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Showing papers on "Gas metal arc welding published in 2003"


Journal ArticleDOI
TL;DR: In this article, an integrated and user-friendly environment has been developed to slice the part, plan the deposition parameters, and control the deposition process, including travel speed, touch angle, welding current, and arc voltage, to achieve the required density and three-dimensional geometry.

275 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical model combining the methods of enthalpy, effective-viscosity and volume-of-fluid is developed to simulate the metal transfer process in gas metal arc welding.
Abstract: A numerical model combining the methods of enthalpy, effective-viscosity and volume-of-fluid is developed to simulate the metal transfer process in gas metal arc welding. The model describes not only the influence on droplet profile and transfer frequency of electromagnetic force, surface tension, and gravity, but it can also model the nonisothermal phenomena such as heat transfer and phase change. The model has been used to study the shape of the melting interface on the welding wire, the droplet oscillation at wire tip, the characteristics of relevant physical variables and their roles in metal transfer. We find that the taper formation in spray transfer is closely related to the heat input on the unmelted portion of the welding wire, and the taper formation affects the globular–spray transition by decelerating the transfer process. The formation of satellite drops during the metal transfer process is also considered. High-speed photography, laser-shadow imaging, and metallographic analysis validate the numerical model, and recommendations are made on the topics that require further consideration for a more accurate metal transfer model.

121 citations


Journal ArticleDOI
TL;DR: In this paper, the authors presented predictions for a stationary welding process by the free-burning argon arc and treated the whole region of the welding process, namely, tungsten cathode, arc plasma, and stainless steel anode, in a unified numerical model to take into account the close interaction between the arc plasma and the molten anode.
Abstract: Numerical modeling of free burning arcs and their electrodes is useful for clarifying the heat transfer phenomena in the welding process and to elucidate those effects which determine the weld penetration. This paper presents predictions for a stationary welding process by the free-burning argon arc. The whole region of the welding process, namely, tungsten cathode, arc plasma and stainless steel anode is treated in a unified numerical model to take into account the close interaction between the arc plasma and the molten anode. The time dependent development of two-dimensional distributions of temperature and velocity, in the whole region of the welding process, are predicted at a current of 150 A. The weld penetration geometry as a function of time is thus predicted. It is shown also that different surface tension properties can change the direction of re-circulatory flow in the molten anode and dramatically vary the weld penetration geometry.

97 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the heat transfer efficiency of the pulsed gas metal arc welding (GMAW-P) process and calculated the arc power and heat input from arc current and voltage measurements and the heat input was also measured with a liquid nitrogen calorimeter.
Abstract: This study investigates the heat transfer efficiency of the pulsed gas metal arc welding (GMAW-P) process. The arc power and heat input were calculated from arc current and voltage measurements and the heat input was also measured with a liquid nitrogen calorimeter. The measured heat transfer efficiency for GMAW-P varied slightly over a wide range of pulse parameters, with an average value of 70%, a maximum of 72% and a minimum of 68%. Welding heat transfer efficiency based on arc power calculated as the product of average current and voltage was too high (averaging 82%), while that calculated using the product of the root mean square (RMS) of the average current and voltage was too low (averaging 61%). Both also varied significantly with pulsing parameters. Mathematical analysis shows that average instantaneous power values must be used when current and voltage vary significantly with time. The experimental differences between the average instantaneous power and the other calculated values are ex...

86 citations



Patent
30 May 2003
TL;DR: In this article, a method of controlling an arc welding system during a welding process is described, which includes dynamically regulating a rate of advancement and instantaneous melt rate of the electrode during each welding cycle in response to predetermined events occurring during the welding process.
Abstract: A method of controlling an arc welding system during a welding process is disclosed. The welding process has a plurality of welding cycles in which a consumable electrode (14) is advanced towards a workpiece (16). The method includes dynamically regulating a rate of advancement and instantaneous melt rate of the electrode during each welding cycle in response to predetermined events occurring during the welding process. The melt rate may be coordinated with the rate of advancement of the electrode to provide a wide range of stable deposition rates with a shielding gas such as CO2. An arc welding system for carrying out the method is also disclosed.

74 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe several methods for the determination of arc stability in MAG/MIG welding, which are based on measurement of time-varying welding current and welding voltage.

68 citations


Journal ArticleDOI
TL;DR: In this article, a numerical procedure to simulate metal transfer and the model will be used to analyze the transport processes involved in gas metal arc welding (GMAW). Advanced Computational fluid dynamics (CFD) techniques used in this model include a two-step projection method for solving the incompressible fluid flow; a volume of fluid (VOF) method for capturing free surface; and a continuum surface force (CSF) model for calculating surface tension.
Abstract: The present article describes a numerical procedure to simulate metal transfer and the model will be used to analyze the transport processes involved in gas metal arc welding (GMAW). Advanced Computational fluid dynamics (CFD) techniques used in this model include a two-step projection method for solving the incompressible fluid flow; a volume of fluid (VOF) method for capturing free surface; and a continuum surface force (CSF) model for calculating surface tension. The electromagnetic force due to the welding current is estimated by assuming several different types of current density distribution on the free surface of the drop. The simulations based on the assumption of Gaussian current density distribution show that the transition from globular to spray transfer mode occurs over a narrow current range and the size of detached drops is nonuniform in this transition zone. The analysis of the calculation results gives a better understanding of this physical procedure. Comparisons between calculated results and experimental results are presented. It is found that the results computed from the Gaussian assumption agree well with those observed in experiments.

62 citations


Journal ArticleDOI
TL;DR: In this paper, the authors dealt with multiple-wire submerged-arc welding and cladding with metal-powder addition, and found that the use of metal powder will increase the deposition rate, and the welding-arc efficiency and reduce the shielding-flux consumption.

59 citations


Proceedings ArticleDOI
03 Mar 2003
TL;DR: In this paper, the effects of many process parameters such as welding current, arc voltage, welding speed, defocusing distance, laser-to-arc distance on penetration depth, bead shape, spatter, arc stability and plasma formation were investigated.
Abstract: Researches and developments of laser and arc hybrid welding has been curried out since in 1978. Especially, CO 2 laser and TIG hybrid welding has been studied for increasing the penetration depth and welding speed. Recently laser and MIG/MAG/Plasma hybrid welding processes have been developed and applied to industries. It was recognized as a new welding process that promote the flexibility of the process for increasing the penetration depth, welding speed and allowable joint gap and improving the quality of the welds. In the present work, CO 2 Laser-MAG hybrid welding of carbon steel (SM490) was investigated to make clear the phenomenon and characteristics of hybrid welding process comparing with laser welding and MAG process. The effects of many process parameters such as welding current, arc voltage, welding speed, defocusing distance, laser-to-arc distance on penetration depth, bead shape, spatter, arc stability and plasma formation were investigated in the present work. Especially, the interaction of laser plasma and MAG arc plasma was considered by changing the laser to arc distance (=D LA ).

58 citations


Patent
06 Jan 2003
TL;DR: In this paper, an electric arc GMAW welder is provided, which welder includes a high speed switching power supply (10) with a controller (130) for creating a first or second weld process across the gap between a workpiece (W) and a welding wire (E) advanced toward the workpiece.
Abstract: An electric arc GMAW welder (A) is provided, which welder (A) includes a high speed switching power supply (10) with a controller (130) for creating a first or second weld process across the gap between a workpiece (W) and a welding wire (E) advanced toward the workpiece (W). The first process uses a first current waveform and the second process uses a second current waveform. A circuit is provided for shifting between the first and second weld processes. The shifting circuit includes a counter (212) for counting the waveforms in the first and second processes and a circuit (190) to shift from the process being processed to the other weld process when the waveform count of the weld process being processed reaches a preselected number for such weld process.

Journal ArticleDOI
TL;DR: In this article, the welding of duplex stainless steels has been reassessed by questioning traditional requirements of the weld metal and/or the heat affected zone (HAZ) using thin foil transmission electron microscopy (TEM).

Journal Article
TL;DR: In this paper, a welding system using electromagnetic arc oscillation was developed for narrow groove welding, where the electromagnet for applying a magnetic field to the welding arc was designed from the electromagnetic analysis results.
Abstract: Narrow groove welding is an important technique for increasing productivity in the manufacture of thickwalled components. The nature of the process demands an automated approach and precise control to ensure consistently high weld quality. The most important objective of narrow groove welding is to maintain uniform and sufficient penetration at both groove faces. Several different approaches, such as wire bending technique and wire rotating method, have been adopted in an attempt to minimize the incomplete fusion in the narrow groove GMAW process. In this study, a welding system using electromagnetic arc oscillation was developed for narrow groove welding. The electromagnet for applying a magnetic field to the welding arc was designed from the electromagnetic analysis results. This paper shows the arc and bead characteristics in narrow groove GMAW using electromagnetic arc oscillation. Based on the results, the appropriate welding and oscillation conditions were selected to satisfy high weld quality. Consequently, magnetic arc oscillation resulted in uniform and sufficient penetration to both groove faces. Arc signal characteristics for automatic joint tracking were also investigated. The periodic change of welding current in electromagnetic arc oscillation was examined by experiments and numerical analysis. To establish the mathematical model of the arc sensor, some assumptions were needed to calculate the arc length. Analytical results using these assumptions showed good agreement with experimental ones. The periodic signal was adopted to develop an automatic joint tracking system in narrow groove GMAW.

Book ChapterDOI
05 Aug 2003

Journal Article
TL;DR: In the second phase of a project to evaluate the feasibility of friction stir welding (FSW) to enhance weld performance and reduce fabrication coasts for the Advanced Amphibious Assault Vehicle (AAAV), a single-pass FSW butt-joint weld was made at 1.6 in/min travel speed in 1-in. 2519-T87 aluminum armor plate.
Abstract: The Advanced Amphibious Assault Vehicle (AAAV) is an armored personnel carrier under development by General Dynamics Amphibious Systems for the U.S. Marine Corps. Concuurent Technologies Corp. (CTC), through the National Center for Excellence in Metalworking Technology (NCEMT), recently completed the second phase of a project to evaluate the feasibility of friction stir welding (FSW) to enhance weld performance and reduce fabrication coasts for the AAAV. in phase I, single-pass butt-joint welds were made at 1.6 in./min travel speed in 1-in. 2519-T87 aluminum armor plate that exibited dramatically superior strength and ductility than those made by gas metal arc welding (GMAW) (Ref. 1). Ballistic shock test panels made using FSW butt-joint welds passed the ballistic shock impact test at velocities 30% more than MIL-STD-1946A requirements. Conventional 2519 GMAW butt-joint welds have never passed this demanding test requirement. Similar results were reported by General Dynamics Land Systems and the Edison Welding Institute for two-pass FSW butt-joint welds in 1.25-in. 2519 plates (Ref. 2). In phase II, the objective was to fabricate and test an AAAV floor section (used to verify mine blast performance of the AAAV hull) that would incorporate both FSW joints and extruded 2519 T-stiffeners. Design and construction of the test section required consideration of many pratical manufacturing issues, including developpment of procedures for joining the floor to the side-walls by friction stir welded corner joints, FSW around the chine actuator mount, and FSW of the floor panel to the lower glacis. Improved tool designs were developed and process parameters were optimized to increase the travel speed during FSW while improving the mechanical properties attained in Phase I. This article describes FSW process parameter and welding tool optimazation, fabrication and testing of the ballistic shock test panels, and construction of the AAAV floor test section.

Patent
01 Apr 2003
TL;DR: In this article, a combined welding method with a filler wire using both a YAG laser and an electric arc was proposed, whereby an arc was induced to the filler wire by a plume (plasma-activated gas and the metal vapor) inside and outside of a keyhole.
Abstract: A combined welding method with a filler wire using both a YAG laser and an electric arc, and a combined welding device with a filler wire using both a YAG laser and an electric arc. The welding is performed by directing a laser focus of a YAG laser on base materials and for welding in the vicinity of the focus by a filler wire, connecting a power source for applying a voltage to the filler wire between the filler wire and the base materials for welding, irradiating a YAG laser on the base materials for welding in the connecting condition, whereby an arc is induced to the filler wire by a plume (plasma-activated gas and the metal vapor), and holding the plume generated by YAG laser inside and outside of a keyhole.

Proceedings ArticleDOI
03 Mar 2003
TL;DR: In this article, a hybrid welding of TIG, MIG arc and YAG laser was developed for high-efficiency low-strain welding, taking the most advantages of both the laser and arc welding.
Abstract: Laser welding is capable of high-efficiency low-strain welding, and so its applications are started to various products. We have also put the high-power YAG laser of up to 10 kW to practical welding use for various products. On the other hand the weakest point of this laser welding is considered to be strict in the welding gap aiming allowance. In order to solve this problem, we have developed hybrid welding of TIG, MIG arc and YAG laser, taking the most advantages of both the laser and arc welding. Since the electrode is coaxial to the optical axis of the YAG laser in this process, it can be applied to welding of various objects. In the coaxial MIG, TIG-YAG welding, in order to make irradiation positions of the YAG laser beams having been guided in a wire or an electrode focused to the same position, the beam transmitted in fibers is separated to form a space between the separated beams, in which the laser is guided. With this method the beam-irradiating area can be brought near or to the arc-generating point. This enables welding of all directions even for the member of a three-dimensional shape. This time we carried out welding for various materials and have made their welding of up to 1 mm or more in welding groove gap possible. We have realized high-speed 1-pass butt welding of 4m/min in welding speed with the laser power of 3 kW for an aluminum alloy plate of approximately 4 mm thick. For a mild steel plate also we have realized butt welding of 1m/min with 5 kW for 6 mm thick. Further, in welding of stainless steel we have shown its welding possibility, by stabilizing the arc with the YAG laser in the welding atmosphere of pure argon, and shown that this welding is effective in high-efficiency welding of various materials. Here we will report the fundamental welding performances and applications to various objects for the coaxial MIG, TIG-YAG welding we have developed.

01 Jan 2003
TL;DR: Gas metal arc welding (GMAW) is a semi-automatic or automatic arc welding process in which a continuous and consumable wire electrode and a shielding gas are fed through a welding gun as discussed by the authors.
Abstract: Gas metal arc welding (GMAW), sometimes referred to by its subtypes metal inert gas (MIG) welding or metal active gas (MAG) welding, is a semi-automatic or automatic arc welding process in which a continuous and consumable wire electrode and a shielding gas are fed through a welding gun. A constant voltage, direct current power source is most commonly used with GMAW, but constant current systems, as well as alternating current, can be used. There are four primary methods of metal transfer in GMAW, called globular, short-circuiting, spray, and pulsed-spray, each of which has distinct properties and corresponding advantages and limitations.

Book
01 Jan 2003
TL;DR: In this article, the authors present a real-time measurement of welding temperature field using a calorimetric imaging method and an automatic seam-tracking machine with an arc sensor.
Abstract: Part 1 Dynamic behaviour of arc welding: Theoretical analysis Dynamic characteristics of power sources Experimental study. Part 2 Welding arc control: Control method QH-ARC 101 Control method QH-ARC 102 and 103 Arc control CO2 welding and AC MIG welding. Part 3 Arc sensors and seam tracking: Sensors for weld-seam tracking Mathematical models of arc sensors Processing of arc sensor signals An automatic seam-tracking machine with an arc sensor. Part 4 Real time measurement of welding temperature- field: Principles of the calorimetric imaging method Study of the calorimetric imaging method Design of a calorimetric imaging apparatus Practical measurement and application. Part 5 Automatic path programming of robot: Vision systems and automatic path programming.

Journal ArticleDOI
TL;DR: Weld production tests were made using friction stir (FSW) and MIG welding for welding extruded panels Production times were measured using a 2-m long double-skinned EN-AW 6005A-profile joint as a basic unit Production time data were used for productivity calculations of different welding machine arrangements.
Abstract: Weld production tests were made using friction stir (FSW) and MIG welding for welding extruded panels Production times were measured using a 2-m long double-skinned EN-AW 6005A-profile joint as a basic unit Production time data were used for productivity calculations of different welding machine arrangements Furthermore, a cost comparison was made based on the production time, machine investment, license, consumable and tooling costs MIG welding costs were dominated by labour wages and machine investment and by a lesser degree by filler material costs FSW costs were dominated by machine investment, fabrication license and labour wages FSW was more economical than MIG when the annual production volume was large enough, in the order of some tens of km of weld per year


Journal ArticleDOI
01 Sep 2003
TL;DR: In this paper, a 20-mm thick austenitic stainless steel was welded using narrow gap configuration with a multi-pass technique, in which narrow gap and filler wire was applied.
Abstract: Laser welding has shown many advantages over traditional welding methods in numerous applications. The advantages are mainly based on very precise and powerful heat source of laser light, which change the phenomena of welding process when compared with traditional welding methods. According to the phenomena of the laser welding, penetration is deeper and thus welding speed is higher. Because of the precise power source and high-welding speed, the heat input to the workpiece is small and distortions are reduced. Also, the shape of laser weld is less critical for distortions than traditional welds. For welding thick sections, the usability of lasers is not so practical than with thin sheets, because with power levels of present Nd:YAG lasers depth of penetration is limited up to about 10 mm by single-pass welding. One way to overcome this limitation is to use multi-pass laser welding, in which narrow gap and filler wire is applied. By this process, thick sections can be welded with smaller heat input and then smaller distortions and the process seems to be very effective comparing “traditional” welding methods, not only according to the narrower gap. Another way to increase penetration and fill the groove is by using the so-called hybrid process, in which laser and GMAW (gas metal arc welding) are combined. In this paper, 20-mm thick austenitic stainless steel was welded using narrow gap configuration with a multi-pass technique. Two welding procedures were used: Nd:YAG laser welding with filler wire and with addition of GMAW, the hybrid process. In the welding experiments, it was noticed that both processes are feasible for welding thicker sections with good quality and with minimal distortions. Thus, these processes should be considered when the evaluation of the welding process is done for joining vacuum vessel sectors of ITER.

Journal Article
TL;DR: In this paper, the authors used an artificial neural network (ANN) to estimate spatter rate for the short circuiting transfer mode of the gas metal arc (GMA) welding process.
Abstract: This study was conducted to develop the best model to estimate spatter rate for the short circuiting transfer mode of the gas metal arc (GMA) welding process. Utilizing an artificial neural network. The spatter rate generated during welding is a barometer of process stability for metal transfer, and it depends on the periodic waveforms of the welding current and arc voltage in the short circuiting mode. delve factors representing the characteristics of the waveforms as inputs and the spatter rate as an output were employed as variables for the neural network. Two neural network models were evaluated for estimating the spatter rate: one model did not consider arc extinction; the other model did. The input vector and the nodes of hidden layers for each model were optimized to provide an adequate fit. and estimated performance of each optimized model to the spatter rate was assessed and compared with the previously proposed model. It was, in addition, demonstrated in this study that the combined neural network model was more effective in predicting the spatter rate than other models through evaluation of the estimated performance of each optimized model.

Journal ArticleDOI
01 Nov 2003
TL;DR: In this paper, a numerical approach is presented in order to support the control of distortion and overall quality of sound welds, which is the main targets in the design and manufacturing of sound welding.
Abstract: The control of distortion and the overall quality are the main targets in the design and manufacturing of sound welds. In this paper a numerical approach is presented in order to support th...

Journal ArticleDOI
TL;DR: In this article, the nitrogen absorption by iron, Fe-20Cr-10Ni alloy, and SUS329J1 duplex stainless steel during CO2 laser welding in an Ar-N2 gas mixture was investigated and compared with equilibrium data predicted on Sieverts' law and data on absorption during arc and YAG laser welding.
Abstract: Nitrogen absorption by iron, Fe-20Cr-10Ni alloy, and SUS329J1 duplex stainless steel during CO2 laser welding in an Ar-N2 gas mixture was investigated and compared with equilibrium data predicted on Sieverts’ law and data on absorption during arc and YAG laser welding. The nitrogen absorption during CO2 laser welding is lower than that during arc welding, but higher than that during YAG laser welding. Compared with arc welding, the lesser contact of monatomic nitrogen with the weld pool surface and the higher partial pressure of metal vapor in the keyhole may result in the lower nitrogen absorption during CO2 laser welding, while the very low density of monatomic nitrogen in the atmosphere during YAG laser welding due to the low-temperature plume may lead to the lower nitrogen absorption during YAG laser welding than during CO2 laser welding.

Proceedings ArticleDOI
03 Mar 2003
TL;DR: Hybrid welding was carried out on Type 304 stainless steel plate under various conditions using YAG laser combined with TIG arc as mentioned in this paper, and it was found that hybrid welding possessed many features in comparison with YAG Laser welding.
Abstract: Hybrid welding was carried out on Type 304 stainless steel plate under various conditions using YAG laser combined with TIG arc. During arc and laser-arc hybrid welding, arc voltage variation was measured, and arc plasma, laser-induced plume and evaporation spots as well as keyhole behavior and liquid flow in the molten pool were observed through CCD camera and X-ray real-time transmission apparatus. It was consequently found that hybrid welding possessed many features in comparison with YAG laser welding. The deepest weld bead could be produced when the YAG laser beam of high power density was shot on the molten pool made beforehand stably with TIG arc. A keyhole was long and narrow, and its behavior was rather stable inside the molten pool. It was also confirmed that porosity was reduced by the suppression of bubble formation in hybrid welding utilizing a laser of a moderate power density.

Journal ArticleDOI
TL;DR: In this paper, the authors exploited low heat input characteristics of laser welding to effectively control grain coarsening in the fusion zone (FZ) and in the heat affected zone (HAZ).
Abstract: One of the major factors influencing weldability of stabilized 17 wt% Cr ferritic stainless steels is extensive grain coarsening in the fusion zone (FZ) and in the heat affected zone (HAZ). This study aimed at exploiting low heat input characteristics of laser welding to effectively control grain coarsening in the FZ and HAZ of 1.2-mm thick stabilized 17 wt% Cr ferritic stainless steel weldment. The study demonstrated that as compared with gas tungsten arc welding (GTAW), laser welding brought about significant grain refinement in the FZ and HAZ. Laser weldments exhibited superior ductility over their GTA counterparts. An important observation of the study was that, in contrast to GTA weldment, laser weldment was associated with weaker interfaces along columnar grain boundaries in the FZ that served to arrest crack propagation normal to them.

Patent
03 Mar 2003
TL;DR: In this article, a welding wire comprising a flux core having a core composition alloyed with a combination of alloying elements is described, wherein the flux core comprises between 10% and 50% of the total weight of the weld wire.
Abstract: A welding wire comprising a flux core having a core composition alloyed with a combination of alloying elements is described. The alloying elements comprise Cr and N, wherein the flux core comprises between 10% and 50% of the total weight of the weld wire. A metal sheath encapsulates the flux core, wherein the metal sheath comprises between about 90% and 50% of the total weight of the welding wire and wherein the welding wire can be used in a welding process without destabilizing a welding arc. One of the applications of the wire and welding process of the present invention is hard surfacing of the steel mill rolls, which are hollow cylinders usually on continuous casters. As an example, the rolls welded by the wire and method of the present invention can have a diameter of about 12 inches or less. Additionally, a welding apparatus comprising a welding gun with a device for feeding an electrode into the welding gun is described. The corresponding welding process calls for gas shielding of the electrode to reduce spatter and smoke emission while creating a smooth weld bead surface requiring less grinding and finishing. The resulting weld deposit has enhanced resistance to pitting corrosion.

Journal ArticleDOI
01 May 2003
TL;DR: In this paper, sound generated during the gas-metal arc welding process in the short-circuit mode was studied, and theoretical and experimental analyses of the acoustic signals have shown that t...
Abstract: In this paper sound generated during the gas-metal arc welding process in the short-circuit mode was studied. Theoretical and experimental analyses of the acoustic signals have shown that t...

Journal ArticleDOI
TL;DR: In this article, the effects of micro-plasma arc welding on the morphology and quality of stainless steel edge joint welds were investigated and the results indicated that the collimated shape of the low current plasma arc was mainly responsible for the low sensitivity of the weld morphology to variations in the nozzle standoff distances.
Abstract: The effects of the process parameters of micro-plasma arc welding (micro-PAW) on the morphology and quality of stainless steel edge joint welds were investigated. Micro-PAW was applied on type 304 stainless steels to produce an edge joint weld. Welding experiments were carried out for various combinations of arc current, welding speed, arc length, shielding gas, and clamp distance, with all other operating conditions held constant. The experimental results indicated that the collimated shape of the low current plasma arc was mainly responsible for the low sensitivity of the weld morphology to variations in the nozzle standoff distances. The arc voltage increased with increasing quantity of added hydrogen in the argon shielding gas. It was also found that satisfactory edge joint welds can be formed using a clamp distance of 0.35 mm, and that the edge joint penetration on a 0.1 mm thickness stainless steel is about 60% of the clamp distance.