Integrated Models of a Gas Metal ARC Welding Process and Inverter based Power Supply for Process Control Simulation Studies

The objective in this paper was to combine the simulation of a Gas Metal Arc Welding (GMAW) process model with the simulation model of an inverter-based power machine. The GMAW process was considered as an electrical circuit and the mathematical model was based on physical descriptions of several parts of the GMAW process, as were the electric circuit of the power supply, the arc dynamics, and the electrode melting process. A simple welding application was simulated and the welding parameters were derived from several experimental conditions. Next, the dynamic behaviour of a full-bridge DC-DC converter was simulated and a suitable discrete PI controller proposed for welding current feedback control. Both models, the GMAW model and the inverter power supply model, were combined into a new simulation model of the GMAW process application together with an inverter based welding machine. DOI: http://dx.doi.org/10.5755/j01.eee.20.7.8016


I. INTRODUCTION
The gas metal arc welding process is also called the MIG/MAG welding process, and is almost a substitute for the stick-electrode arc welding process within industry nowadays.This process is often used to weld aluminium using an inert shielding-gas (MIG -metal inert gas) or for welding certain ferrous metals using active shielding-gases (MAG).GMAW is an economical process suitable for welding most of metals at all positions using lover energy variations of the process.It is appropriate for usages in semi-automatic or automatic welding applications applied throughout high production industry.
Several research studies, for example [1]- [4], categorize the GMAW process as an electrical circuit.A mathematical model of the GMAW process is normally developed first.A description of the electric arc is then presented and all equations are combined into a general model that describes the GMAW process.Simulation methods are used to illustrate the behaviour of the GMAW process.During these simulations the welding power source's dynamic behaviour is often simplified.Today, in modern welding machines the inverter-based transformer technologies are used for Manuscript received January 14, 2014; accepted April 25, 2014.This research was funded by a grant (No.L2-2303) from the Ministry of Higher Education, Science and Technology, Republic of Slovenia.transforming a high voltage and a low current into low voltage and a strong current.The main advantages are the small volume, being lightweight, excellent control performance and good dynamic characteristics, which allow fast adaptation ability to arc load's change.This is important for welding process stability and for the possibility of realizing different welding applications, such as pulsed DC welding, pulsed AC welding, and others.The quality of the output welding current and voltage of a GMAW power source has an important influence on the dynamic behaviour of the GMAW process and on the quality of the welded product.With the aim of maintaining a high quality of welding results, the output welding current and voltage must be controlled during the welding process.Furthermore, a real time control system is an important element of modern GMAW welding machine [5], [6].
Modern GMAW equipment is the combination of a sophisticated power electronic device and high performance microprocessor-based control systems.The development process of inverter-based welding power source with the corresponding control system is a complex and expensive process that requires extensive human and material resources [7].When using the simulation technique the quality of design process can be improved and the design cost can be significantly reduced.Therefore, with the aim of improving the design process, an attempt was made to combine the simulation model of GMAW process with the simulation model of an inverter based welding power source [8].
This paper studies the dynamic behaviour of full-bridge inverter circuit together with the GMAW model.Both models are combined into a simulation model of the GMAW welding application with an inverter-based welding machine.The simulation results are useful for the rapid development of control algorithms of new power sources.

II. MODELLING OF THE GMAW PROCESS
As the GMAW process consists of several subsystems including the power supply, the melting process of the feeding wire, the dynamics of welding arc, the drop dynamics and the material transfer process, as illustrated in Fig. 1, its dynamic behaviour depend on the characteristics of each subsystems.The GMAW process can be presented as an electrical circuit with control voltage u as the input variable.The circuit consists of the power source inductance L and resistance R, i is the welding current, Rl is the electrode stick-out resistance, and Uarc is the arc voltage.Electrode stick-out resistance Rl is dependent on the electrical resistivity of the electrode stick , cross-sectional area of the electrode wire A, and the electrode stick-out length l, and can be calculated as Rl = l/A.It is assumed that u, R, L, , and A are constant parameters and i, l, Uarc are dependent variables.We assume that welding process is stationary process and welding signals features are time invariant: E(i(t)) = const., and Var(i(t)) = σ 2 .A model of the electrical circuit is described using (1) .
The electrode resistance Rl depends on total the length of the electrode stick-out length and drop length l = ls + ld.The dynamics of ls depend on the feeding speed of electrode ve, the melting speed vm, and on the vertical velocity of the contact tip vc.The contact tip to workpiece distance (CTWD) is indicated by H, and by ignoring the length of the drop (ld = 0 and l = ls) the length of the arc h is The dynamic of electrode stick-out is given by ( 3) .
With respect to (2) and ( 3), the arc length speed is .
In regard to the presented model, the dynamics of the melting speed vm and arc voltage Uarc need to be described in greater detail.When the current flows through the electrode and the arc the electrode is heated by the current flowing through it.This heat depends on the resistance of the electrode.Numerous studies have described the physical background of this phenomenon.In [9] the research results from a study of anode and cathode melting rates are presented and in [10] the characteristic of melting rate as a function of current, type of gas, and other parameters is reported.In these and other related works [11] the expression for the total melting velocity vm is proposed as An arc appears during the welding process between the electrode-stick (anode) and the workpiece (cathode).It can be presented as a discharge of electricity between the electrodes, characterized by a high current density and a low voltage drop between electrodes.The simplest model of the electrical arc is a voltage equation .
The total arc voltage uarc, is made up of three separate parts: the anode and cathode drop voltage ua+c, the drop voltage in the arc column, which is a function of the electric field strength E and the arc length h, and the drop voltage, that depends on current i and arc resistance Rarc.In our model we suppose that ua+c is constant.
The model of the consumable electrode GMAW process is composed of ( 1), ( 4)-( 6) and is .
Further parts of GMAW process dynamics, for example the welding drop dynamics, or drop detachment process are also important, but in this model are neglected.On the other hand, in GMAW not only the spray transfer conditions are widely employed but also the short-circuiting arc's conditions with a relatively small current.This type of material transfer is within the mainstream of high-speed welding regarding thin sheet or overhead position welding of line pipes.Short-circuiting welding is a complicated process in which short-circuiting and arc generations are repeated intermittently.This should be the subject of our further research and will be included in the model.

III. MODEL OF INVERTER POWER SUPPLY
The inverter-based welding power supply consists of a rectifier, an inverter switch circuit, a high-frequency ferrite transformer, high-frequency rectifier, and an inductor as is presented in Fig. 2. Most inverter switch circuits are realized with full-bridge DC-DC converters based on semiconductor power elements such as MOSFETs, or IGBT transistors.The switch circuits are controlled by microprocessor-based PWM controller units.The schematic of a simulation model of a full-bridge DC-DC converter is shown in Fig. 3.
The conventional DC-DC converter operates using a Pulse Width Modulation (PWM) current controller.In paper [12] the authors investigated the implementations of different PWM control techniques on a microcontroller.These modulation techniques are used in order to enhance the performances of three-phase inverters.The duty cycles are usually controlled using feedback controller (voltage, current, or both).In [13] and [14] the implementation studies of proportional-integral-derivative (PID) controller are presented, but we decided to use a PI controller because it satisfies control performances well, and the lack of derivative action may make the control system stabile in the case of noisy data.The discrete parallel form is where KP is the proportional gain, TI is the integral time constant, and TS is the sampling time.

IV. SIMULATION RESULTS
An automatic welding application was assumed.Those parameters derived from the experimental conditions are shown in Table I.A constant welding speed was supposed.The welding torch was positioned 16 mm (H) from the work distance.
The selected welding wire feed rate ve 50 mm/s and the open circuit voltage u = 24 V were set.The first simulation was performed to find the welding current response when the CTWD was changed from 16 mm to 12 mm (at time 2.5 s) and back (at time 7.5 s).In addition, the electrode feeding speed v was changed from 50 cm/min to 75 cm/min at time t = 5 s.
Fig. 2 shows the changes in the welding voltage and current time responses, and the changes of the arc length.The welding current rose and fell with the changes of H and ve, as expected.It can be seen from the first plot in Fig. 2 that the arc length h (dotted curve) decreased after the H changed from 16 mm to 12 mm and then increased back to the previous length.Accordingly, the electrode length l changed from 11.25 mm to 7.5 mm, which meant that the electrode melted at a higher speed when the current increased.In the second plot of Fig. 2 the electrode feeding speed was increased from 50 mm/s do 70 mm/s.This led a reduction of the arc resistance and an increasing of welding current.
A full-bridge circuit is simulated as the topology of the main inverter circuit.The load of the inverter depended on GMAW simulation model and was continuously changing.In Table II the design specification of the DC-DC converter and the circuit parameters are described, respectively.The simulation results from the welding using current control feedback and the PWM full-bridge DC-DC converter are shown in Fig. 5.
Constant welding speed was supposed.The welding torch was positioned at 16 mm (H) from work distance (CTWD) and after 5 ms H was increased to 18 mm, as is presented in the first graph of Fig. 5.The welding wire feed-rate ve was set at 70 mm/s.After 1 ms the welding current's set point was increased to 100 A, after 3 ms to 200 A, and finally after 7 ms to 150 A. The fourth plot in Fig. 5 presents the current control system transient response, which was stable with a small overshoot and was sufficiently fast.On the fifth plot the time response of the primary current is shown.For a better presentation of the generated PWM signals the same simulation results were plotted within a time window from about 3 ms to 4 ms, and marked with an arrow in the fourth graph in Fig. 5.In the first plot of Fig. 6, the PWM frequency generator is compared with current controller output (duty cycle).In second and third plots the PWM signals for driving the fullbridge DC-DC converter switches are presented.The periods of pulses A1 and A2 changes depended on the duty cycle determined by the discrete PI controller.The maximum simulation step-size was 0.1 μs and the discrete PI controller sample time was 100 μs.

V. CONCLUSIONS
A simulation application has been developed for simulating the GMAW process and inverter-based welding source.The mathematical model is based on physical descriptions of several parts of the GMAW process, as are the electric circuits of the power supply, the arc dynamics, the electrode melting process, etc.Further process parts, for example the welding drop dynamics and drop detachment process will be the subject of further research and should also be included in simulation model of the GMAW process.The simulation of inverter power source for welding power supply has been proposed and tested together with the GMAW simulation model.The simulation results showed that the conventional full-bridge DC-DC converter with appropriate current feedback controller makes the output welding current follow the set references.
The proposed models and simulations, which are combine together to simulate the power source circuits using simulations of the GMAW process, are suitable for the development new power source circuits, for example resonant converters.By establishing appropriate models of the GMAW process and the full-bridge DC-DC converter model, simulation is an effective tool for investigating new welding technologies, for example the Pulsed GMAW process, or Surface Tension Transfer welding process (STT).Simulation results could be very useful for the rapid development of new control algorithms and for the designing of new inverter control units.

Fig. 3 .
Fig. 3. DC-DC converter circuit using full-bridge PWM inverter with corresponding control unit.The DC-DC converter operates at constant switching frequency, which is usually limited to 20 kHz-50 kHz.The amplitude of the welding current depends on the change of the phase shift between transistors S1, S2, S3, and S4.The PWM signals are generated using a simple circuit and are used for driving four transistors by changing the duty cycle.In paper[12] the authors investigated the implementations of different PWM control techniques on a microcontroller.These modulation techniques are used in order to enhance the performances of three-phase inverters.The duty cycles are usually controlled using feedback controller (voltage, current, or both).In[13] and[14] the implementation studies of proportional-integral-derivative (PID) controller are presented, but we decided to use a PI controller because it satisfies control performances well, and the lack of derivative action may make the control system stabile in the case of noisy data.The discrete parallel form is

Fig. 4 .
Fig. 4. Simulated results of contact to workpiece voltage waveform (third plot) and welding current waveform (fourth plot).Simulation response of the GMAW model when the CTWD was changed from 16 mm to 12 mm (first plot) and the electrode feeding speed ve was changed from 0.5 m/min to 0.7 m/min (second plot).

Fig. 5 .
Fig. 5. Simulation results of the welding process with current control feedback and PWM full-bridge DC-DC converter-based welding power source.The upper plot shows the change of the CTWD from 16 mm to 18 mm.The forth plot presents the welding current transient response, and on the fifth plot the time response of the primary current is shown.

Fig. 6 .
Fig. 6.Simulation results of generated PWM signals, which depend on the duty cycle controlled with simple PI controller.The second and third plots show the PWM signals for driving the full-bridge DC-DC converter switches.The fourth and fifth plots show the corresponding changes of primary current and secondary-welding current.

TABLE I .
GMAW PROCESS SIMULATION PARAMETERS.