- Email: [email protected]
Process control of laser materials processing
25
Process control of laser materials processing
R. T. D e a m, Swinburne University of Technology, Australia
Abstract: Materials processing using a laser can be fast and precise. Quality control is usually achieved by “open-loop” adjustment of the laser process for the particular task and workpiece being processed. Each different type of workpiece to be laser processed requires the development of a new procedure. This chapter looks at the conditions under which closed loop control of laser processes is practical. If on-line, closed loop control is not possible then quality control can only be achieved by on-line monitoring and then accepting or rejecting the work after processing. Key words: laser processing, monitoring and control.
25.1
Introduction
One of the major advantages of laser processing is the possibility of processing at high speeds; that is above about one metre per minute. Laser processing also has a reputation for high quality, which is mostly achieved through “open-loop” control. Open-loop laser materials processing technologies, such as welding, cutting, drilling and cladding have developed into a widely used technology in industrial production (Steen, 1998). The processes are, however, inherently difficult to control and are currently limited to “nondemanding applications”, which have a large process operating window. A new range of applications could emerge if highly reflective and highly heatconductive materials could be processed. Nowadays, this is limited by the fact that relatively minor differences in surface condition of the metal, and instability of the laser focus will cause dramatic effects on the absorbed laser energy. Here advanced and intelligent process control is the key to further applications. The monitoring and control of these processes is therefore an active area of research. Techniques such as optical and acoustic emission, pyrometry and plasma charge sensing have been investigated and reported (Duley, 1998, Norrish, 1992, Deam et al., 2003, Prokoshev et al., 2001, Haferkamp et al., 2000, Smith and Kannatey-Asibu, 1999, Grunenwald et al., 1993). Also the control of arc welding systems has been an active area of development (Prokoshev et al., 2001, Nagarajan et al., 1989, Deam, 1989, Salter and Deam, 1987). While these have reported promising results 792 © Woodhead Publishing Limited, 2010
Process control of laser materials processing
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there are no reports discussing the broader question of the conditions under which control of these processes is practical. In order to provide a better understanding of the limitations of a closed-loop control, a series of experiments was conducted using a PID controller developed by LZH (Laser Zentrum Hannover e.V., 2006). The complications of including phase changes in the study of the system response meant that only a laser heat treatment series of experiments was carried out. This not only makes interpretation of the results easier to understand, but also the modelling of the feedback process. The study therefore looks at the response solely due to heat conduction within the solid material being treated; in this case mild steel being heat treated along a narrow strip, the width of the heat treated area is desired to be controlled within certain tolerances. The problem facing a production engineer is: How fast can the material be treated and the desired tolerances on the heat treated area met? The principle of the findings can be applied to other processes that involve the molten phase. However, it is not the purpose of this study to argue whether or not the molten pool has a shorter or longer response time than the response time due to heat conduction. If the molten pool has a response time that is shorter than the time response from conduction in the solid, then the results of this study will give a good indication of the maximum processing speed, since the response of the system will be controlled by the longest time response. This is because the heat has to flow through the molten pool to be removed by heat conduction; or in electrical terms the system is in series. If the molten pool has a much slower response time than the time response from conduction in the solid, then the results of this study will overestimate the maximum controllable processing speed. A good practical analogy to what is studied here is given by the following example. Suppose you want to paint a straight vertical line on a wall (freehand between predetermined marks). This line is to serve a decorative purpose. Therefore there is a tolerance on the width variation that you will accept. On the other hand, decorating is not enjoyable to you and so you would like to finish the job as fast as possible. There is obviously a trade off between the speed that you can paint and the quality of the job. A slow and careful job looks brilliant, but may take too much time.
25.2
Theory
The theory developed here will use the frequency domain properties of the diffusion equation to formulate how a control system would perform, given perfect instantaneous knowledge of the heated area formed by a laser being scanned over a workpiece. The arguments given will not follow a strict mathematical development. A quick summary of how we arrive at the results can be stated as:
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Advances in laser materials processing
The size of the heat treated area depends on the heat flow from its edge. The heat treated area will therefore shrink or grow as quickly as the information about the temperature distribution in the rest of the workpiece is adjusted to balance the heat flow. The properties of the heat diffusion equation mean that temperature information travels at a speed proportional to the square root of the frequency. The temperature information has to travel faster than the heat treatment process (the speed that the laser scans across the workpiece) to be useful to a control system. Thus high frequency temperature information has to be used to “keep ahead” of the laser scan, thus imposing a low frequency limit on the control system. Unfortunately, in order to meet the quality requirements of the resultant heat treated area, the temperature information has to travel from a certain distance away from the heat source, in order for the control system to “sense” changes in the heat flow, which introduces a phase delay to the control system. The phase delay cannot be too great (less than p), or the control system becomes unstable. Since the phase delay increases with frequency, this imposes an upper limit on the frequency that can be used by the control system. Thus too high a frequency will lead to instability of the control system and too low a frequency will not allow the control system to “sense” changes ahead of the moving laser beam. These two constraints limit the maximum controllable laser processing speed.
25.2.1 Flow of temperature information Control systems must use information to control a process. In this case the information is transmitted by heat or temperature waves. The feedback system will use a control algorithm to try and keep the heated area within a quality specification, a set point or desired temperature. The stability of control systems is usually analysed in terms of the frequency response of the system as a whole. The physics of the system that is to be controlled dictates the fastest response of the feedback control that is possible. The analysis below is intended to find out what constraints are required for stable control of a fast moving laser heat source. The results of the analysis could be applied to controlling a weldpool size, if it were assumed that heat transport in the molten pool is very much faster than in the solid. Thus the heat flow in the solid will be the limiting response time of the system when a controlled procedure is used. The speed at which temperature information can travel in the solid is given by the group velocity.
25.2.2 Group velocity The heat diffusion equation at the surface of the workpiece is given by
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Process control of laser materials processing
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ˆ Ê ∂T + U · —T ˜ – — · (k—T ) = q rC p Á ¯ Ë ∂t where q· is the laser power absorbed, and is what the control system will vary to control the heat input. The equation for convective heat flow in the solid is given by ∂T + U · —T – nth — 2 T = 0 ∂t which for the purpose of this analysis can be written ignoring the convective term: ∂T – nth — 2 T = 0 ∂t Fourier Transform these equations in time and space: (iw + iU · k – nth Ík2 Í)T = 0 and for the equation ignoring convection: (iw – nth Ík2Ô)T = 0 The Dispersion relation is derived by equating the expression inside the brackets to zero: iw + iU · k – nth Ík2Ô = 0 and for the case ignoring convection: iw – nth Ík2Ô = 0 The group velocity is given by the expression cg = ∂w ∂k Thus the group velocity of “temperature” waves can be derived from the heat diffusion equation in the solid. cg = 2nw (1 + i )
[25.1]
where the real part is the speed of information transfer and the imaginary part the damping of the amplitude or loss of information signal strength. The convection term would be added (a vector add) to get the speed in relation to the moving source. In the direction of the laser movement, for information ahead of the laser spot, the group velocity has to exceed the speed of the laser head, U.
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Advances in laser materials processing
The damping of the temperature waves will make the stable control of the treatment size or temperature more difficult (more prone to instability and as the return signal to noise becomes smaller).
25.2.3 Typical length scale This length scale will depend on the geometry of the heat source. It will be different for keyhole welding and conduction welding. For the heat treatment case taken here it will be the size of the laser spot. The typical length scale is l. The time taken to travel this length is given by t= l cg
[25.2]
25.2.4 Quality Information must arrive at the heat source before moving distance l. This defines a time within which the temperature information must be given to the heat source: l > Ut
[25.3]
Therefore 1 l>U l =U cg 2nw (1 + i )
[25.4]
Thus frequency must be higher than 2 2 w > U l2 2nl
[25.5]
for the information to arrive in time. This leads to the definition of a quality length scale, l. The larger this value is the lower the quality of the weld bead or treated area. It represents the tolerable length over which the treated area may lie outside the intended, treatment temperature, size or position. It would be expected that the quality length scale l, would be a fraction of the typical length scale l. For example the typical length scale in a heat treatment application would be the intended width or depth, so if a 20% variation in the width of the treated area were tolerable then l = 0.2l. Figure 25.1 shows a schematic of the quality length for a laser heat treated region. For the heat treatment case considered here it is the maximum continuous length that the temperature is tolerated to be “out of specification”. The temperature overshoot and undershoot as well as the degree of
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Process control of laser materials processing
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Treated region width
Quality length, l Temp. Set temp.
25.1 Bead quality schematic.
thinning and thickening of the treated area will depend on the “challenge” that the control system has to face. A small perturbation to the heat flow will result in a small variation in width along the quality length, whereas a large perturbation will result in a large change in width, that the control system will be able compensate for, over the quality length.
25.2.5 Phase shift However, as the frequency increases, a growing phase shift is introduced. If this phase shift is too great then the information will cause instability if used in a feedback loop to control the quality; this shown in equation 25.6. w
[25.6]
The phase shift must be less than 180 degrees (p radians).
25.2.6 Stable operating window This leads to an upper and lower limit on the frequency component that can be used for feedback to control the heat source. Using equations 25.5 and 25.6: U 2 l 2 < w < pU l 2nl 2
[25.7]
Frequencies above the lower limit ensure that the information will arrive in time. Frequencies below the upper limit will not be out of phase.
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Advances in laser materials processing
25.2.7 Maximum controllable speed Information between these frequency bounds can be used only if a stable control system is to be employed. This leads to a natural limit on the speed of laser processing: U<
2npl l2
[25.8]
above this speed there is no frequency window in which stable control is possible.
25.3
Experiments
a series of experiments were designed to test the response of a controlled laser processing system to abrupt changes in thickness of a workpiece at different travel speeds. The experiments were performed using a 2.5 kW Rofin Sinar laser and 0.6 mm diameter step-index fibre terminated with 200 mm focal length collimating and focusing lenses positioned so that they formed a laser spot about 3.5 mm on the surface of the substrate. The surface temperature under the laser spot was measured using a maurer two-colour pyrometer capable of measuring temperatures between 500 and 1500 °C and TemCon control software and hardware developed by LZH. The pyrometer was mounted vertically above the substrate and at 90° to the collimating lens via a bending cube. The workpiece used was 10 mm thick mild steel plate with 50 mm wide sections milled from one side so that its thickness varied discontinuously in steps (Fig. 25.2). The wall thickness of the milled sections was 2 mm, 0.98 mm and 1.1 mm. The top surface of the sample, which was flat, was cleaned and grit blasted. The sample was mounted under the laser beam with the milled section in the opposite side from the laser beam. The control system was optimised to try and keep the temperature of the surface under the laser Pyrometer Fibre optic 90° beam bender Laser beam 2 mm
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25.2 Schematic of experimental layout.
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Process control of laser materials processing
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spot at 1200 °C, in order to avoid any issues associated with the melt phase. The melting point of mild steel is 1538 °C.
25.4
Experimental results
25.4.1 Initialisation of control parameters A series of experiments were carried out to optimise the control parameters for a one metre per minute travel speed on 10 mm thick mild steel. The system was set up to control the temperature under the laser beam spot to a set point of 1200 °C. Table 25.1 summarises the results of the PID tunning experiments. The system response was determined to be slightly underdamped. This can be seen in the control signal in Figs 25.4 to 25.6.
25.4.2 Measurements The first set of experiments compared an uncontrolled run with a controlled run over the 10 mm plate with the 0.98 mm and 1.1 mm thick sections. Figure 25.3 shows the results. The fixed power run shows a measured surface temperature of about 900 °C over the 10 mm thick sections, about 1350 °C over the 0.98 mm thick section and about 1150 °C over the 1.1 mm thick section. The controlled run maintains about 1200 °C (the set-point), except for overshoots and undershoots, which occur at the thickness transitions. A series of runs was made at different travel speeds, with the control system activated. These were at 2, 1, 0.5, 0.25 and 0.125 metres per minute. The results are shown in Figs 25.4 to 25.8.
25.5
Discussion
The size of the hot region (above 1200 °C) will decrease as the travel speed increases. As the travel speed drops below about 0.5 m/min, the depth of the hot region begins to be affected by the 2 mm thick region. This is seen in the control signal in Figs 25.6 to 25.8. The performance of the control Table 25.1 Control parameters used Parameter
Value
Temperature set point Sample rate Smoothing P (proportional control constant) I (Integral control constant)
1200 °C 1000 Hz 50 samples 0.0003 0.01
No differential control term was used.
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25.3 Test comparisons at 1 m/min. Control set point 1200 °C, and fixed power.
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25.4 Surface temperature and control signal: 2 m/min travel speed.
system is good at travel speeds below 0.5 m/min. Figures 25.4 to 25.6 show overshoot and undershoot excursions (300 °C at a travel speed of 2 m/min). The overall performance of the control system can be measured by recording the maximum deviation in the measured temperature from the set point of 1200 °C over at the thickness transitions which occurred at about 50 mm,
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Process control of laser materials processing
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25.6 Surface temperature and control signal: 0.5 m/min travel speed.
100 mm, 150 mm, 200 mm and 250 mm along the plate. The full traces are shown in Figs 25.4 to 25.8 and the maximum temperature deviations are shown in Table 25.2. However, the maximum deviations tell only part of the story. The length of the treated area that does not conform to the specified tolerance is also very important.
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Advances in laser materials processing
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25.8 Surface temperature and control signal: 0.125 m/min travel speed.
Although this is a very crude assessment of quality of the laser heat treatment process, it gives a numerical measure to what can be clearly seen in the traces. The thickness transition from 10 mm to 2 mm and back to 10 mm result in temperature deviations that are indistinguishable from the inherent noise. The inherent noise has a standard deviation from the set point
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Table 25.2 Control performance vs. travel speed Travel speed (m/min)
TD at 150 mm (°C)
TD at 200 mm (°C)
TD at 250 mm (°C)
0.125 0.25 0.5 1 2
99 123 224 256 300
–77 –127 –287 –257 –234
92 101 188 198 146
TD = Temperature deviation.
of about 30 °C and is most probably caused by variation in the absorption of the laser beam by the workpiece. Developing a robust control system that will cope with this noise is part of the control engineer’s challenge. For thickness steps to 0.98 mm and 1.1 mm, clear overshoot and undershoot in the controlled temperature are seen. Below a travel speed of about 0.5 m/min this control system can cope with the severe test of a sudden change in plate thickness. Such rapid changes in the heat sink configuration are not uncommon in engineering structures. Thick reinforcement webs often support thin plate. Holes and slots are usually part of engineering structures and can act as powerful changes to the heat flow, if fast laser processing is carried out near them. This suggests an alternative approach to the control problem. If more gentle changes in the heat sink could be designed into the structure, then higher quality laser processing could be achieved at higher speed. However in practice, the system would still have to respond to unforeseen changes, such as step changes in the absorption due to uncontrolled changes in surface condition (i.e., rust and roughness).
25.5.1 Theory and experiment In the tests reported here, the system had to respond to a change in plate thickness, from very thick to about 1 mm. This means that the temperature information had to travel from the top of the plate (where the laser spot strikes the plate), to the back-face of the plate and back to the top again to be part of the control loop. The diameter of the spot was 3.5 mm. So that the leading edge of the spot would experience the changes in section thickness, before the trailing edge. The spot diameter will be taken as the typical length scale. Thus knowing the thermal diffusivity of mild steel, equation 25.9 can be used to predict a minimum quality length for any particular travel speed: 2 l = Ul 2 pn
[25.9]
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Using, n = 5.2 10–6 m2s–1, from Kaye and Laby (Kaye and Laby, 1986) and l = 3.5 mm (diameter of the laser spot), the minimum predicted quality length is plotted against travel speed shown in Fig. 25.9, together with the measured quality length on the 10 mm to 0.98 mm transition (150 mm along the plate), the 0.98 to 10 mm transition (at 200 mm), and the 10 mm to 1.1 mm transition (at 250 mm along the plate). The measured quality length was taken as the width of the overshoot at each transition. Agreement of the measured quality length and the predicted quality length is good. Note that the quality length tells the control engineer nothing about the size of the overshoot; just how far along the treated length it takes the control system to recover its set point. Thus the production engineer may have the freedom to minimise the perturbations that the control system is subjected to, but Fig. 25.9 shows that demanding higher quality (smaller quality length) requires a lower travel speed. This reinforces what engineers know well. Higher quality takes more time.
25.6
Conclusions
A simple model of the performance of a control system for laser processing has been presented and compares well with an idealised experimental test. The model predicts that the maximum controllable travel speed depends on the quality required of the laser treated material. Higher quality requires a slower travel speed.
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2 Lambda predicted
25.9 Comparison of quality length at three thickness transitions.
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Process control of laser materials processing
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Acknowledgements
This work was carried out at the Industrial Research Institute Swinburne, which is part of the Faculty of Engineering and Industrial Sciences, Swinburne University of Technology. Thanks to Mr Brian Dempster for preparing the samples and Prof. Milan Brandt and Dr Jim Harris for running the laser used in the experiments. The author also acknowledges the useful discussions and help given by colleagues many years ago in developing practical control systems for arc welding at Marchwood Engineering Laboratories, (formerly part of the Central Electricity Generating Board near Southampton in England).
25.8
References
Deam, R. T. (1989) Weldpool frequency: A new way to define a weld procedure. In David, S. A. & Vitek, J. M. (Eds.) Recent Trends in Welding Science and Technology. Gatlingburg, Tennessee, USA, ASM International. Deam, R. T., Brandt, M. & Harris, J. (2003) Investigation of capillary waves excited by a Nd:YAG laser using pyrometry. Journal of Physics D: Applied Physics, 36, 10. Duley, W. W. (1998) Laser Welding, New York, John Wiley and Sons. Grunenwald, B., Shen, J., Dausinger, F. & Hugel, H. (1993) Laser cladding with composite powders using pyrometric temperature control and beam combination. ISATA ’93 International Symposium on Automotive Technology and Automation. Aachen, Germany. Haferkamp, H., Goede, M. & Lindemann, K. (2000) Laser Hardening of CVD coated tool steel. 12th International Federation for Heat Treatment and Surface Engineering Congress. Melbourne. Kaye, G. W. C. & Laby, T. H. (1986) Tables of Physical and Chemical Constants, London, Longman. Laser Zentrum Hannover E. V. (2006) Web Page. Laser Zentrum Hannover e.V., Hollerithallee 8, D-30419 Hannover. Nagarajan, S., Groom, K. N. & Chin, B. A. (1989) Infrared sensors for seam tracking in tungsten arc welding processes. In David, S. A. & Vitek, J. M. (Eds.) Recent Trends in Welding Science and Technology. Gatlingburgh, Tennessee, USA, ASM International. Norrish, J. (1992) Advanced Welding Processes, Institute of Physics. Prokoshev, V. G., Abramov, D. V., Danilov, S. Y., Kucherik, A. O. & Arakelian, S. M. (2001) Diagnostics of the high temperature hydrodynamic phenomena for laser processing of the material. Laser Assisted Net Shape Engineering 3, Proceedings of the LANE 2001. Salter, R. J. & Deam, R. T. (1987) A practical frontface penetration control system. 2nd International Conference on Developments in Automatic and Robotic Welding. London, The Welding Institute. Smith, E. T. & Kannatey-Asibu, E. (1999) Visualization and Acoustic Monitoring of Laser Weld Pool Oscillatory Behavior. ICALEO 1999. Laser Institute of America. Steen, W. M. (1998) Laser Material Processing, London, Springer-Verlag
© Woodhead Publishing Limited, 2010
Process control of laser materials processing
R. T. D e a m, Swinburne University of Technology, Australia
Abstract: Materials processing using a laser can be fast and precise. Quality control is usually achieved by “open-loop” adjustment of the laser process for the particular task and workpiece being processed. Each different type of workpiece to be laser processed requires the development of a new procedure. This chapter looks at the conditions under which closed loop control of laser processes is practical. If on-line, closed loop control is not possible then quality control can only be achieved by on-line monitoring and then accepting or rejecting the work after processing. Key words: laser processing, monitoring and control.
25.1
Introduction
One of the major advantages of laser processing is the possibility of processing at high speeds; that is above about one metre per minute. Laser processing also has a reputation for high quality, which is mostly achieved through “open-loop” control. Open-loop laser materials processing technologies, such as welding, cutting, drilling and cladding have developed into a widely used technology in industrial production (Steen, 1998). The processes are, however, inherently difficult to control and are currently limited to “nondemanding applications”, which have a large process operating window. A new range of applications could emerge if highly reflective and highly heatconductive materials could be processed. Nowadays, this is limited by the fact that relatively minor differences in surface condition of the metal, and instability of the laser focus will cause dramatic effects on the absorbed laser energy. Here advanced and intelligent process control is the key to further applications. The monitoring and control of these processes is therefore an active area of research. Techniques such as optical and acoustic emission, pyrometry and plasma charge sensing have been investigated and reported (Duley, 1998, Norrish, 1992, Deam et al., 2003, Prokoshev et al., 2001, Haferkamp et al., 2000, Smith and Kannatey-Asibu, 1999, Grunenwald et al., 1993). Also the control of arc welding systems has been an active area of development (Prokoshev et al., 2001, Nagarajan et al., 1989, Deam, 1989, Salter and Deam, 1987). While these have reported promising results 792 © Woodhead Publishing Limited, 2010
Process control of laser materials processing
793
there are no reports discussing the broader question of the conditions under which control of these processes is practical. In order to provide a better understanding of the limitations of a closed-loop control, a series of experiments was conducted using a PID controller developed by LZH (Laser Zentrum Hannover e.V., 2006). The complications of including phase changes in the study of the system response meant that only a laser heat treatment series of experiments was carried out. This not only makes interpretation of the results easier to understand, but also the modelling of the feedback process. The study therefore looks at the response solely due to heat conduction within the solid material being treated; in this case mild steel being heat treated along a narrow strip, the width of the heat treated area is desired to be controlled within certain tolerances. The problem facing a production engineer is: How fast can the material be treated and the desired tolerances on the heat treated area met? The principle of the findings can be applied to other processes that involve the molten phase. However, it is not the purpose of this study to argue whether or not the molten pool has a shorter or longer response time than the response time due to heat conduction. If the molten pool has a response time that is shorter than the time response from conduction in the solid, then the results of this study will give a good indication of the maximum processing speed, since the response of the system will be controlled by the longest time response. This is because the heat has to flow through the molten pool to be removed by heat conduction; or in electrical terms the system is in series. If the molten pool has a much slower response time than the time response from conduction in the solid, then the results of this study will overestimate the maximum controllable processing speed. A good practical analogy to what is studied here is given by the following example. Suppose you want to paint a straight vertical line on a wall (freehand between predetermined marks). This line is to serve a decorative purpose. Therefore there is a tolerance on the width variation that you will accept. On the other hand, decorating is not enjoyable to you and so you would like to finish the job as fast as possible. There is obviously a trade off between the speed that you can paint and the quality of the job. A slow and careful job looks brilliant, but may take too much time.
25.2
Theory
The theory developed here will use the frequency domain properties of the diffusion equation to formulate how a control system would perform, given perfect instantaneous knowledge of the heated area formed by a laser being scanned over a workpiece. The arguments given will not follow a strict mathematical development. A quick summary of how we arrive at the results can be stated as:
© Woodhead Publishing Limited, 2010
794
Advances in laser materials processing
The size of the heat treated area depends on the heat flow from its edge. The heat treated area will therefore shrink or grow as quickly as the information about the temperature distribution in the rest of the workpiece is adjusted to balance the heat flow. The properties of the heat diffusion equation mean that temperature information travels at a speed proportional to the square root of the frequency. The temperature information has to travel faster than the heat treatment process (the speed that the laser scans across the workpiece) to be useful to a control system. Thus high frequency temperature information has to be used to “keep ahead” of the laser scan, thus imposing a low frequency limit on the control system. Unfortunately, in order to meet the quality requirements of the resultant heat treated area, the temperature information has to travel from a certain distance away from the heat source, in order for the control system to “sense” changes in the heat flow, which introduces a phase delay to the control system. The phase delay cannot be too great (less than p), or the control system becomes unstable. Since the phase delay increases with frequency, this imposes an upper limit on the frequency that can be used by the control system. Thus too high a frequency will lead to instability of the control system and too low a frequency will not allow the control system to “sense” changes ahead of the moving laser beam. These two constraints limit the maximum controllable laser processing speed.
25.2.1 Flow of temperature information Control systems must use information to control a process. In this case the information is transmitted by heat or temperature waves. The feedback system will use a control algorithm to try and keep the heated area within a quality specification, a set point or desired temperature. The stability of control systems is usually analysed in terms of the frequency response of the system as a whole. The physics of the system that is to be controlled dictates the fastest response of the feedback control that is possible. The analysis below is intended to find out what constraints are required for stable control of a fast moving laser heat source. The results of the analysis could be applied to controlling a weldpool size, if it were assumed that heat transport in the molten pool is very much faster than in the solid. Thus the heat flow in the solid will be the limiting response time of the system when a controlled procedure is used. The speed at which temperature information can travel in the solid is given by the group velocity.
25.2.2 Group velocity The heat diffusion equation at the surface of the workpiece is given by
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ˆ Ê ∂T + U · —T ˜ – — · (k—T ) = q rC p Á ¯ Ë ∂t where q· is the laser power absorbed, and is what the control system will vary to control the heat input. The equation for convective heat flow in the solid is given by ∂T + U · —T – nth — 2 T = 0 ∂t which for the purpose of this analysis can be written ignoring the convective term: ∂T – nth — 2 T = 0 ∂t Fourier Transform these equations in time and space: (iw + iU · k – nth Ík2 Í)T = 0 and for the equation ignoring convection: (iw – nth Ík2Ô)T = 0 The Dispersion relation is derived by equating the expression inside the brackets to zero: iw + iU · k – nth Ík2Ô = 0 and for the case ignoring convection: iw – nth Ík2Ô = 0 The group velocity is given by the expression cg = ∂w ∂k Thus the group velocity of “temperature” waves can be derived from the heat diffusion equation in the solid. cg = 2nw (1 + i )
[25.1]
where the real part is the speed of information transfer and the imaginary part the damping of the amplitude or loss of information signal strength. The convection term would be added (a vector add) to get the speed in relation to the moving source. In the direction of the laser movement, for information ahead of the laser spot, the group velocity has to exceed the speed of the laser head, U.
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The damping of the temperature waves will make the stable control of the treatment size or temperature more difficult (more prone to instability and as the return signal to noise becomes smaller).
25.2.3 Typical length scale This length scale will depend on the geometry of the heat source. It will be different for keyhole welding and conduction welding. For the heat treatment case taken here it will be the size of the laser spot. The typical length scale is l. The time taken to travel this length is given by t= l cg
[25.2]
25.2.4 Quality Information must arrive at the heat source before moving distance l. This defines a time within which the temperature information must be given to the heat source: l > Ut
[25.3]
Therefore 1 l>U l =U cg 2nw (1 + i )
[25.4]
Thus frequency must be higher than 2 2 w > U l2 2nl
[25.5]
for the information to arrive in time. This leads to the definition of a quality length scale, l. The larger this value is the lower the quality of the weld bead or treated area. It represents the tolerable length over which the treated area may lie outside the intended, treatment temperature, size or position. It would be expected that the quality length scale l, would be a fraction of the typical length scale l. For example the typical length scale in a heat treatment application would be the intended width or depth, so if a 20% variation in the width of the treated area were tolerable then l = 0.2l. Figure 25.1 shows a schematic of the quality length for a laser heat treated region. For the heat treatment case considered here it is the maximum continuous length that the temperature is tolerated to be “out of specification”. The temperature overshoot and undershoot as well as the degree of
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Treated region width
Quality length, l Temp. Set temp.
25.1 Bead quality schematic.
thinning and thickening of the treated area will depend on the “challenge” that the control system has to face. A small perturbation to the heat flow will result in a small variation in width along the quality length, whereas a large perturbation will result in a large change in width, that the control system will be able compensate for, over the quality length.
25.2.5 Phase shift However, as the frequency increases, a growing phase shift is introduced. If this phase shift is too great then the information will cause instability if used in a feedback loop to control the quality; this shown in equation 25.6. w
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The phase shift must be less than 180 degrees (p radians).
25.2.6 Stable operating window This leads to an upper and lower limit on the frequency component that can be used for feedback to control the heat source. Using equations 25.5 and 25.6: U 2 l 2 < w < pU l 2nl 2
[25.7]
Frequencies above the lower limit ensure that the information will arrive in time. Frequencies below the upper limit will not be out of phase.
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25.2.7 Maximum controllable speed Information between these frequency bounds can be used only if a stable control system is to be employed. This leads to a natural limit on the speed of laser processing: U<
2npl l2
[25.8]
above this speed there is no frequency window in which stable control is possible.
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Experiments
a series of experiments were designed to test the response of a controlled laser processing system to abrupt changes in thickness of a workpiece at different travel speeds. The experiments were performed using a 2.5 kW Rofin Sinar laser and 0.6 mm diameter step-index fibre terminated with 200 mm focal length collimating and focusing lenses positioned so that they formed a laser spot about 3.5 mm on the surface of the substrate. The surface temperature under the laser spot was measured using a maurer two-colour pyrometer capable of measuring temperatures between 500 and 1500 °C and TemCon control software and hardware developed by LZH. The pyrometer was mounted vertically above the substrate and at 90° to the collimating lens via a bending cube. The workpiece used was 10 mm thick mild steel plate with 50 mm wide sections milled from one side so that its thickness varied discontinuously in steps (Fig. 25.2). The wall thickness of the milled sections was 2 mm, 0.98 mm and 1.1 mm. The top surface of the sample, which was flat, was cleaned and grit blasted. The sample was mounted under the laser beam with the milled section in the opposite side from the laser beam. The control system was optimised to try and keep the temperature of the surface under the laser Pyrometer Fibre optic 90° beam bender Laser beam 2 mm
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25.2 Schematic of experimental layout.
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spot at 1200 °C, in order to avoid any issues associated with the melt phase. The melting point of mild steel is 1538 °C.
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Experimental results
25.4.1 Initialisation of control parameters A series of experiments were carried out to optimise the control parameters for a one metre per minute travel speed on 10 mm thick mild steel. The system was set up to control the temperature under the laser beam spot to a set point of 1200 °C. Table 25.1 summarises the results of the PID tunning experiments. The system response was determined to be slightly underdamped. This can be seen in the control signal in Figs 25.4 to 25.6.
25.4.2 Measurements The first set of experiments compared an uncontrolled run with a controlled run over the 10 mm plate with the 0.98 mm and 1.1 mm thick sections. Figure 25.3 shows the results. The fixed power run shows a measured surface temperature of about 900 °C over the 10 mm thick sections, about 1350 °C over the 0.98 mm thick section and about 1150 °C over the 1.1 mm thick section. The controlled run maintains about 1200 °C (the set-point), except for overshoots and undershoots, which occur at the thickness transitions. A series of runs was made at different travel speeds, with the control system activated. These were at 2, 1, 0.5, 0.25 and 0.125 metres per minute. The results are shown in Figs 25.4 to 25.8.
25.5
Discussion
The size of the hot region (above 1200 °C) will decrease as the travel speed increases. As the travel speed drops below about 0.5 m/min, the depth of the hot region begins to be affected by the 2 mm thick region. This is seen in the control signal in Figs 25.6 to 25.8. The performance of the control Table 25.1 Control parameters used Parameter
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system is good at travel speeds below 0.5 m/min. Figures 25.4 to 25.6 show overshoot and undershoot excursions (300 °C at a travel speed of 2 m/min). The overall performance of the control system can be measured by recording the maximum deviation in the measured temperature from the set point of 1200 °C over at the thickness transitions which occurred at about 50 mm,
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25.6 Surface temperature and control signal: 0.5 m/min travel speed.
100 mm, 150 mm, 200 mm and 250 mm along the plate. The full traces are shown in Figs 25.4 to 25.8 and the maximum temperature deviations are shown in Table 25.2. However, the maximum deviations tell only part of the story. The length of the treated area that does not conform to the specified tolerance is also very important.
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25.8 Surface temperature and control signal: 0.125 m/min travel speed.
Although this is a very crude assessment of quality of the laser heat treatment process, it gives a numerical measure to what can be clearly seen in the traces. The thickness transition from 10 mm to 2 mm and back to 10 mm result in temperature deviations that are indistinguishable from the inherent noise. The inherent noise has a standard deviation from the set point
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Table 25.2 Control performance vs. travel speed Travel speed (m/min)
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TD at 250 mm (°C)
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92 101 188 198 146
TD = Temperature deviation.
of about 30 °C and is most probably caused by variation in the absorption of the laser beam by the workpiece. Developing a robust control system that will cope with this noise is part of the control engineer’s challenge. For thickness steps to 0.98 mm and 1.1 mm, clear overshoot and undershoot in the controlled temperature are seen. Below a travel speed of about 0.5 m/min this control system can cope with the severe test of a sudden change in plate thickness. Such rapid changes in the heat sink configuration are not uncommon in engineering structures. Thick reinforcement webs often support thin plate. Holes and slots are usually part of engineering structures and can act as powerful changes to the heat flow, if fast laser processing is carried out near them. This suggests an alternative approach to the control problem. If more gentle changes in the heat sink could be designed into the structure, then higher quality laser processing could be achieved at higher speed. However in practice, the system would still have to respond to unforeseen changes, such as step changes in the absorption due to uncontrolled changes in surface condition (i.e., rust and roughness).
25.5.1 Theory and experiment In the tests reported here, the system had to respond to a change in plate thickness, from very thick to about 1 mm. This means that the temperature information had to travel from the top of the plate (where the laser spot strikes the plate), to the back-face of the plate and back to the top again to be part of the control loop. The diameter of the spot was 3.5 mm. So that the leading edge of the spot would experience the changes in section thickness, before the trailing edge. The spot diameter will be taken as the typical length scale. Thus knowing the thermal diffusivity of mild steel, equation 25.9 can be used to predict a minimum quality length for any particular travel speed: 2 l = Ul 2 pn
[25.9]
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Using, n = 5.2 10–6 m2s–1, from Kaye and Laby (Kaye and Laby, 1986) and l = 3.5 mm (diameter of the laser spot), the minimum predicted quality length is plotted against travel speed shown in Fig. 25.9, together with the measured quality length on the 10 mm to 0.98 mm transition (150 mm along the plate), the 0.98 to 10 mm transition (at 200 mm), and the 10 mm to 1.1 mm transition (at 250 mm along the plate). The measured quality length was taken as the width of the overshoot at each transition. Agreement of the measured quality length and the predicted quality length is good. Note that the quality length tells the control engineer nothing about the size of the overshoot; just how far along the treated length it takes the control system to recover its set point. Thus the production engineer may have the freedom to minimise the perturbations that the control system is subjected to, but Fig. 25.9 shows that demanding higher quality (smaller quality length) requires a lower travel speed. This reinforces what engineers know well. Higher quality takes more time.
25.6
Conclusions
A simple model of the performance of a control system for laser processing has been presented and compares well with an idealised experimental test. The model predicts that the maximum controllable travel speed depends on the quality required of the laser treated material. Higher quality requires a slower travel speed.
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25.9 Comparison of quality length at three thickness transitions.
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Acknowledgements
This work was carried out at the Industrial Research Institute Swinburne, which is part of the Faculty of Engineering and Industrial Sciences, Swinburne University of Technology. Thanks to Mr Brian Dempster for preparing the samples and Prof. Milan Brandt and Dr Jim Harris for running the laser used in the experiments. The author also acknowledges the useful discussions and help given by colleagues many years ago in developing practical control systems for arc welding at Marchwood Engineering Laboratories, (formerly part of the Central Electricity Generating Board near Southampton in England).
25.8
References
Deam, R. T. (1989) Weldpool frequency: A new way to define a weld procedure. In David, S. A. & Vitek, J. M. (Eds.) Recent Trends in Welding Science and Technology. Gatlingburg, Tennessee, USA, ASM International. Deam, R. T., Brandt, M. & Harris, J. (2003) Investigation of capillary waves excited by a Nd:YAG laser using pyrometry. Journal of Physics D: Applied Physics, 36, 10. Duley, W. W. (1998) Laser Welding, New York, John Wiley and Sons. Grunenwald, B., Shen, J., Dausinger, F. & Hugel, H. (1993) Laser cladding with composite powders using pyrometric temperature control and beam combination. ISATA ’93 International Symposium on Automotive Technology and Automation. Aachen, Germany. Haferkamp, H., Goede, M. & Lindemann, K. (2000) Laser Hardening of CVD coated tool steel. 12th International Federation for Heat Treatment and Surface Engineering Congress. Melbourne. Kaye, G. W. C. & Laby, T. H. (1986) Tables of Physical and Chemical Constants, London, Longman. Laser Zentrum Hannover E. V. (2006) Web Page. Laser Zentrum Hannover e.V., Hollerithallee 8, D-30419 Hannover. Nagarajan, S., Groom, K. N. & Chin, B. A. (1989) Infrared sensors for seam tracking in tungsten arc welding processes. In David, S. A. & Vitek, J. M. (Eds.) Recent Trends in Welding Science and Technology. Gatlingburgh, Tennessee, USA, ASM International. Norrish, J. (1992) Advanced Welding Processes, Institute of Physics. Prokoshev, V. G., Abramov, D. V., Danilov, S. Y., Kucherik, A. O. & Arakelian, S. M. (2001) Diagnostics of the high temperature hydrodynamic phenomena for laser processing of the material. Laser Assisted Net Shape Engineering 3, Proceedings of the LANE 2001. Salter, R. J. & Deam, R. T. (1987) A practical frontface penetration control system. 2nd International Conference on Developments in Automatic and Robotic Welding. London, The Welding Institute. Smith, E. T. & Kannatey-Asibu, E. (1999) Visualization and Acoustic Monitoring of Laser Weld Pool Oscillatory Behavior. ICALEO 1999. Laser Institute of America. Steen, W. M. (1998) Laser Material Processing, London, Springer-Verlag
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