, and part of ultrasonic energy is also delivered into the weld pool through the plasma arc. Therefore, ultrasound certainly affects the fluid flow and heat transfer in the weld pool, and the keyhole dynamics is changed correspondingly. During the U-PAW process the interaction of ultrasonic vibration with the plasma arc will vary the distribution and magnitude of the arc pressure. First, the influence of ultrasound on the plasma arc pressure is taken into consideration, and a modified formula is derived to calculate the plasma arc pressure in U-PAW. In PAW, the average arc pressure on anode is related to the velocity of plasma jet striking on the workpiece surface [13],
Pave =
ρAr Qplas Snoz
E + Qe U =
m = ρAr Qplas Δt v1 =
1 2 mvm 2
(4)
Qplas Snoz
Qe = IΔt v2
(3)
where Qe is the number of charges carried by the plasma, U is the arc voltage, v2 is the velocity of plasma near the workpiece surface, v1 is the velocity of plasma gas at the nozzle exit.
(5) (6)
where I is the electric current, and Δt is the time interval. In fact, most of the electric energy of the plasma arc is converted into the arc heat, and only a small part is used to accelerate the plasma [15]. Therefore, ηv is introduced to characterize the conversion efficiency of electric energy to plasma kinetic energy. ηv is relatively small, generally on the order of 10−3-10-2. Based on Eqs. (3)–(6), we obtain
(1)
where Pave is the average value of arc pressure on anode, ρAr is the argon density, Qplas is the plasma gas flow rate, Snoz is the area of nozzle exit, and v2 is the velocity of plasma near the workpiece surface. In U-PAW, when ultrasonic vibration interacts with the plasma arc, it is easy to produce additional high-frequency vibration, which increases the velocity of charged particles in the plasma arc along the vibration direction. Therefore, the effect of the acoustic energy on the plasma jet velocity must be considered. The total vibration energy E is the sum of the potential energy and the kinetic energy, and E is simply equal to the maximum potential or kenetic energy during a cycle [14],
E=
1 1 mv22 − mv12 2 2
1 2 1 mvm + ηv IΔtU = ρAr Qplas Δt (v22 − v12) 2 2
(7)
Since the phase angle of the sound pressure and the vibration speed are the same, the vibration speed vm in Eq. (7) is determined by the sound pressure amplitude [16].
(2)
vm =
where m is the mass of the plasma gas ejected from the nozzle within the time interval Δt , and vm is the maximum value of vibration velocity.
pm ρAr cAr
(8)
where pm is the sound pressure amplitude at the tungsten tip, which is 604
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
plasma arc pressure: (1) the process parameters like welding current I, arc voltage U, plasma gas flow rate Qplas and argon density ρAr ; (2) torch geometry like the nozzle exit area Snoz , and the radius rP of action area of plasma arc pressure; (3) acoustic parameters like ultrasonic pressure Pm and sound velocity in argon cAr . Our previous study has shown that in U-PAW the enhancement of plasma arc pressure by ultrasonic vibration becomes weaker as the welding current increases [10]. To describe this issue, we introduce another correction coefficient ηi by comparison of the measured and calculated peak values of plasma arc pressure,
calculated by a method introduced in our previous work [17], ρAr is the argon density, cAr is the sound velocity in argon. And substitute Eq. (8) into (7), we can obtain
pm2
v2 =
+
2 2 ρAr cAr
Qplas ⎞2 2ηv IU +⎛ ρAr Qplas ⎝ Snoz ⎠ ⎜
⎟
(9)
Combining Eqs. (1) and (9), we may write
Pave =
ρAr Qplas
pm2
Snoz
2 2 ρAr cAr
+
Qplas ⎞2 2ηv IU +⎛ ρAr Qplas ⎝ Snoz ⎠ ⎜
⎟
(10)
ηi = 1 + e−0.02I
Therefore, the plasma arc force at anode can be described by following formula: 2 Fplas = Snoz Pave = πrnoz ρAr
2 Qplas pm2 2 2 2 ρAr cAr Snoz
+
2ηv IUQplas 2 ρAr Snoz
Qplas ⎞ +⎛ ⎝ Snoz ⎠ ⎜
(19)
Finally, we get,
4
P (x , y, z ) =
⎟
(11)
where rnoz is the nozzle exit radius. During plasma arc welding, the plasma arc pressure distribution is assumed to follow Gaussian function [18],
2 ηi 3rnoz ρAr QPlas AI S noz
−3
2ηv IU 2Pe2 Q 2 μ0 I 2 + + Plas exp ⎜⎛ 2 2 2 ρAr QPlas ρAr c Snoz 4π 2rp2 ⎝
x 2 + y2 ⎞ ⎟ rp2 ⎠
(20)
where Pe is the effective sound pressure which is determined by,
⎛ 3r 2 ⎞ exp ⎜− 2 ⎟ ⎝ rp ⎠
Parc = Pmax
Pe =
(12)
where Pmax is the maximum plasma arc pressure at the center of the plasma arc, r is the radial distance away from the arc axis, and rP is the radius of action area of plasma arc pressure. Therefore,
∫0
Fplas =
Pmax =
∞
Parc⋅2πr dr =
∫0
∞
Pmax πrp2 3r 2 Pmax exp ⎜⎛− 2 ⎟⎞⋅2πr dr = 3 ⎝ rp ⎠
(13)
(14)
Substituting Eqs. (11) and (14) into (12), a specific expression of plasma arc pressure is obtained:
P (x , y ) = 3
2 rnoz ρ rp2 Ar
−
2 Qplas pm2 2 2 2 ρAr cAr Snoz
+
2ηv IUQplas 2 ρAr Snoz
4
Qplas ⎞ ⎛ +⎛ exp ⎜ ⎝ Snoz ⎠ ⎝ ⎜
⎟
3(x 2 + y 2 ) ⎞ ⎟ rp2 ⎠
3. Modeling of keyhole and weld pool behavior in U-PAW (15)
The U-PAW process involves complicated physical phenomena. To study the dynamic behaviors and keyhole and weld pool, some simplifications and assumptions have to be made: (1) the fluid flow in weld pool is incompressible and laminar; (2) the influence of the gas shear force on the molten pool flow and the keyholing process is not considered, because of its little influence on the keyholing process [20]; (3) the sound pressure delivered into molten pool is temporarily neglected as it is much lower than arc pressure; (4) the effect of ultrasonic vibration on plasma arc shape is temporarily not considered. Fig. 3 shows the selected calculation domain. In fact, it is less than the size of real test workpiece but with the same thickness (stainless steel plates of thickness 4 mm) in order to save the calculation cost. As shown in Fig. 3, due to the symmetry of the workpiece, half of the calculation domain is used in the calculation. The calculation domain includes three layers: air, workpiece, and air. The coordinate origin
Eq. (16) is derived by using the continuous plasma impact theory, and only the electric field force and the acoustic driving force are considered to accelerate the plasma. In order to comprehensively consider the effect of electromagnetic field, Eq. (15) needs to be modified to reflect the effect of magnetic field on plasma. Arc plasma is essentially an electric conductor. Under the action of its own magnetic field, the plasma is subjected to the following magnetic field force [19],
FM =
μ0 I 2 4π 2
(16)
Since the dimension of magnetic force is Newton, a dimensionless magnetic force coefficient βM is introduced to correct the plasma arc pressure,
βM =
μ0 I 2 1 ⋅ 4π 2 AI
(17)
Table 1 Welding process parameters.
where AI is a constant, and μ0 is the permeability in vacuum. Put this correction factor into Eq. (15), we have
P (x , y ) =
1 2 ⋅3rnoz ρAr AI −3
x 2 + y2 ⎞ ⎟ rp2 ⎠
(21)
The plasma arc pressure in both PAW and U-PAW were measured under the welding process parameters in Tables 1 and 2. The detailed measurement method and description may be referred to [10]. With the torch design and acoustic parameters listed in Table 2, Pm = 732 Pa. If Pm = 0 , ηi = 1, Eqs. (20) and (21) can be used to calculate the plasma arc pressure in PAW. Eqs. (20) and (21) were employed to calculate the plasma arc pressure at the workpiece surface under the welding process parameters in Tables 1 and 2. Fig. 2 shows the comparison of predicted plasma arc pressure in PAW and U-PAW with the experimentally measured ones. It is clear that both are in good agreement, especially for U-PAW. Thus, Eq. (20) is verified and can be used to predict the plasma arc pressure in U-PAW.
3Fplas πrp2
Pm 2
2 2η IUQPlas QPlas Pm2 Q 4 μ0 I 2 ⎛ + v 2 + Plas exp ⎜ 2 2 2 4 ρAr cAr Snoz ρAr Snoz Snoz 4π 2rp2 ⎝
(18)
Eq. (18) contains following groups of parameters influencing the 605
Case
Welding current (A)
Arc voltage (V)
Welding speed (mm/min)
Welding process
A1 B1 A2 B2 A3 B3
80 80 100 90 95 95
19.5 19.8 20.6 20.2 20.5 20.7
100 100 110 110 100 115
PAW U-PAW PAW U-PAW PAW U-PAW
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
∂ρ v)=0 + ∇⋅(ρ→ ∂t
Table 2 Other parameters used in calculation of plasma arc pressure. Parameters
Value
Plasma gas flow rate (L/min) Nozzle diameter (m) Distance from nozzle exit to workpiece (m) Shielding gas flow rate (L/min) Effective radius of plasma arc pressure (m) Density of Ar (kg/m3) Sound velocity in Ar (m/s) Space permeability (H/m)
2.8 0.003 0.005 20 0.0036 1.784 341 1.256 × 10−6
(22)
where ρ is the density of molten metal, t is the time, and → v is the fluid velocity vector. Energy equation
∂ (ρH ) + ∇⋅(→ v ρH ) = ∇⋅(k∇T ) + Q v ∂t
(23)
where H is the enthalpy, k is the thermal conductivity, T is the temperature, and Q v is the source term of energy equation. Momentum equation
locates at the top surface of workpiece, the x axis is along the welding direction, and z axis is along the thickness direction of the workpiece.
3.1. Governing equations The governing equations describe the behaviors of weld pool and keyhole are as follows. Continuity equation
∂p ∂ (ρu) + ∇⋅(ρu→ v)=− + ∇⋅∇ (μ u) + Fx ∂t ∂x
(24)
∂p ∂ (ρv ) + ∇⋅(ρv→ v)=− + ∇⋅∇ (μ v ) + Fy ∂y ∂t
(25)
∂p ∂ (ρw ) + ∇⋅(ρw→ v)=− + ∇⋅∇ (μ w ) + Fz ∂z ∂t
(26)
where (u , v , w ) are the velocity components in x, y and z directions, p is the pressure in fluid, μ is viscosity, Fx , Fy and Fz are the momentum
Fig. 2. The calculated and measured plasma arc pressure. 606
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 3. Calculation domain.
action area of plasma arc transforms into a curved surface (keyhole wall). Thereby, the distribution mode of heat flux on the keyhole wall should be further modified by accounting for this dynamic variation of the action area of plasma heat flux. According to the experimentally measured results of plasma arc heat flux [22], a coefficient χp is introduced to characterize the dynamic change process of plasma arc heat flux with the depth of keyhole.
⎛ q (x , y, z ) = χp qmax exp ⎜− ⎝
3(x 2 + y 2 ) ⎞ ⎟ rq2 ⎠
(28)
2
Γ (x , y ) ⎞ χp = 1 − ⎛ ZL + Hnw ⎠ ⎝ ⎜
ηUI =
qmax exp ⎛⎜− Γ (x , y ) ⎝
∫
(29)
3(x 2 + y 2 ) ⎞ ⇀ ⇀ ⎟d s ⋅ k rq2 ⎠
(30)
where qmax is the maximum heat flux, Γ (x , y ) is the function of keyhole wall, ZL is the thickness of the workpiece, and Hnw is the distance from the nozzle to the workpiece surface, U is the arc voltage, I is the ⇀ welding current, d⇀ s is the area element, k is the unit vector from nozzle to workpiece along z direction. The source term QV in Eq. (23) is mainly related to the element cells on the keyhole wall, which include two parts, the deposited plasma arc heat QV 1 and heat loss QV 2 . The grid sizes in x , y , z directions are defined as x g , yg , z g , as shown in Fig. 4. The energy in the control volume is QV 1⋅x g⋅yg ⋅z g , and the plasma arc heat flux acting on the control volume is q (x , y, z )⋅x g⋅yg . Due to energy conservation, we have
Fig. 4. Heat flux on the control volume at keyhole wall.
source terms in x, y, and z directions, respectively. VOF equation
∂ (ϕ) + ∇⋅(ϕ→ vs ) = 0 ∂t
⎟
(27)
where vs is the fluid velocity at the interface, and the function ϕ is defined as follows. If ϕ = 0 , the cell is full with the plasma arc; if ϕ = 1, the cell is full with the molten metal; if 0 < ϕ < 1, the cell is occupied by both the plasma arc and the molten metal. Solving Eq. (27), we get the volume fraction ϕ to track the gas-liquid free surface, i.e., the keyhole wall.
QV 1⋅x g⋅yg ⋅z g = q (x , y, z )⋅x g⋅yg
(31)
QV 1 = q (x , y, z ) z g
(32)
For heat loss from the control volume,
QV 2 = −ah (T − T0) z gs
3.2. Boundary conditions
(33)
where ah is combined heat loss coefficient, T is the weld pool temperature, T0 is the ambient temperature. Therefore, the energy source term in Eqs. (23) is as follows:
The heat flux deposited on the weld pool surface is taking the Gaussian distribution mode [21]. As the weld pool surface gets depressed, the specific distribution changes subsequently. Initially the depression of weld pool surface is the depth of blind keyhole. Then the keyhole depth becomes larger and larger until open keyhole is established. During this fast evolution of weld pool surface, the initial planar
QV = QV 1 + QV 2
(34)
The top surface of any element cell (control volume) is flat. When keyhole is formed, the top surface of control volume along the keyhole 607
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
cos α =
nz n x2 + n y2 + nz2
(36)
where n x , n y , n z is the component of the normal vector of the keyhole interface. The function ϕ is used to determine the normal vector of the keyhole wall (⇀ n ).
⇀ ⇀ ⇀ ϕx i + ϕy j + ϕx k ∇ϕ ⇀ ⇀ ⇀ ⇀ n = = nx i + n y j + nz k = |∇ϕ| ϕx2 + ϕy2 + ϕz2
(37)
The source term QV is just available at the physical boundary, i.e., keyhole wall and gas-liquid interface of the molten pool. To limit this source term within the grid nodes along the physical boundary, following functions are defined as follows [21], Fig. 5. The relation between the curved and flat surface of control volume. Table 3 Physical parameters in numerical simulation. Parameters
Value
Thermal conductivity of 304 stainless steel (W/K m) Density of 304 stainless steel (Kg/m3) Viscosity (liquid) of 304 stainless steel (Pa∙s) Specific heat (J/Kg∙K) Liquid temperature (K) Solidus temperature (K) Surface tension (N m−1) Surface tension gradient (N (m K)−1)
28.4 6800 0.005 760 1727 1672 1.9993 0.00057
(38)
1ifϕ ≥ ε1 and |∇ϕ| ≥ ε2 δ2 = ⎧ ⎨ ⎩ 0else
(39)
where ε1, ε2 , ε3 are very small constants corresponding to the position and curvature of the nodes in the grid system. If δ1 = 1, the nodes are on the keyhole wall. If δ2 = 1, the nodes locate on the physical boundary including top and bottom surfaces of the molten pool. Thereby, the final energy source term may be written as
Q v = δ1 q (x , y, z ) cosα / z g − δ2 ah (T − T0)/ z g
(40)
Eq. (20) just defines the distribution of the plasma arc pressure on a flat anode surface. When the weld pool surface gets depressed and keyhole depth gets larger, the distribution of the plasma arc pressure on a curved surface (keyhole wall) changes subsequently. A keyhole geometry dependent variable χp defined by Eq. (29) is introduced into Eq. (20) to describe the distribution of the plasma arc pressure on keyhole wall, i.e.,
wall is curved. As demonstrated in Fig. 5, the curved and flat surface areas are written as ds1 and ds2 , and the heat flux on the curved and flat surface areas are written as q1 and q2 . Since the angle between the normal direction → n of the curved surface and the Z axis is α , thus,
q1 = q2 cos α
1ifϕ ≥ ε1 and |∇ϕ| ≥ ε2 andϕz ≥ ε3 δ1 = ⎧ ⎨ ⎩ 0else
(35)
Fig. 6. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case A1(PAW). 608
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 7. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case B1 (U-PAW).
the energy source term. In Eqs. (24)–(26), the momentum source terms are expressed as
Fx = Fex + Fm x + δ2 Fstx / x gs + δ1 Px / x gs
(45)
Fy = Fe y + Fm y + δ2 Fsty / ygs + δ1 Py / ygs
(46)
Fz = Fez + Fmz + ρg + δ2 Fstz / z gs + δ1 Pz / z gs
(47)
where (Fex , Fe y , Fez ) are the electromagnetic force components, (Fm x , Fm y , Fmz ) are the components of the resistance force in mushy zone, (Fstx , Fsty , Fstz ) are the surface tension components, (Px , Py , Pz ) are the plasma arc force components. The equations to determine the surface tension, the electromagnetic force and the resistance force in mushy zone have been introduced in detail in literatures [23,24], and will not be described again here. 4. Results and discussions The governing equations and boundary conditions were numerically solved by ANSYS Fluent 14.5. The welding process parameters are list in Tables 1 and 2. The thermophysical properties of SUS304 stainless steel are list in Table 3. In U-PAW, the ultrasonic output power is 500 W, the vibration frequency is 25 kHz, and the amplitude is 20 μm. Figs. 6 and 7 present the transient development of the keyhole geometry, temperature field and fluid flow at longitudinal cross-section. Different colors represent the temperature scale, and the arrows in the pictures demonstrate the fluid velocity vector inside the weld pool. In both PAW and U-PAW processes, as soon as the plasma arc deposits heat and pressure on the workpiece, it melts immediately, and the weld pool is formed, as shown in Figs. 6(a) and 7 (a). Then, a depression of the weld pool surface is caused by the plasma arc pressure, and a blind keyhole (cavity) is produced, as demonstrated in Figs. 6(b) and 7 (b). For Case A1, it is PAW without ultrasound, and its plasma arc pressure is insufficient to establish an open keyhole. As shown in Fig. 6(d), just a blind keyhole is formed inside the weld pool under the condition of Case A1. For Case B1, although all other welding conditions are the same as those in Case A1, an open keyhole is established, as shown in
Fig. 8. The variation of the keyhole depth with time in Cases A1 and B1.
P (x , y, z ) =
2 χp ηi 3rnoz ρAr QPlas
AI Snoz −3
x2
+ y2 ⎞ ⎟ rp2 ⎠
2ηv IU 2Pe2 Q 2 μ0 I 2 ⎛ + + Plas exp ⎜ 2 2 2 ρAr QPlas ρAr c Snoz 4π 2rp2 ⎝ (41)
The plasma arc pressure acts on the keyhole wall includes the tangential and normal components. Only considered the normal components are taken into consideration,
Px = P (x , y, z ) cos α⋅n x
(42)
Py = P (x , y, z ) cos α⋅n y
(43)
Pz = P (x , y, z ) cos α⋅n z
(44)
The treatment method of the momentum source term is the same as 609
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 9. Schematic diagram of U-PAW welding experiment.
Fig. 10. The captured image of the keyhole exit in PAW and U-PAW.
is established at t = 5.60 s. At initial stage (before t = 2.0 s), the variation of blind keyhole depth in PAW and U-PAW looks similar. But after this moment, keyholing speed in U-PAW increases quickly because ultrasound enhances the arc pressure. PAW and U-PAW experiments were conducted on stainless steel plates of thickness 4 mm. The test system is schematically illustrated in Fig. 9. A vision system was used to capture the images of keyhole exit at bottom side of workpieces. The specific details of experiments may refer to [29]. As is shown in Fig. 10, no images of keyhole exit were observed, which means that no open keyhole was established in PAW (case A1). In U-PAW (case B1), clear images of keyhole exit were captured after t = 4.6 s, which means that open keyhole was formed in this test case. These experimental observation results validate the predicted ones in Figs. 6–8. In Case A2, the welding current is increased to 100 A. Thus, open keyhole is established even in PAW at instant t = 4.671 s, as shown in Fig. 11. For Case B2 with a lower level of welding current (90 A), open keyhole is still formed at an earlier instant (t = 3.811 s) due to action of ultrasound, as shown in Fig. 12. U-PAW can produce open keyhole at faster welding speed. With the same welding current (95 A), in case B3 (U-PAW, welding speed is 115 mm/min) open keyhole is established at instant t = 3.33 s, while in case A3 (PAW, welding speed is 100 mm/min) open keyhole is formed at instant t = 4.403 s, as shown in Figs. 13 and 14. This implies that exerted ultrasound can increase the welding speed by 15 % under the
Fig. 7(d). This is because the interaction of ultrasound with plasma arc increases the arc pressure (peak value) from about 1201 Pa–1450 Pa under the current level of 80 A, as demonstrated in Fig. 2. As shown in Fig. 6(c), there are two flow circulations in the molten pool. The anticlockwise circulation in the lower part of the molten pool is caused by arc pressure and electromagnetic force in PAW. The anticlockwise circulation gradually increases with the volume of the molten pool. The clockwise circulation on the upper surface of the molten pool is caused by Marangoni force. This is consistent with the results described in the literature [25–28]. At t = 6.707 s, the depth of the keyhole does not change any more. As shown in Fig. 6(d), under the action of arc pressure, the liquid metal at the bottom of the molten pool flows to the rear of the molten pool. When the liquid metal meets the solid-liquid interface, it flows to the upper part of the molten pool. In U-PAW, at initial stage the fluid flow trend seems like that in PAW. But as keyhole depth reaches a certain extent, as shown in Fig. 7(c), the counterclockwise circulation in the molten pool is not obvious in U-PAW. After the ultrasonic vibration is applied, open keyhole is rapidly formed while the maximum flow velocity in the molten pool gets larger. Fig. 8 compares the variation of keyhole depth in Case A1 (PAW) and Case B1 (U-PAW). The stainless steel workpieces were 4 mm in thickness. In PAW there is no open keyhole. At t = 6.12 s, the keyhole reaches the thermodynamic equilibrium state, the keyhole depth is around 2.8 mm and does not change with time. In U-PAW open keyhole 610
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 11. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case A2 (PAW,100 A,110 mm/min).
Fig. 12. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case B2 (U-PAW, 90 A, 110 mm/min).
pressure in U-PAW makes the anti-clockwise eddy be dominant in the weld pool, but the clockwise eddy is not obvious. Fan et al. thought that plasma arc shear force had little effect on keyholing process [20]. However, Wu et al. shown that the plasma arc shear stress affected weld pool flow, and resulted in a clockwise eddy at the rear part of the weld pool [26–28]. In this study the influence of plasma arc shear stress on weld pool flow is not considered, and the size
same welding conditions. From the above simulation results, it can be seen that there are clockwise and anti-clockwise eddy in the weld pool. The clockwise eddy depends on Marangoni force. The anti-clockwise eddy depends on plasma arc pressure. Wu et al. found that the Marangoni force has little influence on the weld pool flow [27]. Comparing the PAW case (Fig. 13) and the U-PAW case (Fig.14), the increased plasma arc 611
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
Fig. 13. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case A3 (PAW, 95 A,100 mm/min).
Fig. 14. The evolution of temperature field, fluid flow in the weld pool, and keyhole surface over time in case B3 (U-PAW, 95 A,115 mm/min).
experimental results. Thus, it still needs further investigation.
of the clockwise eddy is smaller than that in literatures. In next step, we will consider the effect of plasma shear force on the weld pool flow. Fig. 15 compares the calculated and measured weld geometry in UPAW (Case B1). Generally, both are in agreement with each other. Since the mathematical model simplifies the effect of ultrasonic vibration on the flow of weld pool and does not consider the plasma arc shear force, there is still some unmatched errors between the simulation and the
5. Conclusions (1) The ultrasonic vibration interacts with the plasma arc, and increases the velocity of charged particles in the plasma arc along the vibration direction. This additional driving force is considered, and 612
Journal of Manufacturing Processes 50 (2020) 603–613
J. Qiao, et al.
[3] Jia CB, Liu XF, Wu CS, Lin SB. Stereo analysis on the keyhole and weld pool behaviorsin K-PAW with triple CCD cameras. J Manuf Processes 2018;32:754–62. [4] Vredeveldt HL. Increased power density plasma arc welding: the effect of an added radial gas flow around the arc root. Delft: Technische Universiteit Delft; 2014. [5] Mahrle A, Rose S, Schnick M, et al. Stabilisation of plasma welding arcs by low power laser beams. Sci Technol Weld Joining 2013;18(4):323–8. [6] Wu CS, Jia CB, Chen MA. A control system for keyhole plasma arc welding of stainless steel plates with medium thickness. Weld J 2010;89(11):225s–31s. [7] Sachin K, Wu CS, Padhy GK, Ding W. Application of ultrasonic vibrations in welding and metal processing: a status review. J Manuf Process 2017;263:295–322. [8] Sun QJ, Lin SB, Yang CL, et al. Penetration increase of AISI 304 using ultrasonic assisted tungsten inert gas welding. Sci Technol Weld Joining 2009;14(8):765–7. [9] Fan YY, Yang CL, Lin SB, et al. Ultrasonic wave assisted GMAW. Weld J 2012;91(3):91s–9s. [10] Wu CS, Zhao CY, Zhang C, et al. Ultrasonic vibration assisted keyholing plasma arc welding. Weld J 2017;96(8):279s–86s. [11] Allum CJ. Gas flow in the column of a TIG welding arc. J Phys D Appl Phys 1981;14(6):1041–59. [12] Lin ML, Eagar TW. Pressures produced by gas tungsten arcs. Metall Mater Trans B 1986;17(3):601–7. [13] Li TQ, Wu CS. An analytic formula describing the plasma arc pressure distribution. China Welding 2014;23(2):7–11. [14] David C. Fundamentals and applications of ultrasonic waves. CRC Press; 2002. [15] Cobine JD. Gaseous conductors: theory and engineering applications. Dover; 1958. [16] Georgy IE, Dmitry GE. Ultrasonic treatment of light alloy melts. CRC Press; 2015. [17] Li YF, Wu CS, Chen MA. Numerical analysis of the ultrasound induced arc pressure increment in plasma arc welding. J Phys D Appl Phys 2019;52:1–14. [18] Lin ML, Eagar TW. Influence of arc pressure on weld pool geometry. Weld J 1985;64:163s–9s. [19] Griffith DJ, Ruppeiner G. Introduction to electrodynamics. Am J Phys 1981;49(12):1188–9. [20] Fan HG, Kovacevic R. Keyhole formation and collapse in plasma arc welding. J Phys D Appl Phys 1999;32(22):2902–9. [21] Li TQ, Wu CS. Numerical simulation of plasma arc welding with keyhole-dependent heat source and arc pressure distribution. Int J Adv Manuf Technol 2015;78(1–4):593–602. [22] Chen SJ, Jiang F, Lu ZY, et al. Measurement and analysis of the welding arc current density and pressure distribution based on split anode method. Proceedings of International Conference on Mechatronics and Automation 2011:1544–9. [23] Chen SJ, Xu B, Jiang F. Blasting type penetrating characteristic in variable polarity plasma arc welding of aluminum alloy of type 5A06. Int J Heat Mass Transf 2018;118:1293–306. [24] Gao XS, Wu CS, Goecke SF, et al. Numerical simulation of temperature field, fluid flow and weld bead formation in oscillating single mode laser-GMA hybrid welding. J Mater Process Technol 2017;242:147–59. [25] Li Y, Wang L, Wu CS. A novel unified model of keyhole plasma arc welding. Int J Heat Mass Transf 2019;133:885–94. [26] Anh NV, Tashiro S, Hanh BV, et al. Experimental investigation on weld pool formation process in plasma keyhole arc welding. J Phys D Appl Phys 2018;51:1–14. [27] Wu DS, Nguyen AV, Tashiro S. Elucidation of the weld pool convection and keyhole formation mechanism in the keyhole plasma arc welding. Int J Heat Mass Transf 2019;131:920–31. [28] Wu DS, Tashiro S, Hua XM, et al. A novel electrode-arc-weld pool model for studying the keyhole formation in the keyhole plasma arc welding process. J Phys D Appl Phys 2019;52:1–15. [29] Zhang GK, Wu CS, Liu XF. Single vision system for simultaneous observation of keyhole and weld pool in plasma arc welding. J Mater Process Technol 2015;215:71–8.
Fig. 15. Comparison of the measured and calculated weld cross section of Case B1.
a formula is derived to calculate the plasma arc pressure on anode in U-PAW. (2) As the weld pool surface gets depressed and keyhole evolves from blind to open status, the distribution modes of plasma arc heat and pressure on keyhole boundary are varied at each time step, and the keyhole geometry and heat transfer and fluid flow in weld pool are numerically simulated. (3) Both numerical simulation and experimental observation show that the exerted ultrasonic vibration improve the keyholing capability. Open keyhole status can be achieved at lower welding current and higher welding speed in U-PAW. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The research was financially supported by the National Natural Science Foundation of China under Grant No. 51775312. References [1] Wu CS, Wang L, Ren WJ, Zhang XY. Plasma arc welding: process, sensing, control and modeling. J Manuf Processes 2014;16:74–85. [2] Liu ZM, Cui SL, Luo Z, Zhang CZ, Wang ZM, Zhang YC. Plasma arc welding: process variants and its recent developments of sensing, controlling and modeling. J Manuf Processes 2016;23:315–27.
613