Journal of Manufacturing Systems Vol. 19/No. 6 2001
Weld Penetration Control System Design and Testing X.C. Li, Rapid Prototyping Laboratory, Stanford University, Stanford, California, USA D. Farson and R. Richardson, Dept. of Industrial, Welding and Systems Engineering, The Ohio State University, Columbus, Ohio, USA
In processes such as welding, where accurate models are difficult to formulate, robust controllers are promising because they can accommodate varying system characteristics. As a robust controller, the H” controller has developed rapidly since Glover and Doyle’ introduced it in 1988. The main advantage of H” optimal control is that it provides a framework for quantifying the trade-off between performance and robust stability in the face of plant model uncertainties. While classical control theories achieve good performance with low robustness, H” control theory achieves both good performance and robustness. Recently, a dynamic input/output model of a GMAW process was developed and used to design an H” penetration control.2J The basic idea of the control was to regulate the temperature at the point of maximum penetration on the bottom surface of the weld base metal to a value slightly higher than the melting temperature of the metal. However, for many applications, access to the back face of the weld for temperature measurement is not possible. Thus, using top-surface temperature measurements, a model calculating the maximum temperature at the bottom surface was developed. This work adapted the previous H” robust control system design for GMA welding control,*v3 implemented it using indirect penetration estimation via top-face temperature measurements, and tested its ability to maintain full penetration in the GTAW process. The control system yielded the potential to enhance welding quality and reduce welding cycle time and cost.
The design, implementation, and testing of a feedback control system for regulating gas tungsten arc weld (GTAW) penetration are presented in this study The derivation of reduced-order transfer function models representing the welding heat flow is also discussed. The control problem was cast in a robust design setting, and an /-F controller was designed for regulating weld penetration. The /-F’ control theory could quantify the trade-off between performance and robustness and achieve both gocd performance and robustness. The feedback control system, which used infrared temperature measurements, was implemented and tested. The dynamic and steady-state responses of the system to step input changes as well as unmodeled base metal width variations were studied by simulation and experimentally The experimental results were similar to the simulation predictions. The controller was able to provide regulation to achieve full penetration for GTAW and was also robust to control weld penetration during perturbations in base metal width. Keywords: W Control, Gas Tungsten Arc Welding (GTAW),
Weld Penetration, Welding Heat Flow Model
Introduction Automation offers the potential to improve welded product quality and consistency. However, ‘hard” or “open-loop” automation requires very repeatable preparation of parts and meticulous care in equipment setup. In practice, feedback control is often desired in automated welding systems to adapt for variations in raw materials, fit-up, and the like. These general comments apply specifically to weld penetration, which is a very important weld quality characteristic because it is closely related to the structural integrity of welds. Major issues in the design and implementation of feedback weld penetration controls are weld process modeling, controller design, and real-time penetration sensing methods. The research described in this paper focuses on the implementation and testing of a robust gas tungsten arc weld (GTAW) penetration control designed using robust P techniques and estimation of weld penetration based on temperature measurements.
Background Arcwelding refers to a process that is used to join metals by melting them with an arc established between an electrode and a workpiece. Although a
Journal of Manufacturing Systems Vol. 19/No. 6 2001
great variety of mechanisms govern the formation of arc welds, heat transfer is usually the dominant phenomena. During arc welding, the thermal cycles produced by the moving heat source cause physical state changes, metallurgical phase transformation, and transient thermal stress and distribution in the finished product and are largely responsible for the final weld bead shape and size (including penetration). Models of the arc welding heat flow phenomena are required for designing feedback weld penetration controls. In the following section, heat flow models of arc welding processes are discussed first. Next, previous investigations of welding penetration control are discussed.
where q. is the maximum heat intensity, B is the distribution parameter, and x,y are spatial coordinates in the plane of the surface. Recently, Boo and Cho* introduced an analytical solution to predict the time-varying temperature distribution in a finite-thickness medium with a distributed surface heat source. This analytical solution was obtained by solving a transient three-dimensional heat conduction equation with convection boundary and a Gaussian heat source distribution. An expression describing the temperature change from the initial plate temperature at point (x, y, z) at time t was written as follows: _ [w+x’(t2_x’(T)]2+ Y+Y'w-Y'(q*
Heat Flow Models of Arc Welding Process The majority of past efforts toward welding heat flow modeling have dealt with the quasi-stationary thermal state, where the temperature field is steady with respect to a coordinate system attached to a linearly-moving heat source (which is further assumed be of constant strength and to move with a constant speed). In a significant early analysis, Rosenthal43 considered conduction from an infinitesimal point or line heat sources moving in a straight line on semi-infinite or infinity-extended thin media, respectively. Those analyses made the following simplifying assumptions:
o2 [email protected]
where un’s are the positive roots of the equation =
with l3, = :,
1. Quasi-stationary state, 2. Concentrated welding heat at a point (in threedimensional analysis) or along a line (in two dimensions), 3. Constant material thermal properties.
4 l3, = X,
and the A,‘s given by
The symbols used in the above equation are defined in Table 1. The moving coordinate system is illustrated in Figure I (the references to Pi and PZ in this figure are explained further below). Because the heat source in Eq. (1) is time varying, this is a reasonable dynamic model on which to base a control design. Although the model still retains the assumption of constant thermal properties, experiments reported by Boo and Cho* indicated that this was not a major source of inaccuracy.
The assumption of concentrated heat source yields good temperature field predictions relatively far from the heat source but results in unacceptably large errors near the source. In a more accurate simulation, the effect of the size and shape of the heat source should be considered (that is, assumption 2 should be removed). Several investigators have measured the actual heat distributions in arcs on watercooled copper anodes. 6~7Experimental results show that the thermal flux into the surface of a medium due to the arc can be approximated by a Gaussian function, as follows:
Weld Penetration Feedback Controls Turning from heat flow modeling, presented next is a brief review of some past work in welding penetration control.
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List of Symbols
Description thermal conductivity density thermal diffusivity half width of the arc specific heat plate thickness effective convection coefficients at the top face effective convection coefficients at the bottom surface spatial coordinates in the plane of the surface x-direction in moving coordinate, w = x - vt time travel speed of heat source in w direction
Parameter K P a CT : hl hz SY W
Feedback Temperature Control Concept and Coordinate System
Hale and Hardt developed a special two-input, two-output GMAW process model, where the inputs of the system were welding velocity and wirefeed rate and the outputs were weld pool width and bead height.’ They later extended their controller by setting the weld bead depth as the third output. lo They set up one model to estimate the penetration using two Gaussian heat sources, one for modeling the welding arc and another for the droplet momentum and buoyancy forces on the bottom surface. A least-squares cost function and a recursive least-square estimator were used to identify the transfer function parameters. A CCD camera was positioned to measure the top-face weld bead width while the depth estimator estimated the penetration. Song and Hardt have developed another penetration control method based on a SISO system. l1 Welding velocity was used to control the weld bead depth. A depth estimator was modified for the time-varying welding conditions. They designed a closed-loop control system with a simple PI controller used in GMAW.
determined from analysis of the infinite-dimensional heat flow model described above. The feedback controller was designed using this relationship so that controlling the sensing point temperature also resulted in regulation of the temperature at the point of maximum penetration, P,, to a desired value. To design the H” control, the infinite-dimensional heat flow model discussed above was approximated by finite-dimensional transfer functions. The derivation of the finite-dimensional transfer functions is sketched below and closely follows the methods described in more detail in the papers of Zeren, Ozbay, and Yang2 and Yang.3 The locations of P1 and P2 were needed to begin the model formulation. Based on plots of the bottom-surface temperature based on Eq. (1) for various typical welding conditions, a location of (w, y, z) = (-11 mm, 0.0 mm, 3 mm) was chosen for P,. Boo and Cho investigated the sensor location PZ at which the temperature has an optimal correlation with the weld pool size.* According to the experimental results in this paper, the optimal point was located region of -12 mm < x < - 10 mm, 3 mm < y < 7 mm, and z = 0 mm, where the measurements are taken in a moving coordinate system as illustrated in Figure 2. In this investigation, the sensing point PZ was chosen in the center of the optimal region: (w, y, z) = (11 mm, 5 mm, 0.0 mm). Defining the temperature change as an output Y and collecting the variables, which are independent of the integration variable T, into K,, terms, Eq. (1) can be rewritten as follows:
H” Penetration Control Using Top-Face Temperature The goal of this work was to implement and test a feedback control for weld penetration. The basic idea of the control is illustrated in Figure 1. Temperature measurements were taken at a topsurface point, P1, in the vicinity of the welding arc. A feedback control was designed to modulate the welding heat input so as to regulate this temperature. The relationship between the temperature at the measuring point P2 and that at the point of maximum weld penetration, PI, was
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Parameters and Physical Constants for GTAW Welding Process
; CL= ld(pc) h
with _[W+“(t-z$+$ 202+4a(l-r) -L2(W
p, 2h,,K pt = h2/K 02 d w
Y Z V
Value 30.3 W/m “K 752 J/kg “K 7860 kg/m3 5.13e-06 50 W/m2 “K 18 W/m2 “K 1.65 0.594 2.25e-6 m2 3mm -11 mm 5mm 0 2 mm/s
=&[cos[%z)+Fsin(kz)] With the parameters given in Table 2, a third-order transfer function H,,(s), from the input q(t) to the temperature at the sensing point Pz, was obtained as
Equation (3) is a convolution integral for a linear time invariant system with input q(t), output Y(t), and the impulse response
0.1213 s3 +1.41s2 +0.6627s+O.1038
Further, the seventh-order transfer function, H,,(s), for the temperature at the point of maximum penetration, PI, was approximated as (7) H,, (s)=
The transfer function of the plant is given by the Laplace transform of the impulse response. The transfer function of this welding process is infinite dimensional, and there are infinitely many of these h,‘s in the impulse response in Eq. (3). However, by analysis of Eq. (2) for typical values of the GTAW process parameters, it was found that the pn’s could be approximated by the following:
0.9~~ +8.8? +175.9s4 +1495.1s3 +5313.7?
These finite-dimensional transfer functions were then used to design an H- controller. Again, the procedure is sketched here; further details can be found in the papers of Zeren, Ozbay, and Yang2 and Yang.’ The H” controller design analysis system is shown in Figure 2. W is the reference input, corresponding
Substituting Eqs. (4) and (5) into (3), it is observed that the h,‘s decay rapidly as y1increases. As a result, a finite-order approximation is quite reasonable from a practical viewpoint. Because the time function h,‘s are impulse responses of infinite-dimensional systems, the h,‘s can be approximated in the finite sum by functions of the form Figure 2
Generalized System Structure
ii, (t) = Cntmne-a"'
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to the desired temperature at Pr. C(s) is the transfer function of the H” controller. K3 and K4 are gains related to the magnitude of the reference signal and gains of the transfer functions HP1 and Hp2. The transfer functions W,(s) and W&s) are weighting functions that are used in the H” design process to specify the importance of different frequency bands in the optimization. In this investigation,
Simulatipnwith the cc&roller
0.6 -1 ... ...... . ..I....... i ... ....,_t___-+-....i . . i .. ....---_---b-_.. .... .. .. . ..... i_...._,....; ..._......_ ______ J__: l*; 0.4 . i.;;,;: ..... ... .. .. ... .. . . . . ... 1 ,1 ..I...2.; . . . .. .5...... ... .... . .. ..... I’ i ,’ i ,. i i i i i i
K3 = 1, K4 = 0.55
0.01 W, = 0.0162 s+0.0001’
An H” controller is obtained as a controller that satisfies the optimal H” performance defined by Zeren, Ozbay, and Yang* as follows:
Figure 3 Simulation Result for Step Input Reference from 0 to 1
Data acquisitkwand feedback controlcomputerwith ND, D/A
w,(K, + CK,H,*- CK,HP,) 1+ CH,,
Current command signal
1 + CH,,
Using the hinfsyn command from the Matlab’” Mu Analysis and Synthesis Toolbox,‘* the controller transfer function was found as follows: C(s)=
13.2~~+ 456.9s’ + 4121 .5s4 +6859s’ + 4673.2s’ + 1449.3s + 170.2 s’ + 42.6.~~+ 590.9~~+ 3 118.6~~+ 5494.7~~+ 4146s’ + 1037.6s - 8.0
The closed-loop system was simulated using MATLAB’“. The reduced-order transfer functions of Eqs. (6) and (7) were used for the plant. Typical simulation results for a step change in the reference input from 0 to 1 are shown in Figure 3. The steadystate sensing point temperature was 0.57 (close to the ideal value of 0.55 corresponding to the gain &), the 10% settling time was 11 seconds, the rise time was 9 seconds, and there was no overshoot.
Figure 4 Control System Block Diagram
feedback control computer sampled the temperature at point P2 and the arc voltage. The difference between the measured and the desired temperature was used by the H” control algorithm to generate a heat input command to the process. The heat input was defined as the product of arc voltage, welding current, and heat efficiency. Using the heat input command given by the controller along with the sampled arc voltage and assumed value of arc efficiency, a welding current command could be calculated and sent to the welding control computer. All input and output signals from the control calculation computer and the system controller were
Control System Implementation The H” control system was configured as shown in Figure 4. The main components were a computercontrolled robotic welding system, a second computer for performing data acquisition and computing the H” feedback control algorithm, and a noncontact temperature measuring system. At each iteration, the
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calibrated so that accurate control signal commands and measurements could be given. A noncontact optical temperature sensing system has been developed and yields good accuracy above 450°C.13 The H” control algorithm given by the transfer function in Eq. (8) was implemented digitally in statespace format, using the controller canonical form. The equivalent state space equations are as follows:
Welding Conditions Electrode Shielding gas Welding velocity Current Arc length
where x’ =
.... , ?”
A, B, C, and D matrices that implement the desired transfer tiction are as follows: A= 0
0 0 0
8.0 -1037.6 -0 0 0 B=
0, 0 0 1
To implement the controller in discrete time, the state-space controller Eqs. (9) were integrated numerically using Euler’s method: X k+l = xk +
Constant Reference Temperature at PI This series of experiments was designed to test the control system for maintaining the commanded bottom maximum temperature. Different reference temperatures were used and for every temperature more than six specimens were made. The rise times, 10% settling times, and overshoots matched each
(Axk + Bd+’ )At cXk+l
Argon, 25 cfh 2mmls O-150 Amps DC 2mm
Experiments were performed to test the ability of the H” control system for maintaining constant penetration of gas tungsten arc welds. Specifically, the controlled system step response and width perturbations on weld penetration were investigated. Under every condition, numerical specimens were made to test the consistency of the controller performance. The nominal welding conditions are listed in Table 3. The material was hot rolled AISI 1025 steel with a dimension of 152 mm x 63 mm x 3 mm. The feedback control program, running at a control iteration frequency of 7 Hz, collected measurements of the optical power and arc voltage as inputs into the Hw control calculation and then sent welding current commands to the welding power supply. However, due to the limitations of the temperature sensing system, accurate temperature measurements could be obtained only when the temperature was higher than about 450°C.13 If no special precautions were taken, it was found that the control was unstable during startup. A special provision for weld startup was implemented at the beginning of the control experiment: the reducedorder dynamic model of the welding heat flow [Eq. (6)] was used to generate temperature “feedback signals” until the theoretical feedback temperature was higher than 450°C. Afterward, the actual temperature measurements were used. Rise time, 10% settling time, and overshoot were used to evaluate the control performance. Rise time was defined as time for the output to change from 10% to 90% of the way to final steady value; the 10% settling time was defined as time needed for output to stay within 10% of the final steady value.
Control System Experimental Tests
where At was taken as 0.143 seconds and k was the iteration number.
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. . ._. __ &at input
Figure 5 Control Results for the Set PI Temperature of 1200°C
Figure 6 Control Results for the Set P, Temperature of 153VC
other well with less than 1.5% differences for different samples under every testing condition. Some typical results are to be presented. Reference temperatures of 1200°C and 1538°C were used in the tests. Because the AISI 1250 material melting point was about 1493”C, 1200°C and 1538°C would achieve partial weld penetration and full penetration, respectively. Because full penetration is necessary to achieve sound welding quality, reference temperatures less than 1493”C, which correspond to partial penetration for welds, were only chosen to test how well the controller controlled the temperatures at point Pi. Typical results are shown in Figures 5 and 6. The measured temperature and heat input command, generated by the H” controller, are plotted as functions of control iteration. Again, note that the control iteration rate was 7 Hz. In Figure 5 (Heat Input unit: Watt, Temperature unit: “C), the Pi temperature was set as 1200°C. Control system simulations predicted a final steadystate P2 temperature of I&* 12OO”C,which is 660°C. The simulated control performance results were 9 seconds rise time, 11 seconds settling time, and zero overshoot. The experimental results show that the controlled final temperature was about 686°C with about 9 seconds rise time, 12 seconds settling time, and 4°C overshoot. A detailed study of the experimental results revealed one discrepancy from the simulation predictions. In the experimental results, there were generally two sudden changes of the welding current. One was at the start point of the control program (at iteration SO) while another was at a temperature of 450°C where the controller stopped using the “theoretical” sensing temperature and began using actual photodiode temperature
measurements (at about iteration 150). The theoretical sensing point temperature was consistently lower than the actual temperature, causing the controller to generate a step change in heat input of about 100 watts. It appeared that the theoretical temperature increase rate was consistently less than the actual one, resulting in the observed discrepancy. Due to the sharp decrease in welding current, the rise time and settling time were a little longer than they would have been otherwise. In Figure 6, the reference maximum bottom temperature was 1538°C. According to the simulation, the final sensing point temperature should be 877°C with 9 seconds rise time, 11 seconds settling time, and zero overshoot. The experimental PZ temperature was found to be about 868°C with about 10 seconds rise time, 13 seconds settling time, 7°C overshoot. The second step change of the current was about 20 amps at iteration 135. From visual inspection of the welds, it was apparent that the different set point temperatures resulted in different weld penetration as expected. Figure 7 presents pictures taken from the backsides of the welds. Partial penetration was obtained for the set Pi temperatures of 1200°C because no melting lines appeared on the backside of the weld. As shown in Figure 7~2,only oxidation lines appeared after the welding. However, a full penetration was clearly achieved for the set 1538°C at Pi because the melting lines appeared and were surrounded by the oxidation lines. Reference Input Step Transition This series of experiments was designed to test the control system by changing the reference Pi tem-
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(a) Reference temperature of 1200°C
Figure 8 Control Results for Step Change of PI Temperature from llOO°C to 1500°C
(b) Reference temperature of 1538°C
Figure 7 Photos of the Welds for Constant PI Temperatures
perature suddenly during the welding process. Different combinations of temperatures were applied to test the controller. At least six specimens were made for every temperature combination. The results for different specimens for a single temperature combination were pretty consistent. The rise times and 10% settling times were about 1% different from each other, and overshoots were different from each other in less than 10°C. Figure 8 shows a typical result for a positive step transition of the reference P, temperature from 1100°C to 1500°C. Before changing the reference P, temperature, the approximate steady-state temperature at P2 was 63O”C, 3°C more than the predicted temperature, 627°C. Immediately after the positive step change at control iteration 300, the heat input increased by about 450 watts. The temperature curve quickly increased to a high point at about 825°C in about 7 seconds, then settled to about 82O”C, 35°C lower than the predicted 855OC. The settling time was about 14 seconds, 3 seconds more than the predicted 11 seconds. Because the “bump,” observed when transferring from simulated to actual temperature measurements, indicated that the theoretical and actual plant transfer functions were somewhat different, the fact that the experimental results still matched the simulated control results suggests that the H- controller was somewhat robust to plant variations. By visual inspection, as shown in Figure 9, there were no melting lines in the 1100°C zone, while melting lines (full penetration) appeared after the temperature was controlled to be 1500°C.
Figure 9 Photo of the Weld for Step Temperature
Base Metal Width Variations This series of experiments tested how the control system responded to unmodeled variations in base metal width. Width changes altered the conditions for heat conduction from the weld area, affecting both the dynamic and steady-state behavior of the welding process. The workpieces were cut to 2 1 mm wide in the midsection symmetrically. More than four testings were performed for each condition. The rise times and 10% settling times were less than 1.7% different from each other, and overshoots were somewhat different from each other up to 20°C. From visual inspection of the welds, the sizes and shapes of welds were fairly consistent. Although the results were not as consistent as the ones in previous sessions, the controller provided adequate regulation for the penetration because base metal width variation was unmodeled. Figures IO and II show a typical result for a reference P, temperature of 149O”C, which was only 3°C lower than the nominal melting point 1493°C of the base metal. At the beginning, the steady-state temperature was about 846”C, only 3°C lower than the predicted 849°C. When the welding arc passed the area with narrower base metal width, the measured temperature fluctuated from 872°C to 820°C.
Journal of Manufacturing Systems Vol. 19/No. 6 2001
,~ -._..__-_ 300
Figure IO Control Results in Base Metal with Width Variation
Figure 12 Results with Constant Heat Input in Base Metal with Width Variation
Figure I I Photo of the Weld in Base Metal with Width Variation
Figure 13 Photo of the Weld with Constant Heat Input in Base Metal with Width Variation
However, in Figure II, it was found that the weld bead width was nearly constant, and little amount of full penetration was observed. These results suggest that the controller was effective at maintaining constant penetration even with the base metal width perturbations. As shown in Figures 12 and 13, a noncontrolled result was obtained by applying a constant heat input, 625 watts, which corresponded to a theoretical reference Pi temperature of 1350°C. The peak temperature reached 9 15°C and the low was at about 792°C. This peak temperature of 915°C was 145°C different from the predicted 770°C. Excessive full penetration was observed throughout the area of the base metal width variation in Figure 13. Obviously, without the controller, the temperature of Pi was unable to be maintained throughout the area of the base metal width variation.
function models representing the welding heat flow was discussed. The control problem was cast in a robust design setting, and an Hm controller was designed to maintain full weld penetration. The H” controller quantified the trade-off between performance and robustness and achieved both good performance and robustness. The dynamic and steadystate responses of the system to step input changes as well as unmodeled base metal width variations were studied by simulation and experimentally. The experimental responses were similar to the simulation predictions. The controller was able to provide regulation to maximum bottom temperatures, and constant full weld penetrations for GTAW were achieved, as well as to provide regulation of weld penetration despite unmodeled changes in workpiece width. However, the implemented temperature measuring system could only provide accurate temperature information above 450°C. At the start of controlled GTAW processes, the measuring limitation generated “bumps” in heat input and might cause fluctuations in weld penetrations. Thus, the measuring system needs improvement to make the control system a better practical solution to industrial welding processes.
Conclusions In this paper, the design, implementation, and testing of a feedback control system for regulating gas tungsten arc weld (GTAW) penetration were presented. The derivation of reduced-order transfer
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11. J.B. Song and D.E. Hardt, “Simultaneous Control of Bead Width and Depth Geometry in GASW” 3rd Int’l Conf on Trends in Welding Research, S.A. David and J.M. Vitek, eds. (Metals Park, OH: ASM, 1992), ~~921-926. 12. G. Balas, A. Packard, J. Doyle, K. Glover, and R. Smith, “Mu-analysis and Synthesis Toolbox for MATLAB’“, Ver. 3.0” (Natick, MA: The Mathworks, 1993). 13. D. Farson, X.C. Li, and R. Richardson, “Infrared Measurement of Base Metal Temperature in Gas Tungsten Arc Welding,” Welding Journal (Sept. 1998), ~~396-404.
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Authors’ Biographies Xiaochun Li is a research assistant at the Rapid Prototyping Laboratory of Stanford University, where he performs research in shape deposition manufacturing of smart metallic structures with embedded sensors and laser and plasma-based material processing. He is a member of the American Society of Mechanical Engineers, the American Welding Society, and the Laser Institute of America. Dave Farson is an assistant professor in the Industrial, Welding and Systems Engineering department at The Ohio State University, where he performs research and teaches in the areas of laser materials processing and process monitoring and control. He previously worked at the Penn State Applied Research Laboratory and Westinghouse Science and Technology Center. He is a past president and fellow of the Laser Institute of America. Richard Richardson is an associate professor in the Industrial, Welding and Systems Engineering department at The Ohio State University, where he performs research and teaches in the area of welding process physics, automation, and control. He is a fellow of the American Welding Society.
(n22, 1990), pp143-151.