Cook, G.E., Anderson, K, Barnett, R.J., Wallace, A.K., Spee, R, Sznaier, M, Sanchez Pena, Rs."Industrial Systems The electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRc Press llc. 2000
Cook, G.E., Anderson, K., Barnett, R.J., Wallace, A.K., Spée, R., Sznaier, M., Sánchez Peña, R.S. “Industrial Systems” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
George E. Cook Kristin anderser 104 Marel Corporation Robert joel Barnett Industrial Systems Alan k. wallace Oregon State University Rene spee 104.1 Welding and Bonding Control System Requirements. System Parameters. Welding Mario sznaier System. Sensing. Modeling .Control. Conclusions 104.2 Large Drives University Park Configurations. Selection and Compatibility. Principles and Features of Operation. Control Aspects. Future Trends Ricardo s. sanchez pena 104.3 Robust Syster iversity of Buenos A Robustness and Feedback. Robust Stability and Performance F Control . Structured Uncertainty. Robust Identification 104.1 Welding and Bonding George E. Cook, Kristinn Andersen, and Robert Joel Barnett Most welding processes require the application of heat or pressure, or both, to produce a bond between the parts being joined. The welding control system must include means for controlling the applied heat, pressure, and filler material, if used, to achieve the desired weld microstructure and mechanical properties. Welding usually involves the application or development of localized heat near the intended joint Welding processes that use an electric arc are the most widely used in industry. Other externally applied heat sources of importance include electron beams, lasers, and exothermic reactions(oxyfuel gas and thermit). For fusion welding pI a high energy density heat source is normally applied to the prepared edges or surfaces of the members to be joined and is moved along the path of the intended joint. The power and energy density of the heat source must be sufficient to accomplish local melting Control System Requir Insight into the control system requirements of the different welding processes can be obtained by consideration of the power density of the heat source, interaction time of the heat source on the material, and effective spot size of the heat source A heat source power density of approximately 10 W/cm2 is required to melt most metals [Eagar, 1986 Below this power density the solid metal can be expected to conduct away the heat as fast as it is being introduced. On the other hand, a heat source power density of 106 or 107 W/cm will cause vaporization of most metals within a few microseconds, so for higher power densities no fusion welding can occur. Thus, it can be concluded that the heat sources for all fusion welding processes lie between approximately 10and 10 W/cm heat intensity. Examples of welding processes that are characteristic of the low end of this range include oxyacetylene welding electroslag welding, and thermit welding. The high end of the power density range of welding is occupied by laser beam welding and electron beam welding. The midrange of heat source power densities is filled in by the various arc welding processes. For pulsed welding, the interaction time of the heat source on the material is determined by the pulse duration, whereas for continuous welding the interaction time is proportional to the spot diameter divided by the travel speed. The minimum interaction time required to produce melting can be estimated from the relation for a planar heat source given by[ Eagar, 1986] c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 104 Industrial Systems 104.1 Welding and Bonding Control System Requirements • System Parameters • Welding System • Sensing • Modeling • Control • Conclusions 104.2 Large Drives Configurations • Selection and Compatibility • Principles and Features of Operation • Control Aspects • Future Trends 104.3 Robust Systems Robustness and Feedback • Robust Stability and Performance • H∞ Control • Structured Uncertainty • Robust Identification 104.1 Welding and Bonding George E. Cook, Kristinn Andersen, and Robert Joel Barnett Most welding processes require the application of heat or pressure, or both, to produce a bond between the parts being joined. The welding control system must include means for controlling the applied heat, pressure, and filler material, if used, to achieve the desired weld microstructure and mechanical properties. Welding usually involves the application or development of localized heat near the intended joint. Welding processes that use an electric arc are the most widely used in industry. Other externally applied heat sources of importance include electron beams, lasers, and exothermic reactions (oxyfuel gas and thermit). For fusion welding processes, a high energy density heat source is normally applied to the prepared edges or surfaces of the members to be joined and is moved along the path of the intended joint. The power and energy density of the heat source must be sufficient to accomplish local melting. Control System Requirements Insight into the control system requirements of the different welding processes can be obtained by consideration of the power density of the heat source, interaction time of the heat source on the material, and effective spot size of the heat source. A heat source power density of approximately 103 W/cm2 is required to melt most metals [Eagar, 1986]. Below this power density the solid metal can be expected to conduct away the heat as fast as it is being introduced. On the other hand, a heat source power density of 106 or 107 W/cm2 will cause vaporization of most metals within a few microseconds, so for higher power densities no fusion welding can occur. Thus, it can be concluded that the heat sources for all fusion welding processes lie between approximately 103 and 106 W/cm2 heat intensity. Examples of welding processes that are characteristic of the low end of this range include oxyacetylene welding, electroslag welding, and thermit welding. The high end of the power density range of welding is occupied by laser beam welding and electron beam welding. The midrange of heat source power densities is filled in by the various arc welding processes. For pulsed welding, the interaction time of the heat source on the material is determined by the pulse duration, whereas for continuous welding the interaction time is proportional to the spot diameter divided by the travel speed. The minimum interaction time required to produce melting can be estimated from the relation for a planar heat source given by [Eagar, 1986] George E. Cook Vanderbilt University Kristinn Andersen Marel Corporation Robert Joel Barnett Vanderbilt University Alan K. Wallace Oregon State University René Spée Oregon State University Mario Sznaier Pennsylvania State University — University Park Ricardo S. Sánchez Peña University of Buenos Aires Argentina
ADVANCED WELDING TORCH concept of variable polarity plasma arc(VPPA)welding employs a variable current waveform that ables the welding system to operate for preset time increments in either of two polarity modes for nost effective joining of troublesome light alloys such as aluminum and magnesium. Although the VPPA concept dates back to 1947, it was never fully developed. ding techniques were inadequate for the job of joining the nuge alun. recog In the late 1970s, when the Space Shuttle was in early development, NASA recognized that the gments of the Shuttle External Tank. Marshall Space Flight Center(MSFC) initiated the development of VPPA welding The B&B Precision Machine Variable Polarity Plasma Arc welding torch. Photo courtesy of National Aeronautics and Space Admin m =[pIpal where Pa is the heat source density(watts per square centimeter)and K is a function of the thermal conductivity and thermal diffusivity of the material. For steel, Eagar gives K equal to 5000 W/cm2/s. Using this value for K, one sees that the minimum interaction time to produce melting for the low power density processes, such as beam processes, such as laser beam welding with a power density on the order of 10 W/cm,, is 25 us Interaction times for arc welding processes lie somewhere between these extremes An example of practical process parameters for a continuous gas tungsten arc weld(GTAW) are 100 A, 12 V, gas, 2.4-mm diameter electrode, and 50-degree tip angle has been found to be approximately 8 x 10 W aa and travel speed 10 ipm(4.2 mm/s). The peak power density of a 100-A, 12-v gas tungsten arc with argon shieldi e 2000 by CRC Press LLC
© 2000 by CRC Press LLC tm = [K/pd]2 where pd is the heat source density (watts per square centimeter) and K is a function of the thermal conductivity and thermal diffusivity of the material. For steel, Eagar gives K equal to 5000 W/cm2 /s. Using this value for K, one sees that the minimum interaction time to produce melting for the low power density processes, such as oxyacetylene welding with a power density on the order of 103 W/cm2 , is 25 s, while for the high energy density beam processes, such as laser beam welding with a power density on the order of 106 W/cm2 , is 25 ms. Interaction times for arc welding processes lie somewhere between these extremes. An example of practical process parameters for a continuous gas tungsten arc weld (GTAW) are 100 A, 12 V, and travel speed 10 ipm (4.2 mm/s). The peak power density of a 100-A, 12-V gas tungsten arc with argon shielding gas, 2.4-mm diameter electrode, and 50-degree tip angle has been found to be approximately 8 3 103 W/cm2 . ADVANCED WELDING TORCH he concept of variable polarity plasma arc (VPPA) welding employs a variable current waveform that enables the welding system to operate for preset time increments in either of two polarity modes for most effective joining of troublesome light alloys such as aluminum and magnesium. Although the VPPA concept dates back to 1947, it was never fully developed. In the late 1970s, when the Space Shuttle was in early development, NASA recognized that the thenexisting welding techniques were inadequate for the job of joining the huge aluminum segments of the Space Shuttle External Tank. Marshall Space Flight Center (MSFC) initiated the development of VPPA welding. The B&B Precision Machine Variable Polarity Plasma Arc welding torch. (Photo courtesy of National Aeronautics and Space Administration.) T
In the course of its development, it became apparent that the technique had broad potential for improving weld reliability and lowering costs. Since there were no suitable commercially available tools for VPPA C expanded its development effort to include a welding torch that would have dual utility, as nent of NASAs external tank welding system and as a component of derivative systems for com applications. The torch contract was awarded to B&B Precision Machine, Owens Cross Road, Alabama. B&B, working in cooperation with MSFC's Materials and Processing Laboratory, developed and patented a shuttle-use torch and continued development of VPPA. A major step in the late 1980s was a program to fully automate the system and eliminate the hand of the welder on the controls. In 1989, a NASA decision to change the material of the external tank triggered a B&B development. The new alloy in some cases required"tack"welds prior to robotic seam welding Since tack welds are performed by hand, B&B was assigned to develop a smaller version of the torch that would be easier to manipulate and would meet the needs of applications where access was limited. B&B delivered a prototype small torch in 1992 The small torch has the same features and advantages as the original torch, but it fits in approximately half the space. The VPPA welding system and the B&b torch continue to make all the welds in the external ank of the Space Shuttle and they have been selected as the preferred welding approach for the International pace Station.( Courtesy of National Aeronautics and Space Administration. A small version of the B&B torch is used in commercial sheet metal welding. (Photo courtesy of National Aeronautics and Space Administration.) Assuming an estimated spot diameter of 4 mm, the interaction time(taken here as the spot diameter by the travel speed)is 0.95 s. At the other extreme, 0.2-mm(0.008-in )material has been laser welded in /min(1270 mm/s)at 6 kW average power. Assuming a spot diameter of 0.5 mm, the interaction time is 3.94 104s. Spot diameters for the high density processes vary typically from 0.2 mm to 1 mm, while the spot diameters for arc welding processes vary from roughly 3 mm to 10 mm or more. Assuming a rule of thumb of 1/10 the spot diameter for positioning accuracy, we conclude that typical positioning accuracy requirements for the high power density processes is on the order of 0.1 mm and for the arc welding processes is on the order of l mm. The required control system response time should be on the order of the interaction time and, hence, may vary from seconds to microseconds, depending on the process chosen. With these requirements it can be conclude that the required accuracy and response speed of control systems designed for welding increases as the power c2000 by CRC Press LLC
© 2000 by CRC Press LLC Assuming an estimated spot diameter of 4 mm, the interaction time (taken here as the spot diameter divided by the travel speed) is 0.95 s. At the other extreme, 0.2-mm (0.008-in.) material has been laser welded at 3000 in./min (1270 mm/s) at 6 kW average power. Assuming a spot diameter of 0.5 mm, the interaction time is 3.94 3 10-4 s. Spot diameters for the high density processes vary typically from 0.2 mm to 1 mm, while the spot diameters for arc welding processes vary from roughly 3 mm to 10 mm or more. Assuming a rule of thumb of 1/10 the spot diameter for positioning accuracy, we conclude that typical positioning accuracy requirements for the high power density processes is on the order of 0.1 mm and for the arc welding processes is on the order of 1 mm. The required control system response time should be on the order of the interaction time and, hence, may vary from seconds to microseconds, depending on the process chosen. With these requirements it can be concluded that the required accuracy and response speed of control systems designed for welding increases as the power In the course of its development, it became apparent that the technique had broad potential for improving weld reliability and lowering costs. Since there were no suitable commercially available tools for VPPA welding, MSFC expanded its development effort to include a welding torch that would have dual utility, as a component of NASA’s external tank welding system and as a component of derivative systems for commercial applications. The torch contract was awarded to B&B Precision Machine, Owens Cross Road, Alabama. B&B, working in cooperation with MSFC’s Materials and Processing Laboratory, developed and patented a shuttle-use torch and continued development of VPPA. A major step in the late 1980s was a program to fully automate the system and eliminate the hand of the welder on the controls. In 1989, a NASA decision to change the material of the external tank triggered a new B&B development. The new alloy in some cases required “tack” welds prior to robotic seam welding. Since tack welds are performed by hand, B&B was assigned to develop a smaller version of the torch that would be easier to manipulate and would meet the needs of applications where access was limited. B&B delivered a prototype small torch in 1992. The small torch has the same features and advantages as the original torch, but it fits in approximately half the space. The VPPA welding system and the B&B torch continue to make all the welds in the external tank of the Space Shuttle and they have been selected as the preferred welding approach for the International Space Station. (Courtesy of National Aeronautics and Space Administration.) A small version of the B&B torch is used in commercial sheet metal welding. (Photo courtesy of National Aeronautics and Space Administration.)
INDIRECIWELD PARAMEIERS_(IWP) PARAMETERS_(DWP) VOLTAGE MATERIAL BEAD WIDT PARAMATERS NETRATION ELECTRODE FEED RATE MECHANICAL ELECTRODE EXTENSION MICROSTRUCTURE RAVEL ANGLE :GRAINSIZE FOCUSED SPOT SIZE EPTH OF FOCUS PULSE DURATION DISCONTINUITIES: EPETITION RATE POROSITY BEAM POWER INCOMPLETE FUSION FIGURE 104.1 Input and output variables of welding process. density of the process increases. Furthermore, it is clear that the high power density processes must be automated because of the humans inability to react quickly and accurately enough System Parameters The variables of the welding process are separated here into direct weld parameters(DwP)and indirect weld parameters(IWP)[Cook, 1981]. The DWP are those pertaining to the weld reinforcement and fusion zone ies of the completed weld, weld microstructure, and discontinuities. The IWP are those inpu collectively control the DWP. The IWP are the welding equipment setpoint variables, e.g travel speed, electrode feed rate, travel angle, electrode extension, focused spot size,and beam power Welding System The various DWP, or process variables, that we would like to control and the many possible IWP, or equipment variables, that we may set to achieve the desired output are shown in Fig. 104.1. From the standpoint of feedback control, the welding process depicted in Fig. 104.1 presents two principal problems: (1)in most cases the relationships between the IWP and DwP are nonlinear, and(2)the variables are generally highly coupled With most production welding today, the designer of the welded part specifies the desired weld characteristics he DwP), including acceptable tolerance windows. The job of the welding engineer then is to determine a set of IwP that will produce the desired DwP. Most automated welding systems today may be expected to have ood control over the IWP, including joint tracking for heat source positioning. Therefore, if production floor onditions do not differ too much from the laboratory conditions under which the weld procedures were developed, then the welding operation can be expected to satisfy quality inspection and control procedures. If not, human operators must be depended upon to provide the necessary feedback to make corrective actions in the welding equipment settings The human involvement in this scenario can be reduced or eliminated by sensing selected DWP, comparing he sensed variables with desired values, and implementing a multivariable controller that will reduce auto- matically the error between the desired and sensed DwP to zero or an acceptably low difference Dynamic and steady-state process models are required for both design and stable operation of the multivariable feedback control system. However, the models do not need to be as globally accurate as the models required for open loop control. In exchange for accuracy, the models used for control system purposes must be computable in real time, and generally, it is important that they provide both steady-state and dynamic information of the nterrelationships between the coupled variables of the system. It is generally important that these relationships e 2000 by CRC Press LLC
© 2000 by CRC Press LLC density of the process increases. Furthermore, it is clear that the high power density processes must be automated because of the human’s inability to react quickly and accurately enough. System Parameters The variables of the welding process are separated here into direct weld parameters (DWP) and indirect weld parameters (IWP) [Cook, 1981]. The DWP are those pertaining to the weld reinforcement and fusion zone geometry, mechanical properties of the completed weld, weld microstructure, and discontinuities. The IWP are those input variables that collectively control the DWP. The IWP are the welding equipment setpoint variables, e.g., voltage, current, travel speed, electrode feed rate, travel angle, electrode extension, focused spot size, and beam power. Welding System The various DWP, or process variables, that we would like to control and the many possible IWP, or equipment variables, that we may set to achieve the desired output are shown in Fig. 104.1. From the standpoint of feedback control, the welding process depicted in Fig. 104.1 presents two principal problems: (1) in most cases the relationships between the IWP and DWP are nonlinear, and (2) the variables are generally highly coupled. With most production welding today, the designer of the welded part specifies the desired weld characteristics (the DWP), including acceptable tolerance windows. The job of the welding engineer then is to determine a set of IWP that will produce the desired DWP. Most automated welding systems today may be expected to have good control over the IWP, including joint tracking for heat source positioning. Therefore, if production floor conditions do not differ too much from the laboratory conditions under which the weld procedures were developed, then the welding operation can be expected to satisfy quality inspection and control procedures. If not, human operators must be depended upon to provide the necessary feedback to make corrective actions in the welding equipment settings. The human involvement in this scenario can be reduced or eliminated by sensing selected DWP, comparing the sensed variables with desired values, and implementing a multivariable controller that will reduce automatically the error between the desired and sensed DWP to zero or an acceptably low difference. Dynamic and steady-state process models are required for both design and stable operation of the multivariable feedback control system. However, the models do not need to be as globally accurate as the models required for openloop control. In exchange for accuracy, the models used for control system purposes must be computable in real time, and generally, it is important that they provide both steady-state and dynamic information of the interrelationships between the coupled variables of the system. It is generally important that these relationships FIGURE 104.1 Input and output variables of welding process
be tunable"in real time to permit calibrating the multivariable system controller to the actual operating nditions at any given time. Successful implementation of multivariable weld process control involves(1)sensing,(2)modeling, and (3) control Issues dealing with each of these will be discussed in the following sections Sensing In recent years, great strides have been made in sensor technology, particularly in areas or o arc sensing, and infrared, acoustic, and ultrasonic sensing Optical Sensing Optical sensing technology has been developed and used for a number of applications, including joint tracking and fill control, sensing of molten pool width, sensing of weld bead profile, arc length sensing and control, sensing and control of electrode extension in gas metal arc welding(GMAW), and sensing of weld depth penetration. Yi [1991] and Barnett [1993] have investigated the ability to estimate GTA weld penetration by means of measuring the weld pool vibration frequency. Yi and Barnett used the reflection of the welding arc from the weld pool surface as a means of sensing the weld pool vibration. Digital signal processing was usee to estimate the oscillation frequency of the weld pool from the sensed optical signal. References to other work dealing with weld pool vibration sensing and analysis may be found in Yi [ 1991] and Barnett [1993]. Other potential applications include sensing of proper fusion characteristics at the sidewalls, detection of surface ntaminants,and sensing of metal transfer mode in GMAW. Liu [1991] has demonstrated that the drople rate in GMAW can be extracted from the arc infrared signal by means of power spectral estimation. Liu establishes the relationships between the metal droplet rate and the welding parameters, arc voltage, arc current wire-feed speed, and the contact tube-to-workpiece distance(CTWD). Liu proposes a PC-based digital control system for controlling the metal droplet rate in GMaW One of the first real-time optical tracking systems, and certainly one of the more novel approaches, was a coaxial viewing system developed by Richardson [Richardson et al, 1984]. With this approach, the imaging system is integrated into the welding torch. The point of welding is viewed coaxially with the welding electrode from within the welding torch. Advantages reported for this system of viewing include(1) the bright core of the arc is blocked by the electrode/contact tip, ( 2)the entire weld area can be viewed without obstruction and without distortion by the viewing angle, and(3)the system is nonintrusive into the weld area and is nondi- A number of optical tracking systems make use of a projected laser strip or a scanned laser beam to provide structured lighting that permits three-dimensional profiling of the joint, typically in front of the heat source. Several such tracking systems are commercially available and offer robust solutions to the joint tracking problem. A viewing system that provides remarkably good images of the electrode and molten pool area has been eveloped from laser and night imaging technology. The systems operation is based on the use of a high intensity pulsed laser or strobe light synchronized with an image intensifier and camera to suppress the arc light and produce a clear view of the arc area. The excellent image obtained with this system offers a great deal of potential for various types of optical process sensing requirements Are sensing Arc sensing(or through-the-arc sensing) has many applications, some, such as automatic voltage control, dating back 30 years or more. The obvious advantage of arc sensing is that use of the arc itself as a sensor means there is not any need for external sensors, with the associated concern for their reliability in the harsh environment One of the most widely reported recent applications of arc sensing is for purposes of vertical and lateral tracking and width control [Cook, 1983]. For this application, the sensing method is based on the changes current and/or voltage when the arc is weaved back and forth across the joint Inventions have been disclosed for both nonconsumable arc welding processes and consumable arc welding processes(see references in Cook et al., 1990). Applications range from pipe welding to robotic arc welding to turbine blade repair For submerged c2000 by CRC Press LLC
© 2000 by CRC Press LLC be “tunable” in real time to permit calibrating the multivariable system controller to the actual operating conditions at any given time. Successful implementation of multivariable weld process control involves (1) sensing, (2) modeling, and (3) control. Issues dealing with each of these will be discussed in the following sections. Sensing In recent years, great strides have been made in sensor technology, particularly in the areas of optical sensors, arc sensing, and infrared, acoustic, and ultrasonic sensing. Optical Sensing Optical sensing technology has been developed and used for a number of applications, including joint tracking and fill control, sensing of molten pool width, sensing of weld bead profile, arc length sensing and control, sensing and control of electrode extension in gas metal arc welding (GMAW), and sensing of weld depth or penetration. Yi [1991] and Barnett [1993] have investigated the ability to estimate GTA weld penetration by means of measuring the weld pool vibration frequency. Yi and Barnett used the reflection of the welding arc from the weld pool surface as a means of sensing the weld pool vibration. Digital signal processing was used to estimate the oscillation frequency of the weld pool from the sensed optical signal. References to other work dealing with weld pool vibration sensing and analysis may be found in Yi [1991] and Barnett [1993]. Other potential applications include sensing of proper fusion characteristics at the sidewalls, detection of surface contaminants, and sensing of metal transfer mode in GMAW. Liu [1991] has demonstrated that the droplet rate in GMAW can be extracted from the arc infrared signal by means of power spectral estimation. Liu establishes the relationships between the metal droplet rate and the welding parameters, arc voltage, arc current, wire-feed speed, and the contact tube-to-workpiece distance (CTWD). Liu proposes a PC-based digital control system for controlling the metal droplet rate in GMAW. One of the first real-time optical tracking systems, and certainly one of the more novel approaches, was a coaxial viewing system developed by Richardson [Richardson et al., 1984]. With this approach, the imaging system is integrated into the welding torch. The point of welding is viewed coaxially with the welding electrode from within the welding torch. Advantages reported for this system of viewing include (1) the bright core of the arc is blocked by the electrode/contact tip, (2) the entire weld area can be viewed without obstruction and without distortion by the viewing angle, and (3) the system is nonintrusive into the weld area and is nondirectional. A number of optical tracking systems make use of a projected laser strip or a scanned laser beam to provide structured lighting that permits three-dimensional profiling of the joint, typically in front of the heat source. Several such tracking systems are commercially available and offer robust solutions to the joint tracking problem. A viewing system that provides remarkably good images of the electrode and molten pool area has been developed from laser and night imaging technology. The system’s operation is based on the use of a highintensity pulsed laser or strobe light synchronized with an image intensifier and camera to suppress the arc light and produce a clear view of the arc area. The excellent image obtained with this system offers a great deal of potential for various types of optical process sensing requirements. Arc Sensing Arc sensing (or through-the-arc sensing) has many applications, some, such as automatic voltage control, dating back 30 years or more. The obvious advantage of arc sensing is that use of the arc itself as a sensor means there is not any need for external sensors, with the associated concern for their reliability in the harsh environment of the welding arc. One of the most widely reported recent applications of arc sensing is for purposes of vertical and lateral tracking and width control [Cook, 1983]. For this application, the sensing method is based on the changes in current and/or voltage when the arc is weaved back and forth across the joint. Inventions have been disclosed for both nonconsumable arc welding processes and consumable arc welding processes (see references in Cook et al., 1990).Applications range from pipe welding to robotic arc welding to turbine blade repair. For submerged
arc welding(SAW), for example, current variations of approximately 10%at the sidewalls have been observed while welding in a joint consisting of a 45-degree included angle with a 5-mm root opening. with a nominal current of 580 A at the center of the joint, the current at the sidewalls is approximately 640 A. Variations of this magnitude may be used to implement robust control algorithms for joint tracking and width control Shepard [1991] presents a thorough treatment of the mechanisms that establish and influence self-regulation in GMAW. Components of a dynamic GMAw process model are identified, including the power source, joule ceating in the electrode, electrode burn-off rate, and arc voltage. A numerical simulation of the nonlinear dynamic model for self-regulation is implemented, computing current I and electrode extension in response to CTWD, voltage, and feed rate. The I/CTWD response is shown to be frequency dependent, increasing significantly at higher frequencies. The frequency at which the response increases is shown to be primarily dependent on electrode current density, occurring at lower frequencies for lower current densities. A linearized closed-form model for the I/CTWD frequency response is derived from the simulation equations and is shown to provide accurate results. The closed-form model clearly indicates the relationships between the model parameters that establish the observed characteristics of self-regulation dynamics. Initial implementations of through-the-arc seam tracking methods use simple current levels to identify the lateral limits of the weld joint, djusting the torch centerline to maintain symmetry. The dynamic model developed by Shepard provides a asis to infer actual joint geometry from position and current information acquired during cross-seam oscil lation. The relationships developed by Shepard also refine the basis for selection of welding procedures in GMAW applications, particularly for through-the-arc sensing applications. The models define the relationships to generate surfaces to facilitate selection of electrode diameter, feed rate, voltage, electrode extension, and CTWD to optimize desired characteristics such as low-frequency sensitivity, high-frequency sensitivity, and transition frequency subject to requirements on heat input and deposition rate. These interrelationships may be used as extensions to existing expert systems for selection of welding procedures Arc sensing has been proposed as a means of sensing gta pool motion after excitation from pulsations in the current. The concept of using weld pool motion as a pool geometry sensing method is based on the fluid dynamics of the constrained weld pool, which depend on the properties of the molten pool material, the surface tension, and the shape of the pool. a Another potential application of arc sensing is detection of the metal-transfer mode in GMAW. The droplet transfer mode in the GMaw process has a large effect on weld pool metallurgy, influencing penetration, solidification, heat flow, and mass input. Researchers have attempted to correlate perturbations in the electrical arc signals with droplet transfer. This work has demonstrated the ability to detect the detachment of individual droplets and to distinguish among the three transfer modes: globular, spray, and streaming, as defined by Lancaster [1986] Measurements of the incremental arc resistance by Shepard [1991] suggest that the metal-transfer mode of the gas metal arc may also be detected by the rapid transitions of the incremental arc resistance at the transition regions of metal transfer(particularly at the spray-to-streaming transition). The incremental resistance was obtained by perturbing the voltage with a 1-Vp-p 15-Hz sinusoidal variation In the arc resistance measurements, CTWD and electrode extension(and hence arc length) were held constant and data were taken over a wide range of current. A nominal CTWD of 25. 4 mm was used, with a 15-mm electrode extension. Feed rate was varied from the globular/spray transition point to the upper ranges imposed by equipment limitations. A small (1Ve-p), high-frequency(15 Hz) sinusoidal perturbation was superimposed on the power source voltage to allow measurement of the incremental resistance at each operating point. The frequency was sufficiently high that the electrode extension did not vary significantly. For each data point, an 8-s record was acquired at 1 kHz sample rate. The frequency response function(FRF)was used to compute the incremental resistance by calculating the current produced in response to the sinusoidal voltage perturbation. The FrF gives the magni tude and phase angle of a linear model of the arc V-I characteristic about the given operating point, making up the total resistance of arc plus electrode. Results of the incremental arc resistance measurements were plotted as a function of current. The most significant feature of these data was the large peak in incremental resistance in the region of the projected/streaming transition. The height of the peak is roughly twice the nominal resistance at higher currents. The incremental arc resistance increases sharply at the upper end of projected transfer mode, peaking just after the transition to decline to a relatively steady level through the upper end of the streaming transfer range e 2000 by CRC Press LLC
© 2000 by CRC Press LLC arc welding (SAW), for example, current variations of approximately 10% at the sidewalls have been observed while welding in a joint consisting of a 45-degree included angle with a 5-mm root opening. With a nominal current of 580 A at the center of the joint, the current at the sidewalls is approximately 640 A. Variations of this magnitude may be used to implement robust control algorithms for joint tracking and width control. Shepard [1991] presents a thorough treatment of the mechanisms that establish and influence self-regulation in GMAW. Components of a dynamic GMAW process model are identified, including the power source, joule heating in the electrode, electrode burn-off rate, and arc voltage. A numerical simulation of the nonlinear dynamic model for self-regulation is implemented, computing current I and electrode extension in response to CTWD, voltage, and feed rate. The I/CTWD response is shown to be frequency dependent, increasing significantly at higher frequencies. The frequency at which the response increases is shown to be primarily dependent on electrode current density, occurring at lower frequencies for lower current densities. A linearized closed-form model for the I/CTWD frequency response is derived from the simulation equations and is shown to provide accurate results. The closed-form model clearly indicates the relationships between the model parameters that establish the observed characteristics of self-regulation dynamics. Initial implementations of through-the-arc seam tracking methods use simple current levels to identify the lateral limits of the weld joint, adjusting the torch centerline to maintain symmetry. The dynamic model developed by Shepard provides a basis to infer actual joint geometry from position and current information acquired during cross-seam oscillation. The relationships developed by Shepard also refine the basis for selection of welding procedures in GMAW applications, particularly for through-the-arc sensing applications. The models define the relationships to generate surfaces to facilitate selection of electrode diameter, feed rate, voltage, electrode extension, and CTWD to optimize desired characteristics such as low-frequency sensitivity, high-frequency sensitivity, and transition frequency subject to requirements on heat input and deposition rate. These interrelationships may be used as extensions to existing expert systems for selection of welding procedures. Arc sensing has been proposed as a means of sensing GTA pool motion after excitation from pulsations in the current. The concept of using weld pool motion as a pool geometry sensing method is based on the fluid dynamics of the constrained weld pool, which depend on the properties of the molten pool material, the surface tension, and the shape of the pool. Another potential application of arc sensing is detection of the metal-transfer mode in GMAW. The droplet transfer mode in the GMAW process has a large effect on weld pool metallurgy, influencing penetration, solidification, heat flow, and mass input. Researchers have attempted to correlate perturbations in the electrical arc signals with droplet transfer. This work has demonstrated the ability to detect the detachment of individual droplets and to distinguish among the three transfer modes: globular, spray, and streaming, as defined by Lancaster [1986]. Measurements of the incremental arc resistance by Shepard [1991] suggest that the metal-transfer mode of the gas metal arc may also be detected by the rapid transitions of the incremental arc resistance at the transition regions of metal transfer (particularly at the spray-to-streaming transition). The incremental resistance was obtained by perturbing the voltage with a 1-Vp-p, 15-Hz sinusoidal variation. In the arc resistance measurements, CTWD and electrode extension (and hence arc length) were held constant and data were taken over a wide range of current. A nominal CTWD of 25.4 mm was used, with a 15-mm electrode extension. Feed rate was varied from the globular/spray transition point to the upper ranges imposed by equipment limitations. A small (1 Vp – p), “high-frequency” (15 Hz) sinusoidal perturbation was superimposed on the power source voltage to allow measurement of the incremental resistance at each operating point. The frequency was sufficiently high that the electrode extension did not vary significantly. For each data point, an 8-s record was acquired at 1- kHz sample rate. The frequency response function (FRF) was used to compute the incremental resistance by calculating the current produced in response to the sinusoidal voltage perturbation. The FRF gives the magnitude and phase angle of a linear model of the arc V-I characteristic about the given operating point, making up the total resistance of arc plus electrode. Results of the incremental arc resistance measurements were plotted as a function of current. The most significant feature of these data was the large peak in incremental resistance in the region of the projected/streaming transition. The height of the peak is roughly twice the nominal resistance at higher currents. The incremental arc resistance increases sharply at the upper end of projected transfer mode, peaking just after the transition to decline to a relatively steady level through the upper end of the streaming transfer range
For weld procedures that include cross-seam oscillation, or weaving, of the heat source, arc sensing provides a reliable indicator of sidewall/adjacent bead fusion. As the sidewall or adjacent bead is approached in the weave cycle, the electrical signals change in response to the change in CTWD for GMAW or arc gap for GTAw. This change is, of course, the signal used for tracking control in through-the-arc tracking; however, it provides a useful indicator of proper penetration into the sidewall or adjacent bead independently of whether arc sensing andersen et al. 1989]have reported the use of arc signal parameters as a potential control means for gMav short-circuiting transfer Digital signal processing was used to extract from the electrical signals various features, including average and peak values of voltage and current, short- circuiting frequency, arc period, shortin period, and the ratio of the arcing to shorting period. Additionally, a joule heating model was derived that accurately predicted the melt-back distance during each short. The ratio of the arc period to short period was found to be a good indicator for monitoring and control of stable arc conditions. Any change in the arcing ge, for a given power circuit condition, leads to corresponding changes in the arcing/shorting time ratio. Such changes in arcing voltage may occur with change in the shielding gas, in the surface condition(in the rm of contaminates)of the electrode wire and work, and in their composition, such as the presence of rare earths. in the wire electrode or work materials that affect the arc characteristics. andersen et al. [ 1989] show that if the average arc current may be assumed nominally constant because of constant electrode feed, then the arcing/shorting time ratio serves as a sensitive index of the operation of the GMAW short-circuiting system. The arcing/shorting time ratio can be used to control the short-circuiting gas metal arc in a feedback loop by adjusting the open circuit voltage to compensate for variations in the arcing Finally, the electrical arc signals vary as a function of contaminants on the workpiece and/or electrode, and hese variations may be sensed and correlated with the changes observed in surface cone Infrared Sensing Infrared sensing has inherent appeal for weld sensing Potential applications include cooling rate measurements, discontinuity sensing, penetration estimation, seam tracking, and weld pool geometry measurement. Acoustical Sensing The acoustical signals generated by the welding arc are a principal source of feedback for manual welders. Recently, acoustical signals have been studied as a sensing means for automated welding as well. Sound generated by the electric arc of a gas tungsten arc weld has been used for arc length control. with this system the current is pulsed a small amount at an audible rate to generate an audible tone at the arc. The intensity of the arc-generated tone has been shown to be proportional to the arc length and, hence, can be Acoustical signals generated by gas metal arcs have been correlated with the detachment of individual droplets from the filler wire. Research has demonstrated the ability to detect the detachment of individual droplets and to distinguish among transfer modes: globular, spray, and streaming transfer. This may lead to a means of closed-loop control of the heat and mass input during both pulsed and nonpulsed GMAw. Acoustical signals have also been reported as a means of plasma monitoring in laser beam welding(LBw) Specifically, experiments have been conducted to characterize the interaction between the incident laser light, the plasma formation, and the target material during pulse welding with an Nd: YAG laser In the experiments, the acoustical signal, picked up by a microphone, was used to signal plasma initiations and propagation. A correlation was observed between the number of plasmas generated and the weld pool penetration in a target. Acoustic emission has been used for monitoring LBW in real time. The acoustic sensor has been reported to detect laser misfiring, loss of power, improper focus, and excess root opening Ultrasonic sensing The use of ultrasonics for weld process sensing has the potential to detect weld pool geometry and discontinuities n real time. However, to be useful in realistic production systems, a means must be developed for injecting the ultrasound and receiving it with noncontacting sensors. Lasers have been proposed as a sound source, and electromagnetic acoustic transducers(EMATs) have been proposed for ultrasound reception. with this proposed c2000 by CRC Press LLC
© 2000 by CRC Press LLC For weld procedures that include cross-seam oscillation, or weaving, of the heat source, arc sensing provides a reliable indicator of sidewall/adjacent bead fusion. As the sidewall or adjacent bead is approached in the weave cycle, the electrical signals change in response to the change in CTWD for GMAW or arc gap for GTAW. This change is, of course, the signal used for tracking control in through-the-arc tracking; however, it provides a useful indicator of proper penetration into the sidewall or adjacent bead independently of whether arc sensing is used for tracking purposes. Andersen et al. [1989] have reported the use of arc signal parameters as a potential control means for GMAW, short-circuiting transfer. Digital signal processing was used to extract from the electrical signals various features, including average and peak values of voltage and current, short- circuiting frequency, arc period, shorting period, and the ratio of the arcing to shorting period. Additionally, a joule heating model was derived that accurately predicted the melt-back distance during each short. The ratio of the arc period to short period was found to be a good indicator for monitoring and control of stable arc conditions. Any change in the arcing voltage, for a given power circuit condition, leads to corresponding changes in the arcing/shorting time ratio. Such changes in arcing voltage may occur with change in the shielding gas, in the surface condition (in the form of contaminates) of the electrode wire and work, and in their composition, such as the presence of rare earths, in the wire electrode or work materials that affect the arc characteristics. Andersen et al. [1989] show that if the average arc current may be assumed nominally constant because of constant electrode feed, then the arcing/shorting time ratio serves as a sensitive index of the operation of the GMAW short-circuiting system. The arcing/shorting time ratio can be used to control the short-circuiting gas metal arc in a feedback loop by adjusting the open circuit voltage to compensate for variations in the arcing voltage. Finally, the electrical arc signals vary as a function of contaminants on the workpiece and/or electrode, and these variations may be sensed and correlated with the changes observed in surface conditions. Infrared Sensing Infrared sensing has inherent appeal for weld sensing. Potential applications include cooling rate measurements, discontinuity sensing, penetration estimation, seam tracking, and weld pool geometry measurement. Acoustical Sensing The acoustical signals generated by the welding arc are a principal source of feedback for manual welders. Recently, acoustical signals have been studied as a sensing means for automated welding as well. Sound generated by the electric arc of a gas tungsten arc weld has been used for arc length control. With this system the current is pulsed a small amount at an audible rate to generate an audible tone at the arc. The intensity of the arc-generated tone has been shown to be proportional to the arc length and, hence, can be suitably processed to provide a feedback signal for arc length control. Acoustical signals generated by gas metal arcs have been correlated with the detachment of individual droplets from the filler wire. Research has demonstrated the ability to detect the detachment of individual droplets and to distinguish among transfer modes: globular, spray, and streaming transfer. This may lead to a means of closed-loop control of the heat and mass input during both pulsed and nonpulsed GMAW. Acoustical signals have also been reported as a means of plasma monitoring in laser beam welding (LBW). Specifically, experiments have been conducted to characterize the interaction between the incident laser light, the plasma formation, and the target material during pulse welding with an Nd:YAG laser. In the experiments, the acoustical signal, picked up by a microphone, was used to signal plasma initiations and propagation. A correlation was observed between the number of plasmas generated and the weld pool penetration in a target. Acoustic emission has been used for monitoring LBW in real time. The acoustic sensor has been reported to detect laser misfiring, loss of power, improper focus, and excess root opening. Ultrasonic Sensing The use of ultrasonics for weld process sensing has the potential to detect weld pool geometry and discontinuities in real time. However, to be useful in realistic production systems, a means must be developed for injecting the ultrasound and receiving it with noncontacting sensors. Lasers have been proposed as a sound source, and electromagnetic acoustic transducers (EMATs) have been proposed for ultrasound reception. With this proposed
pproach, the pulsed laser is directed to impinge on the molten pool, setting up stress waves that are transmitted through the workpiece and picked up by the EMAT receiver. Modeling Weld process models intended for control purposes are characterized by the need to be computable in real time. This rules out many of the more exact numerical models that have been developed for finite element and nite difference methods. However, these computationally intensive numerical models may be quite useful in developing simpler models that can be used in the control of multivariable weld feedback control systems. Another important aspect of process models used for control purposes is that they generally need to provide both static and d ic information Analytical Models Since the 1940s considerable research has been focused on developing steady-state models that would predict DWP, given a set of IWP. Easily computed analytical models, based solely on conductive heat transfer, are reasonably accurate but primarily are of value in establishing approximate relationships. Improvements to these arly analytical models have been proposed that permit obtaining a better match to actual conditions and that may be calibrated in real time; however, accuracy remains limited in the absence of modeling extensions that require computationally intensive numerical solution. Empirical and Statistical Models Other approaches taken to developing steady-state weld process models include: empirically derived relation- te, ps between the IWP and DWP, with coefficients chosen to match experimental data and statistically derived ationships. Both of these approaches have proven to possess only a limited range of applicability, and they do not lend themselves to real-time "tuning"in a multi-variable control system application. Artificial Neural Network Models A promising method based on an artificial neural network(ANN) has been studied and found to be accurate and computationally fast in the application mode. Furthermore, the ann can be refined at any time with the addition of new training data and thus promises a method of continuously adapting to the actual welding Andersen [1992] has reported the application of an ann to mapping between the IWP's arc current, travel speed, arc length, and plate thickness and the DwP's bead width and penetration for GTAW. A back-propa gation network, using 10 nodes in a single hidden layer Fig. 104.2), was used for the modeling. A variety of Speed different network configurations were initially evaluated for this purpose. Generally, it was found that one hidden layer was sufficient for weld modeling, and the best Lengt training rate was obtained with on the order of 5 to 20 nodes in the hidden layer. The same plate material was Plate Bead ssumed throughout the experiment, which eliminated Thickness the need for specifying any of the material parameters included thermal conductivity, diffusivity, etc. IGURE 104.2 A neural netw A total of 72 welds, produced on two material thick nesses of 3.175 and 6.350 mm, were used for the purpose of training and testing the network for modeling purposes. Weld current values of 80, 100, 120, and 140 A, travel speeds of 2.12, 2.75, and 3. 39 mm/s, and arc engths of 1.52, 2.03, and 2.54 mm were used. Eight of the welds, which were randomly selected, were not used in the training phase but were reserved for testing the model. with a learning rate parameter of 0.6 and a momentum term of 0.9, the network was trained for 200,000 iterations e 2000 by CRC Press LLC
© 2000 by CRC Press LLC approach, the pulsed laser is directed to impinge on the molten pool, setting up stress waves that are transmitted through the workpiece and picked up by the EMAT receiver. Modeling Weld process models intended for control purposes are characterized by the need to be computable in real time. This rules out many of the more exact numerical models that have been developed for finite element and finite difference methods. However, these computationally intensive numerical models may be quite useful in developing simpler models that can be used in the control of multivariable weld feedback control systems. Another important aspect of process models used for control purposes is that they generally need to provide both static and dynamic information. Analytical Models Since the 1940s considerable research has been focused on developing steady-state models that would predict DWP, given a set of IWP. Easily computed analytical models, based solely on conductive heat transfer, are reasonably accurate but primarily are of value in establishing approximate relationships. Improvements to these early analytical models have been proposed that permit obtaining a better match to actual conditions and that may be calibrated in real time; however, accuracy remains limited in the absence of modeling extensions that require computationally intensive numerical solution. Empirical and Statistical Models Other approaches taken to developing steady-state weld process models include: empirically derived relationships between the IWP and DWP, with coefficients chosen to match experimental data and statistically derived relationships. Both of these approaches have proven to possess only a limited range of applicability, and they do not lend themselves to real-time “tuning” in a multi-variable control system application. Artificial Neural Network Models A promising method based on an artificial neural network (ANN) has been studied and found to be accurate and computationally fast in the application mode. Furthermore, the ANN can be refined at any time with the addition of new training data and thus promises a method of continuously adapting to the actual welding conditions. Andersen [1992] has reported the application of an ANN to mapping between the IWP’s arc current, travel speed, arc length, and plate thickness and the DWP’s bead width and penetration for GTAW. A back-propagation network, using 10 nodes in a single hidden layer (Fig. 104.2), was used for the modeling. A variety of different network configurations were initially evaluated for this purpose. Generally, it was found that one hidden layer was sufficient for weld modeling, and the best training rate was obtained with on the order of 5 to 20 nodes in the hidden layer. The same plate material was assumed throughout the experiment, which eliminated the need for specifying any of the material parameters. Otherwise, additional input parameters might have included thermal conductivity, diffusivity, etc. A total of 72 welds, produced on two material thicknesses of 3.175 and 6.350 mm, were used for the purpose of training and testing the network for modeling purposes. Weld current values of 80, 100, 120, and 140 A, travel speeds of 2.12, 2.75, and 3.39 mm/s, and arc lengths of 1.52, 2.03, and 2.54 mm were used. Eight of the welds, which were randomly selected, were not used in the training phase but were reserved for testing the model. With a learning rate parameter of 0.6 and a momentum term of 0.9, the network was trained for 200,000 iterations. FIGURE 104.2 A neural network used for weld modeling
Once the network had been trained with the 64 training welds, the remaining 8 welds were applied to test the modeling network. The root mean square(RMS) values of the errors were calculated separately for the bead width and penetration, resulting in about 5% and 18% RMS errors, respectively. These results agree with experiments reported by Andersen, ically on the order of 10-20 Weld modeling studies have also been carried out on the variable polarity plasma arc welding(VPPAw) process Modeling of the crown and root width in the keyhole welding mode was of specific interest, and the model inputs were the forward and reverse current values, the torch standoff distance, and the travel speed. The crown and root width errors of the model were generally determined to be on the order of 10-20% or better. An observation relating to the weld modeling experiments should be noted here. The precision of the bead measurements was 0. 1 mm, which corresponds to 2 and 7% precision for the average bead width and pene- tration,respectively. Furthermore, inaccuracies in measurements of the data, which were used to train the neural network model, tend to degrade the general performance of the model. width measurements are generally more reliable than penetration measurements, as they are made in several locations along the top of the bead. A penetration measurement is usually made on a single cross section, and it requires chemical etching, which results in a relatively blurred boundary between the bead and the surrounding base metal. This difference is reflected in the consistently lower accuracy of the penetration modeling, compared with the width modeling A back-propagation network was also constructed by Andersen [1992] to model the inverse relations, i.e., the DWP-IWP relations, of the weld sample set used in the forward modeling study. A number of neural network configurations were initially used in attempting to train networks to determine the necessary current, travel speed, and arc length for desired bead width and penetration. Preliminary attempts did not result in acceptable training convergence. Closer examination revealed that welds which resulted in full or almost full penetration yielded very irregular bead measurements. It was hypothesized that these irregularities might ntribute to the poor training performance. These welds(total of five), which represented the largest pool dimensions on the 3. 175-mm test plate, were removed from the training data, and to maintain an equally large data set for the 6.350-mm plate, the five largest welds were ignored there as well. Six welds were randomly selected from the remaining data for each plate thickness for testing only Using the revised data set, a network of 50 nodes in a single hidden layer was successfully trained. The learning rate was 0.6, the momentum term was 0.9, and the network was trained for 300,000 iterations. The equipment parameters, or IWP, suggested by the neural network were compared with the actual parameters used to produce the test welds. The RMs deviations between these were current, 9.7%; travel speed, 23.9%; and arc length, 25.5%. Although these deviations between the IwP used to produce the original training set and the IWP suggested by the Ann are rather large, the results are not unexpected because of the nonuniqueness of the inverse problem. The results do not imply that the resulting bead geometries would be accordingly erroneous, because a given width-penetration pair may be attained through multiple nonunique combinations of equipment parameters. For example, an arc current increase may be largely offset by a corresponding increase To assess the reliability of the ann for equipment parameter selection, the parameters suggested by the inverse model were used to produce a new set of welds, and bead width and penetration measurements were carried out as before. These widths and penetrations were compared with the original data set. The RMS errors were width, 5.5%, and penetration, 19.9%. These differences between the new geometry parameters and the original ones are approximately the same as the errors observed from the weld model. Again, it is suggeste that uncertainty in bead measurements contributes significantly to these errors When compared to other control modeling methodologies, neural networks have certain drawbacks as well as advantages Of the drawbacks, the most notable is the lack of comprehension of the physics of the process Relating the qualitative effects of the network structure or parameters to the process parameters is usually impossible. On the other hand, other control modeling methods resort to substantial simplifications of either the physical process or more exact numerical models and therefore also trade computability for comprehensi bility. The advantages of neural models include relative accuracy and generality. If the training data for a neural network is general enough, spanning the entire ranges of process parameters, the resulting model will capture the complexion of the process, including nonlinearities and parameter cross couplings, over the same ranges. Model development is much simpler than for most other models. Instead of theoretical analysis and develop- ment for a new model, the neural network tailors itself to the training data. The network can be refined at any c2000 by CRC Press LLC
© 2000 by CRC Press LLC Once the network had been trained with the 64 training welds, the remaining 8 welds were applied to test the modeling network. The root mean square (RMS) values of the errors were calculated separately for the bead width and penetration, resulting in about 5% and 18% RMS errors, respectively. These results agree with other similar experiments reported by Andersen, in that modeling accuracy is typically on the order of 10-20%. Weld modeling studies have also been carried out on the variable polarity plasma arc welding (VPPAW) process. Modeling of the crown and root width in the keyhole welding mode was of specific interest, and the model inputs were the forward and reverse current values, the torch standoff distance, and the travel speed. The crown and root width errors of the model were generally determined to be on the order of 10–20% or better. An observation relating to the weld modeling experiments should be noted here. The precision of the bead measurements was 0.1 mm, which corresponds to 2 and 7% precision for the average bead width and penetration, respectively. Furthermore, inaccuracies in measurements of the data, which were used to train the neural network model, tend to degrade the general performance of the model. Width measurements are generally more reliable than penetration measurements, as they are made in several locations along the top of the bead.A penetration measurement is usually made on a single cross section, and it requires chemical etching, which results in a relatively blurred boundary between the bead and the surrounding base metal. This difference is reflected in the consistently lower accuracy of the penetration modeling, compared with the width modeling. A back-propagation network was also constructed by Andersen [1992] to model the inverse relations, i.e., the DWP-IWP relations, of the weld sample set used in the forward modeling study. A number of neural network configurations were initially used in attempting to train networks to determine the necessary current, travel speed, and arc length for desired bead width and penetration. Preliminary attempts did not result in acceptable training convergence. Closer examination revealed that welds which resulted in full or almost full penetration yielded very irregular bead measurements. It was hypothesized that these irregularities might contribute to the poor training performance. These welds (total of five), which represented the largest pool dimensions on the 3.175-mm test plate, were removed from the training data, and to maintain an equally large data set for the 6.350-mm plate, the five largest welds were ignored there as well. Six welds were randomly selected from the remaining data for each plate thickness for testing only. Using the revised data set, a network of 50 nodes in a single hidden layer was successfully trained. The learning rate was 0.6, the momentum term was 0.9, and the network was trained for 300,000 iterations. The equipment parameters, or IWP, suggested by the neural network were compared with the actual parameters used to produce the test welds. The RMS deviations between these were current, 9.7%; travel speed, 23.9%; and arc length, 25.5%. Although these deviations between the IWP used to produce the original training set and the IWP suggested by the ANN are rather large, the results are not unexpected because of the nonuniqueness of the inverse problem. The results do not imply that the resulting bead geometries would be accordingly erroneous, because a given width-penetration pair may be attained through multiple nonunique combinations of equipment parameters. For example, an arc current increase may be largely offset by a corresponding increase in travel speed. To assess the reliability of the ANN for equipment parameter selection, the parameters suggested by the inverse model were used to produce a new set of welds, and bead width and penetration measurements were carried out as before. These widths and penetrations were compared with the original data set. The RMS errors were width, 5.5%, and penetration, 19.9%. These differences between the new geometry parameters and the original ones are approximately the same as the errors observed from the weld model. Again, it is suggested that uncertainty in bead measurements contributes significantly to these errors. When compared to other control modeling methodologies, neural networks have certain drawbacks as well as advantages. Of the drawbacks, the most notable is the lack of comprehension of the physics of the process. Relating the qualitative effects of the network structure or parameters to the process parameters is usually impossible. On the other hand, other control modeling methods resort to substantial simplifications of either the physical process or more exact numerical models and therefore also trade computability for comprehensibility. The advantages of neural models include relative accuracy and generality. If the training data for a neural network is general enough, spanning the entire ranges of process parameters, the resulting model will capture the complexion of the process, including nonlinearities and parameter cross couplings, over the same ranges. Model development is much simpler than for most other models. Instead of theoretical analysis and development for a new model, the neural network tailors itself to the training data. The network can be refined at any