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Feedback control of HVOF thermal spray process: A study of the effect of process disturbances on closed-loop performance
Process Systems Engineering 2003 B. Chen and A.W. Westerberg (editors) 9 2003 Published by Elsevier Science B.V.
Feedback
control
of HVOF
the effect of process
1193
thermal
disturbances
spray
process:
on closed-loop
A study
of
performance
Mingheng Li, Dan Shi and Panagiotis D. Christofides Department of Chemical Engineering, University of California, Los Angeles, CA 90095 A b s t r a c t This work focuses on feedback control of the high velocity oxygen-fuel (HVOF) thermal spray process in the presence of significant variations in the process operating conditions. Based on the predictions of a fundamental model which is capable of capturing the essential features of the HVOF process, and available experimental observations, the control problem is formulated as the one of regulating volume-based averages of the temperature and velocity of the particles at the point of impact on substrate by manipulating the oxygen/fuel ratio and the combustion chamber pressure, respectively. A feedback control system is developed and applied to a detailed mathematical model of the process. Closed-loop simulations show that the feedback control system ensures process operation at the desired set-point values in the presence of significant variations in the spray distance, initial particle velocity and size distribution of the powder. Keywords tribution
HVOF thermal spray, process modeling, feedback control, powder size dis-
1. I N T R O D U C T I O N The high velocity oxygen-fuel (HVOF) thermal spray technology is widely used to deposit a large variety of metal and ceramic coatings in order to modify the surface properties of a base material. By coating a substrate with another high performance material, several substrate properties such as abrasion resistance, corrosion protection, and thermal insulation, can be significantly improved. In order to reduce product variability and to improve robustness with respect to variations in the operating conditions in industrial HVOF thermal spray processes, it is important to implement excellent real-time process diagnosis and control which could lead to the fabrication of coatings with microstructures that yield the desired properties. Despite the recent progress on the modeling of the various phenomena that affect droplet motion, deposition, solidification and microstructure development in HVOF processes, at this stage, there exists no systematic framework for integrated on-line diagnosis and control of the HVOF thermal spray process which will be capable of achieving precise regulation of the microstructure and ultimate mechanical and thermal properties of the sprayed coatings. In addition, incorporation of advanced real-time diagnosis and control schemes into thermal spray processes is expected to reduce operational cost and environmental impact, and allow depositing nanostructured and complex (multi-material) coatings with very low variability. Since the application of optimization and control techniques to spray casting processes has been reported to lead to significant improvements in their opera-
1194 Nozzle I_ Combustion _1_ _[_ 1- Chamber "-~ "-~
Barrel
__1
-I
Oxidant Fuel Powder injection Cooling Water in
Figure i. Schematic of an HVOF
Cooling Water Out
thermal spray process.
tion and performance, it is important to develop real-time computer control systems for thermal spray processes by integrating fundamental models that accurately describe the inherent relationships between the coating microstructure and the processing parameters with on-line state-of-the-art diagnostic techniques and control algorithms. This work focuses on feedback control of the high velocity oxygen-fuel (HVOF) thermal spray process in the presence of significant variations in the process operating conditions. Following our previous work [4], the control problem is formulated as the one of regulating volume-based averages of the temperature and velocity of the particles at the point of impact on substrate by manipulating the oxygen/fuel ratio and the combustion chamber pressure, respectively. A feedback control system is developed and applied to a detailed mathematical model of the process. Closed-loop simulations show that the feedback control system ensures process operation at the desired set-point values in the presence of significant variations in the spray distance, initial particle velocity and size distribution of the powder. 2. P R O C E S S D E S C R I P T I O N Fig. 1 shows the schematic diagram of a commonly used HVOF thermal spray process. It consists of a combustion chamber, a Laval nozzle (also known as convergent/divergent nozzle), and a barrel. High pressure and high temperature combustion gases, which are generated by the reaction of fuel gases (typically propylene, propane and hydrogen etc.) and oxygen (or/and air) in the combustion chamber, are accelerated to supersonic velocity through the Laval nozzle. Outside of the gun, the supersonic free jet adjusts to the ambient pressure by a series of compression and expansion waves, and visible shock diamonds are formed downstream of the barrel exit. The solid particles of metal or ceramic powders are injected nearly axially into the gas stream at the exit of the nozzle, where the pressure is not so high as that in the combustion chamber so that powders can easily enter the gas stream. The powder particles are accelerated and heated in the barrel and in the free jet, and then impinge on the substrate with high velocity to make coatings. Generally speaking, there are three kinds of energy conversions involved in the HVOF processes: chemical energy to thermal energy by the exothermic reaction of fuel and oxygen, occurring mainly in the chamber, thermal energy to kinetic energy, taking place mainly in the nozzle, and thermal and kinetic energy of gases to those of particles, occurring in the barrel and the supersonic jet. These processes are essentially coupled together and make the HVOF very difficult to analyze. Furthermore, the compressible gas behavior and the highly turbulent flow characteristics render this process much more complicated. To be able to develop a fundamental model that is tractable and accounts for the main
1195 features of the process, we will assume that the presence of particles has a negligible effect on the gas velocity and temperature field. This assumption is standard and reasonably accurate because the particle loading, which is defined as the ratio of mass flow rate of particles to that of gases, is typically less than 4%. As a consequence, the two-phase problem can be decoupled so that the gas field can be solved first, followed by the simulation of particle infight behavior. With this assumption, a one dimensional model is employed to simulate the internal and external gas flow/thermal field, and the particle trajectories and temperature histories are solved by momentum transfer and heat transfer equations. To further simplify the analysis, we will also make the following standard assumptions: (1) the flame gas obeys the ideal gas law; (2) chemical equilibrium is reached in the combustion chamber and the composition of the product mixture is frozen at the chamber condition during passage of the Laval nozzle and barrel due to the very short residence time of combustion gases in the HVOF gun (this assumption was validated in Ref. [5] based on the comparison of experimental data and simulation results); (3) the gases behave like a perfect gas during isentropic compression and expansion, and the specific heat ratio (7 = %/c,,) is nearly a constant; and (4) the friction and cooling water effects along the nozzle and barrel are negligible so that laws of isentropic flow of compressible fluids apply. Based on the above assumptions, we solved the gas flow/thermal field and made a control relevant parametric analysis for an HVOF process using propane as fuel and air as oxidant (see [3] for details). The parametric analysis of gas dynamics shows that both the gas velocity and temperature are highly dependent on the equivalence ratio (defined as the fuel/oxygen ratio divided by the stoichiometric fuel/oxygen ratio). Although the gas temperature does increase slightly with pressure, its dependence on the latter is very limited. The influence of pressure on gas velocity is even smaller since v ~ a c< T 1/2. In the normal equivalence ratio range, gas velocity increases monotonically with the equivalence ratio. However, as the equivalence ratio increases, the gas temperature increases first, reaching its peak value at the equivalence ratio about 1.05, and then decreases. Whereas the chamber pressure does not affect gas velocity, its influence on the gas density is significant. As a result, the gas momentum flux (pv 2) is a linear function of chamber pressure. In fact, the gas momentum flux is only dependent on the chamber pressure and has nothing to do with the equivalence ratio since pv 2 = pM2 (',/ P / p) = M2"),P. Because the drag force, which is the dominant force for the motion of particles in the gas field, is approximately proportional to the gas momentum flux, and the gas temperature, whose difference between the particle temperature, provides the driving force for particle heating, it is expected from the above analysis that particle temperature and velocity can be almost independently adjusted by manipulating the equivalence ratio and the combustion pressure. These conclusions are consistent with experimental observations [2] and set the basis for feedback control of the HVOF process. 3. F E E D B A C K
CONTROL
Based on the model predictions, and the available experimental observations, the control problem for the HVOF process is formulated as the one of regulating the temperature and velocity of the particles at impact on the substrate (these are the variables that directly influence coating microstructure and porosity which determine coating strength and hardness) by manipulating the combustion chamber pressure (total inlet flow of com-
1196
A
A
~ 358
754
357
~ 75o Q.
356
~7,~
I
3%
5
~
1'5
20
25
30
35
Time (s)
7%
5
,'o
,'s
2o
2'5
io
35
Time (s)
(a)
(b)
Figure 2. Profiles of volume-based average particle velocity (a) and particle temperature (b) with respect to time in the presence of a 30% disturbance on spray distance. Open-loop system (solid curve) and closed-loop system (dashed curve). bustion gases) and the oxygen/fuel ratio. Owing to the almost decoupled nature of the manipulated input/controlled output pairs, two proportional integral (PI) controllers are used to regulate the process. Specially, the controls have the following form: r
i=1,2
~i
=
Ysv~ - yi,
ui
=
K~,(y~p~ - yi) + l (i + Uo,, Tci
i=1,2
(1)
where ysp~ is the specified output, yl is the averaged particle velocity and y2 is the averaged particle temperature, Kc~ is the proportional gain and Tc~ is the integral time constant. The design and implementation of a model-based feedback control system using techniques proposed in Ref. [1] will be the subject of future work. 4. S I M U L A T I O N R E S U L T S Several simulation runs of the process model under the feedback controller were performed to evaluate the ability of the controller to attenuate the effect of disturbances on process operating conditions. Figs. 2 and 3 show the controlled output and manipulated input profiles in the presence of 30% disturbance in the spray distance (i.e. the spray distance increases from 0.3 m to 0.39 m and then stays at this value) which occurs at t - 10 sec. Without control, the process jumps to a new steady state in a very short time (owing to the very short time of particle flight), and both the particle velocity (solid curve in Fig. 2a) and temperature (solid curve in Fig. 2b) drop instantaneously due to further particle cooling and deceleration. Under feedback control, the process outputs (dashed curves in Fig. 2a, b) move gradually and finally achieve their desired set-point values in about 30 s e a Fig. 4 shows the controlled output profiles in the presence of 20 m / s change in initial particle velocity at t - 10 sec. Without control, the impact particle velocity slightly increases while the particle temperature decreases by about 15 K. The drop of particle temperature is explained by the shortened residence time of particles in the flame gas, which is caused by an increase in the particle velocity during flight, although the particle velocity at the point of impact remains nearly the same. Such a temperature change can have a significant effect on the molten state of the particle and the resulting coating microstructure. Under feedback control, the manipulated inputs drive the process outputs
1197
0.83
c'~ 6.10
~
0.82
-~
0.81
~6.06
~0 6.02
! 5.98(~
5
10
15 20 Time (s)
25
30
35
0.79
5
10
(a)
15 20 Time (s)
25
30
35
(b)
Figure 3. Profiles of chamber pressure (a) and equivalence ratio (b) with respect to time in the presence of a 30% disturbance on spray distance. Open-loop system (solid curve) and closed-loop system (dashed curve). 755
358.8 A
' 358.6 e --o ~ 358.4
s~'~o
a. 745 r
s
lO
1s
2o
Time (s)
(a)
~s
so
s5
74%
s
0
15 20 Time (s)
25
30
35
(b)
Figure 4. Profiles of volume-based average particle velocity (a) and particle temperature (b) with respect to time in the presence of 20 m / s variation in initial particle velocity. Open-loop system (solid curve) and closed-loop system (dashed curve). to their original steady state values in about 35 s e a Also, note that a variation in particle injection velocity has an effect on the process somewhat similar to a change in the injection position; the variations in the particle velocity and temperature at the point of impact on substrate are consistent with the experimental observation in Ref [2]. Another source of disturbance to the process operation, especially in an industrial environment, is the variation of the size distribution of the powder during the operation of the HVOF process. This may have a significant influence on the particle velocity and particle temperature at the point of impact on the substrate based on the analysis of modeling [3,4]. In the following simulation, it is assumed that the process is at steady state in the first 100 sec and then the powder size distribution changes gradually (specifically, # increases following # - #0.[1 +0.05.(1-e-t/I~176 and a 2 is kept constant). Fig. 5 (dashed curves) shows the controlled outputs in the presence of such variation in the powder size distribution. Both particle velocity (Fig. 5a) and temperature (Fig. 5b) fluctuate in a very narrow range and eventually reach the desired set-point values. When no control is used (Fig. 5 solid curves), in which case the chamber pressure and the equivalence ratio are kept constant, both particle velocity and particle temperature decrease with time, which may have an undesirable effect on the resulting coating properties. In summary, the closed-loop system simulations in the presence of disturbances show that the controller attenuates the effect of disturbances and drives the controlled outputs to the desired set-
1198 A
- 355
75O
~o
~'740 345
1::
L730
~34o "r
o 720
335
loo
~
3oo
~
~
8oo
~me ts)
(~)
71,
1~o
2~o
3~o
400
500
600
Time (s)
(b)
Figure 5. Profiles of volume-based average particle velocity (a) and particle temperature (b) with respect to time in the presence variation in powder size distribution. Open-loop system (solid curve) and closed-loop system (dashed curve). point values within about 20 sec. Faster disturbance rejection could be achieved at the expense of using larger control action; for an experimental HVOF system, the optimal speed of disturbance rejection should be determined on the basis of the system response to the disturbances. NOMENCLATURE a
sonic velocity, defined as V/7P/p (m/s)
K~ proportional gain M
P T U V
Y P 7 Tc # (7
Mach number, the ratio of gas velocity to the local sonic velocity (dimensionless) pressure (Pa) temperature (K) manipulated input velocity (m/s) measured output density (kg/m 3) specific heat ratio (dimensionless) integral time constant mean of In dp (dimensionless) standard deviation of In dp (dimensionless)
REFERENCES
1. P.D. Christofides. Model-Based Control of Particulate Processes. Particle Technology Series, Kluwer Academic Publishers, Netherlands, 2002. 2. T.C. Hanson, C. M. Hackett, and G. S. Settles. Independent control of HVOF particle velocity and temperature. J. Thermal Spray Tech., 11:75-85, 2002. 3. M. Li and P. D. Christofides. Modeling and analysis of HVOF thermal spray process accounting for powder size distribution. Chem. Eng. Sci., 58:849-857, 2003. 4. M. Li and P. D. Christofides. Feedback control of HVOF thermal spray process accounting for powder size distribution. J. Thermal Spray Tech., in press. 5. W. D. Swank, J. R. Fincke, D. C. Haggard, and G. Irons. HVOF gas flow field characteristics. In Proc. 7th Natl Thermal Spray Conf., pages 313-318, Boston, Massachusetts, 1994.
Feedback
control
of HVOF
the effect of process
1193
thermal
disturbances
spray
process:
on closed-loop
A study
of
performance
Mingheng Li, Dan Shi and Panagiotis D. Christofides Department of Chemical Engineering, University of California, Los Angeles, CA 90095 A b s t r a c t This work focuses on feedback control of the high velocity oxygen-fuel (HVOF) thermal spray process in the presence of significant variations in the process operating conditions. Based on the predictions of a fundamental model which is capable of capturing the essential features of the HVOF process, and available experimental observations, the control problem is formulated as the one of regulating volume-based averages of the temperature and velocity of the particles at the point of impact on substrate by manipulating the oxygen/fuel ratio and the combustion chamber pressure, respectively. A feedback control system is developed and applied to a detailed mathematical model of the process. Closed-loop simulations show that the feedback control system ensures process operation at the desired set-point values in the presence of significant variations in the spray distance, initial particle velocity and size distribution of the powder. Keywords tribution
HVOF thermal spray, process modeling, feedback control, powder size dis-
1. I N T R O D U C T I O N The high velocity oxygen-fuel (HVOF) thermal spray technology is widely used to deposit a large variety of metal and ceramic coatings in order to modify the surface properties of a base material. By coating a substrate with another high performance material, several substrate properties such as abrasion resistance, corrosion protection, and thermal insulation, can be significantly improved. In order to reduce product variability and to improve robustness with respect to variations in the operating conditions in industrial HVOF thermal spray processes, it is important to implement excellent real-time process diagnosis and control which could lead to the fabrication of coatings with microstructures that yield the desired properties. Despite the recent progress on the modeling of the various phenomena that affect droplet motion, deposition, solidification and microstructure development in HVOF processes, at this stage, there exists no systematic framework for integrated on-line diagnosis and control of the HVOF thermal spray process which will be capable of achieving precise regulation of the microstructure and ultimate mechanical and thermal properties of the sprayed coatings. In addition, incorporation of advanced real-time diagnosis and control schemes into thermal spray processes is expected to reduce operational cost and environmental impact, and allow depositing nanostructured and complex (multi-material) coatings with very low variability. Since the application of optimization and control techniques to spray casting processes has been reported to lead to significant improvements in their opera-
1194 Nozzle I_ Combustion _1_ _[_ 1- Chamber "-~ "-~
Barrel
__1
-I
Oxidant Fuel Powder injection Cooling Water in
Figure i. Schematic of an HVOF
Cooling Water Out
thermal spray process.
tion and performance, it is important to develop real-time computer control systems for thermal spray processes by integrating fundamental models that accurately describe the inherent relationships between the coating microstructure and the processing parameters with on-line state-of-the-art diagnostic techniques and control algorithms. This work focuses on feedback control of the high velocity oxygen-fuel (HVOF) thermal spray process in the presence of significant variations in the process operating conditions. Following our previous work [4], the control problem is formulated as the one of regulating volume-based averages of the temperature and velocity of the particles at the point of impact on substrate by manipulating the oxygen/fuel ratio and the combustion chamber pressure, respectively. A feedback control system is developed and applied to a detailed mathematical model of the process. Closed-loop simulations show that the feedback control system ensures process operation at the desired set-point values in the presence of significant variations in the spray distance, initial particle velocity and size distribution of the powder. 2. P R O C E S S D E S C R I P T I O N Fig. 1 shows the schematic diagram of a commonly used HVOF thermal spray process. It consists of a combustion chamber, a Laval nozzle (also known as convergent/divergent nozzle), and a barrel. High pressure and high temperature combustion gases, which are generated by the reaction of fuel gases (typically propylene, propane and hydrogen etc.) and oxygen (or/and air) in the combustion chamber, are accelerated to supersonic velocity through the Laval nozzle. Outside of the gun, the supersonic free jet adjusts to the ambient pressure by a series of compression and expansion waves, and visible shock diamonds are formed downstream of the barrel exit. The solid particles of metal or ceramic powders are injected nearly axially into the gas stream at the exit of the nozzle, where the pressure is not so high as that in the combustion chamber so that powders can easily enter the gas stream. The powder particles are accelerated and heated in the barrel and in the free jet, and then impinge on the substrate with high velocity to make coatings. Generally speaking, there are three kinds of energy conversions involved in the HVOF processes: chemical energy to thermal energy by the exothermic reaction of fuel and oxygen, occurring mainly in the chamber, thermal energy to kinetic energy, taking place mainly in the nozzle, and thermal and kinetic energy of gases to those of particles, occurring in the barrel and the supersonic jet. These processes are essentially coupled together and make the HVOF very difficult to analyze. Furthermore, the compressible gas behavior and the highly turbulent flow characteristics render this process much more complicated. To be able to develop a fundamental model that is tractable and accounts for the main
1195 features of the process, we will assume that the presence of particles has a negligible effect on the gas velocity and temperature field. This assumption is standard and reasonably accurate because the particle loading, which is defined as the ratio of mass flow rate of particles to that of gases, is typically less than 4%. As a consequence, the two-phase problem can be decoupled so that the gas field can be solved first, followed by the simulation of particle infight behavior. With this assumption, a one dimensional model is employed to simulate the internal and external gas flow/thermal field, and the particle trajectories and temperature histories are solved by momentum transfer and heat transfer equations. To further simplify the analysis, we will also make the following standard assumptions: (1) the flame gas obeys the ideal gas law; (2) chemical equilibrium is reached in the combustion chamber and the composition of the product mixture is frozen at the chamber condition during passage of the Laval nozzle and barrel due to the very short residence time of combustion gases in the HVOF gun (this assumption was validated in Ref. [5] based on the comparison of experimental data and simulation results); (3) the gases behave like a perfect gas during isentropic compression and expansion, and the specific heat ratio (7 = %/c,,) is nearly a constant; and (4) the friction and cooling water effects along the nozzle and barrel are negligible so that laws of isentropic flow of compressible fluids apply. Based on the above assumptions, we solved the gas flow/thermal field and made a control relevant parametric analysis for an HVOF process using propane as fuel and air as oxidant (see [3] for details). The parametric analysis of gas dynamics shows that both the gas velocity and temperature are highly dependent on the equivalence ratio (defined as the fuel/oxygen ratio divided by the stoichiometric fuel/oxygen ratio). Although the gas temperature does increase slightly with pressure, its dependence on the latter is very limited. The influence of pressure on gas velocity is even smaller since v ~ a c< T 1/2. In the normal equivalence ratio range, gas velocity increases monotonically with the equivalence ratio. However, as the equivalence ratio increases, the gas temperature increases first, reaching its peak value at the equivalence ratio about 1.05, and then decreases. Whereas the chamber pressure does not affect gas velocity, its influence on the gas density is significant. As a result, the gas momentum flux (pv 2) is a linear function of chamber pressure. In fact, the gas momentum flux is only dependent on the chamber pressure and has nothing to do with the equivalence ratio since pv 2 = pM2 (',/ P / p) = M2"),P. Because the drag force, which is the dominant force for the motion of particles in the gas field, is approximately proportional to the gas momentum flux, and the gas temperature, whose difference between the particle temperature, provides the driving force for particle heating, it is expected from the above analysis that particle temperature and velocity can be almost independently adjusted by manipulating the equivalence ratio and the combustion pressure. These conclusions are consistent with experimental observations [2] and set the basis for feedback control of the HVOF process. 3. F E E D B A C K
CONTROL
Based on the model predictions, and the available experimental observations, the control problem for the HVOF process is formulated as the one of regulating the temperature and velocity of the particles at impact on the substrate (these are the variables that directly influence coating microstructure and porosity which determine coating strength and hardness) by manipulating the combustion chamber pressure (total inlet flow of com-
1196
A
A
~ 358
754
357
~ 75o Q.
356
~7,~
I
3%
5
~
1'5
20
25
30
35
Time (s)
7%
5
,'o
,'s
2o
2'5
io
35
Time (s)
(a)
(b)
Figure 2. Profiles of volume-based average particle velocity (a) and particle temperature (b) with respect to time in the presence of a 30% disturbance on spray distance. Open-loop system (solid curve) and closed-loop system (dashed curve). bustion gases) and the oxygen/fuel ratio. Owing to the almost decoupled nature of the manipulated input/controlled output pairs, two proportional integral (PI) controllers are used to regulate the process. Specially, the controls have the following form: r
i=1,2
~i
=
Ysv~ - yi,
ui
=
K~,(y~p~ - yi) + l (i + Uo,, Tci
i=1,2
(1)
where ysp~ is the specified output, yl is the averaged particle velocity and y2 is the averaged particle temperature, Kc~ is the proportional gain and Tc~ is the integral time constant. The design and implementation of a model-based feedback control system using techniques proposed in Ref. [1] will be the subject of future work. 4. S I M U L A T I O N R E S U L T S Several simulation runs of the process model under the feedback controller were performed to evaluate the ability of the controller to attenuate the effect of disturbances on process operating conditions. Figs. 2 and 3 show the controlled output and manipulated input profiles in the presence of 30% disturbance in the spray distance (i.e. the spray distance increases from 0.3 m to 0.39 m and then stays at this value) which occurs at t - 10 sec. Without control, the process jumps to a new steady state in a very short time (owing to the very short time of particle flight), and both the particle velocity (solid curve in Fig. 2a) and temperature (solid curve in Fig. 2b) drop instantaneously due to further particle cooling and deceleration. Under feedback control, the process outputs (dashed curves in Fig. 2a, b) move gradually and finally achieve their desired set-point values in about 30 s e a Fig. 4 shows the controlled output profiles in the presence of 20 m / s change in initial particle velocity at t - 10 sec. Without control, the impact particle velocity slightly increases while the particle temperature decreases by about 15 K. The drop of particle temperature is explained by the shortened residence time of particles in the flame gas, which is caused by an increase in the particle velocity during flight, although the particle velocity at the point of impact remains nearly the same. Such a temperature change can have a significant effect on the molten state of the particle and the resulting coating microstructure. Under feedback control, the manipulated inputs drive the process outputs
1197
0.83
c'~ 6.10
~
0.82
-~
0.81
~6.06
~0 6.02
! 5.98(~
5
10
15 20 Time (s)
25
30
35
0.79
5
10
(a)
15 20 Time (s)
25
30
35
(b)
Figure 3. Profiles of chamber pressure (a) and equivalence ratio (b) with respect to time in the presence of a 30% disturbance on spray distance. Open-loop system (solid curve) and closed-loop system (dashed curve). 755
358.8 A
' 358.6 e --o ~ 358.4
s~'~o
a. 745 r
s
lO
1s
2o
Time (s)
(a)
~s
so
s5
74%
s
0
15 20 Time (s)
25
30
35
(b)
Figure 4. Profiles of volume-based average particle velocity (a) and particle temperature (b) with respect to time in the presence of 20 m / s variation in initial particle velocity. Open-loop system (solid curve) and closed-loop system (dashed curve). to their original steady state values in about 35 s e a Also, note that a variation in particle injection velocity has an effect on the process somewhat similar to a change in the injection position; the variations in the particle velocity and temperature at the point of impact on substrate are consistent with the experimental observation in Ref [2]. Another source of disturbance to the process operation, especially in an industrial environment, is the variation of the size distribution of the powder during the operation of the HVOF process. This may have a significant influence on the particle velocity and particle temperature at the point of impact on the substrate based on the analysis of modeling [3,4]. In the following simulation, it is assumed that the process is at steady state in the first 100 sec and then the powder size distribution changes gradually (specifically, # increases following # - #0.[1 +0.05.(1-e-t/I~176 and a 2 is kept constant). Fig. 5 (dashed curves) shows the controlled outputs in the presence of such variation in the powder size distribution. Both particle velocity (Fig. 5a) and temperature (Fig. 5b) fluctuate in a very narrow range and eventually reach the desired set-point values. When no control is used (Fig. 5 solid curves), in which case the chamber pressure and the equivalence ratio are kept constant, both particle velocity and particle temperature decrease with time, which may have an undesirable effect on the resulting coating properties. In summary, the closed-loop system simulations in the presence of disturbances show that the controller attenuates the effect of disturbances and drives the controlled outputs to the desired set-
1198 A
- 355
75O
~o
~'740 345
1::
L730
~34o "r
o 720
335
loo
~
3oo
~
~
8oo
~me ts)
(~)
71,
1~o
2~o
3~o
400
500
600
Time (s)
(b)
Figure 5. Profiles of volume-based average particle velocity (a) and particle temperature (b) with respect to time in the presence variation in powder size distribution. Open-loop system (solid curve) and closed-loop system (dashed curve). point values within about 20 sec. Faster disturbance rejection could be achieved at the expense of using larger control action; for an experimental HVOF system, the optimal speed of disturbance rejection should be determined on the basis of the system response to the disturbances. NOMENCLATURE a
sonic velocity, defined as V/7P/p (m/s)
K~ proportional gain M
P T U V
Y P 7 Tc # (7
Mach number, the ratio of gas velocity to the local sonic velocity (dimensionless) pressure (Pa) temperature (K) manipulated input velocity (m/s) measured output density (kg/m 3) specific heat ratio (dimensionless) integral time constant mean of In dp (dimensionless) standard deviation of In dp (dimensionless)
REFERENCES
1. P.D. Christofides. Model-Based Control of Particulate Processes. Particle Technology Series, Kluwer Academic Publishers, Netherlands, 2002. 2. T.C. Hanson, C. M. Hackett, and G. S. Settles. Independent control of HVOF particle velocity and temperature. J. Thermal Spray Tech., 11:75-85, 2002. 3. M. Li and P. D. Christofides. Modeling and analysis of HVOF thermal spray process accounting for powder size distribution. Chem. Eng. Sci., 58:849-857, 2003. 4. M. Li and P. D. Christofides. Feedback control of HVOF thermal spray process accounting for powder size distribution. J. Thermal Spray Tech., in press. 5. W. D. Swank, J. R. Fincke, D. C. Haggard, and G. Irons. HVOF gas flow field characteristics. In Proc. 7th Natl Thermal Spray Conf., pages 313-318, Boston, Massachusetts, 1994.