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Simulation of adaptive controlled machining
Comput & Indus Engag Vol 4. pp. 69-74 Pergamon Press Ltd.. 1980 Prinled in Greal Britain
SIMULATION OF ADAPTIVE CONTROLLED MACHINING R~cH,,3~ A. WvsK, DELBERTL. KIMBLERand ROBERTP. DAVIS Department of Industrial Engineeringand Operations Research,Virginia PolytechnicInstitute and State University,Blacksburg,VA 24061.U.S.A. (Revised October 1979;receivedfor publication 31 October 1979)
Abstr,et--Thispaperpresentsa basicdigitalsimulationstructureforadaptivecontrolledmachiningprocesses. The use of this approachto determinethe feasibilityof adaptivecontrolis discussedand illustrated in the context of a turningoperation. INTRODUCTION The term "adaptive control" has many meanings to users of control systems. These various meanings have in common the notion of sensing process state(s) and modifying process control parameters through some feedback mechanism. Interpretations differ primarily in the logical structures they assume for the relationship between modification and sensed process state. Adaptive control is defined here as the modification of process controlling parameters to optimize some measure of performance as the process state changes over time. The importance of control in machining has long been recognized, beginning with Taylor's tool-life experiments[l l]. The introduction of tool-life as a limited resource depending on machining parameters led to the idea of selecting speed, feed and depth of cut to achieve some optimal measure of performance, such as minimum time or cost of machining[7]. Tayior's mathematical model has been extended by several researchers[i, 2, 5, 13] to include limits such as machine tool power consumption and applied force, tool temperature, achieved surface finish and physical limits on the machining parameters themselves. Resultant advances in the control of machining processes have led to increases in efficiency and productivity, but the static nature of the control structure which they employ has limited effectiveness due to two implicit assumptions. This static control approach assumes that control is perfect and work-piece composition is homogeneous. In reality, control is imperfect and work-piece composition varies through the cutting path, especially in such characteristics as surface contour and material hardness. These variations lead to a consideration of the simplest form of dynamic control, the use of a feedback control loop. This control method monitors the process state and adjusts the process parameters according to specified functional relations between detected state and corresponding control parameter settings. This type of control is typically implemented through an analog control system. While analog control is an improvement over static control, it has its own limiting assumptions. Due to the nature of the analog control loop, the form of the functional relations between process state and parameter set are fixed. Furthermore, it is extremely difficult to incorporate the optimization of some objective performance measure in the control loop [8]. These difficulties can be overcome by the use of a digital control system. This system would sense the process state, determine the parameter values which optimize some objective performance measure, and adjust the process accordingly. Such a control system would be an adaptive control system from the definition above, yet would be controlled by a digital computer. Should an ideal adaptive controller exist, its use should result in further increases in machining efficiency. A realistic system, however, would be subject to the same delays as analog feedback controllers, as well as additional delay in determining the optimum process parameters. Research is proceeding in the technological development of the adaptive control loop[3, 6, 8, 17] and efficient optimization procedures [4, 8, 9]. As this research continues, on-line adaptive control of machining processes comes closer to reality. 69
70
R.A. WvsK et al.
Given an hypothesized adaptive control system, two questions need to be addressed. First, is the control system feasible? Second, how do changes in segments of the control loop affect its operation? These are central issues in determining a system's operational parameters and feasibility, as well as its economic utility. This research describes the development and use of a digital computer simulation model which addresses these questions. THE A D A P T I V E CONTROL SYSTEM
The adaptive control loop can be regarded as a collection of control processes, as shown in Fig. 1. The process begins by sensing changes in cutting conditions, such as tool forces, vibration and tool-chip interface temperature. These signals are quantified by an analog-todigital (A-D) converter and transferred to a digital optimizer. The optimizer, an optimization algorithm, determines values for machining parameters (typically speed and feed) which satisfy some measure of performance, such as minimum cost or machining time, subject to feasibility constraints due to the machining environment. Once the optimal machining parameters are determined, they are converted to analog signals which drive the modification process. The ensuing modifications in process parameters and changes in the workpiece since the last sensing result in new cutting conditions, and the entire process is repeated. The feasibility of this system depends on several related factors. Of prime importance is the total loop response time (i.e. time from sensor stimulation to completion of response). The modified machining parameters are based on a particular set of cutting conditions, and the machine adjustments must be made before these conditions change substantially. The response time must be as short as possible, while retaining sufficient fidelity in the sensing, conversion and modification process to their inputs. Thus, for a given fidelity of response, there will be a lower bound on response time. A further complication is that response time will vary with the magnitudes of change in machining parameters, primarily due to the modification process and machine inertia. From the nature of the process and the structure of the control system, the optimizer is expected to be the determining factor with respect to system feasibility. Some other important factors are sensing thresholds, sampling rates, sampling strategies and technological advances in conversion, modification servomechanisms, and machine design. Finally, the workpiece itself is part of the control loop, so workpiece geometry and composition must also be considered.
-ISonsin l J A-D I 7 .J 7 c°nv°rter Cutting Conditions
Machining Operation IMachining Parameters
I
Modification
Fig 1 Adaptive control loop.
Optimizer
Simulation of adaptive controlled machining
71
THE SIMULATION MODEL
The adaptive control loop is simulated using a combined continuous/discrete next-event timekeeping system in the GASP IV[10] language, according to the logic flowchart in Fig. 2. Major events are machining, optimizing and process adjusting. Clock advances are determined by the loop delay time for one cycle. The simulation cycle begins with generation of a depth-of-cut value from a random walk process. Sensing and A-D conversion are assumed to have perfect fidelity and require constant times. The depth-of-cut is input to the optimization routine, which determines the optimal speed and feed for the next cycle using a dynamic programming algorithm[4]. The time required for optimization is a random variable.
" Start
)
1
Initialize ]
Simulator
1 Next = Optimize
© Adjust
Machine
1
Accumulate
I
Adjust Delays
Sense
Depth-of-Cut I 1
Set Speed, Feed to Optimal Values
i Accumulate Optimizer Delays
'
Next = Machine
Remaining Tool Life
Determine
Yes
Optimal Speed, Feed
Next = Adjus t
© ]
Outpu~
Simulator
<5
Stop )
Fig. 2. Simulatorlogicflow chart.
Compute blachine Time For Previous Cycle
Optimize
6
R. A.
72
Once optimal of computing proportional
WYSK
et al
values of speed and feed are determined,
servomechanism
times, both of which are
to the magnitudes of changes in feed and speed. After the adjustments
and tool-life
reduced
depth-of-cut
by an amount
depending
on the previous
cycle
are made,
conditions,
a new
is generated and the cycle repeated.
This model allows delays in sensing and conversion, acceleration
times,
depth-of-cut
process could also be modified
to be modified
replaced by a cutting material hardness. The optimization alternative
an adjust event begins. This consists
response times and physical adjustment
to simulate
as well as servo response and machine
a particular
to correspond
machining
environment.
to a particular
force process which would include both surface profile routine can also be modified for real-time
procedures
to be evaluated.
feasibility evaluation. described below.
Accordingly,
The simulation
model is applied
interval
loop delay times and functions
SIMULATION
or
and changes in
measurement,
The emphasis of this particular
The
surface profile,
model,
allowing
however,
is
are chosen to be realistic,
as
RESULTS
to a turning operation
on a mild steel workpiece.
Each
workpiece is 1000 mm in length, with a turning diameter of 100 mm. The machine is limited to 47.5 kN in torque, 60 N in thrust and 2.25 kW in power. Tool-life (see Appendix) is assumed to be described by the expanded Taylor equation: f =
and is constrained
to be between
6
x
10”
c-J
75 d-0.75,
25 and 45 min. The machining parameters
speed:
5 mlmin (_ c 5 400 m/min
feed:
0.3 mm/rev cr f 5 0.75 mm/rev
depth:
1.2 mm I d 5 3.75 mm.
The speed and feed are initially
f-1
set to 100 m/min and 0.75 mm/rev.
and bounds are
respectively.
Tool changing
time is assumed constant at 1.5 min. The adaptive depth-of-cut.
control
loop simulation
This is a uniformly
surface roughness
distributed
of approximately
begins with the generation value between
of a value
for actual
1.2 mm and 3.75 mm, simulating
18 pm. Sensing and signal conversions
a
are assumed to
contribute 3.5 x 10e5set to the loop response time. The optimization time is normally distributed with mean of 0.2 set and standard deviation of 0.05. Servo response times are based on the absolute
amount
of adjustment
required,
with
feed response
at 0.1 mmlsec
and speed
response at 0.5 m/se?. The servo delay is the greater of the two response times. Machine adjustment is the sum of adjustments for speed and feed, and these adjustment times are also proportional
to absolute change. Speed is adjusted at a rate of 0.2 m/set* and feed at 0.05 mm/set.
The to!al loop response time is the increment generations.
for clock advances
between
During each cycle, statistics are collected on speed, feed, depth-of-cut,
depth-of-cut estimated
tool life and production time. Tool life expended during the cycle is computed from the calculated tool life in an interval (based on the above form of Taylor’s equation) and is expressed as a fraction of tool life expended over the cycle length. When remaining tool life is reduced to near zero, a tool change takes place and the clock is advanced by the tool changing time. Upon termination of the simulation, GASP generates statistical summaries for observations of speed, feed, depth-of-cut, tool life, tool-changing frequency and total production time per part. The simulation is validated by running it under a constant depth-of-cut condition. The optimization procedure used is the dynamic programming algorithm described in[4]. With depth-of-cut constant at 3.75 mm, the simulation statistics for machining parameters are speed of 108.1 m/min and feed of 0.75 mm/rev for a production time per part of 4.099 min, which is in agreement with the mathematical solution of the model in[4]. The effect of adaptive control in machining is shown in the comparison of results from simulation experiments under two sets of conditions. First. depth-of-cut is allowed to vary with
Simulation of adaptive
controlled
73
machining
surface roughness and the turning operation is adaptively controlled. The process is then repeated using steady-state optimal speed and feed based on maximum allowable depth-of-cut of 3.75 mm, but with surface roughness (and simulated depth-of-cut) varying as before. As expected, adaptive control results in a reduction of mean production time per part, as show in Table I. This reduction reflects both more efficient cutting, and a lower frequency of unnecessary tool changes per part. The behavior of tool-life in this process illustrates one effect of adaptive control on a more detailed level. The dynamic programming solution for optimal “steady-state” machining parameters is constrained by the lower bound of tool life, i.e. 25min. The adaptive control simulation and the steady-state control simulation both result in feasible tool lives. (Observed tool life in the adaptive control case is below the lower bound because the tool is replaced before beginning a part if the tool is expected to become worn out during cutting.) These tool life values differ because the steady-state machining parameters are selected to allow feasible operation at maximum depth-of-cut, while the adaptive control system modifies machining parameters based on detected depth-of-cut. The pattern of estimated tool-life depletion is also quite different, as shown in Fig. 3. Tool-life depletion in the adaptive control case is smooth, since every machine adjustment is an attempt to minimize cutting time while achieving a specified tool life. The steady-state simulation achieves a higher estimated mean tool life, and tool-life depletion varies with the instantaneous depth-of-cut, since speed and feed are held constant.
1.000
Steady-State --
Adaptive
Control Control
0.992
0.984
0.976
0.96s
U.9h0
0.962
0.944 0
10
20
30
Time
Fig. 3. Plot of remaining
(Seconds)
tool life vs time
40
50
60
74
R. A, WYSKel aL Table 1. Simulation results: mean operating parameters and process times
Depth-of-cut (ram) Feed (mm/rev) Speed (m/sec) Time per part (rain) Tool life (rain)
Adaptive control
Constant control
2.433 0.75 I 15.9 3.839 23.75
2.472 0.75 108.1 4.023 32.62
CONCLUSION
The simulation results presented here deal with two aspects of adaptive controlled machining--production time and tool life depletion. Based on these results, it appears that adaptive control is operationally feasible for this particular turning operation. This paper illustrates the use of simulation in analyzing a hypothetical turning operation. The simulation model described here is easily extended to the study of several important problems in adaptive control. In many cases simulation is the only viable approach for predicting the expected behavior of an adaptive-controlled machine, due to the empirical nature of many machining relationships and the difficulties inherent in the study of actual systems (e.g. cost and time in experimental replication), REFERENCES 1. M. M. Barash & P. B. Berra, Automatic planning of optimal metal cutting operations and its effect on machine4ool design. J. Engng lndust. Trans. ASME (May 1971). 2. G. Boothroyd & P. Rusek, Maximum rate of profit criteria in machining. ASME Paper No. 75-W?dPROI3-22 (1975). 3. B. Daives, J. W. Bruce & A. E. DeBarr, Technological forecast for the computer control of machine tools, Numerical Control Society Proceedings, 12th Annual Meeting (1975). 4. R. P. Davis, R. A. Wysk & M. H. Agee, Characteristics of machine parameter optimization models. AppL Math. Modelling (Dec. 1978). 5. R. P. Davis, R. A. Wysk & M. H. Agee, Optimizing machining parameters in a framework for adaptive control. Dept. o[ IEOR Tech. Rep. 78-02, Virginia Polytechnic Institute and State University (1978). 6. D. S. Ermer, A Bayesian model of machining economics for optimization by adaptive control.IJ. Engng lndust. Trans. ASME (Aug. 1970). 7. W. W. Gilbert, Economics of machining. Machining Theory and Practice. American Society for Metals (1950). 8. M. P. Groover, Adaptive control and adaptive control machining. MAPEC, Purdue University (1977). 9. D. L. Kimbler, R. A. Wysk & R. P. Davis, Alternative approaches to the machining parameter optimization problem. Comput. & lndust. Engng 3, 195-202 (1978). 10. A. A. B. Pritsker, The GASP IV Simulation Language. Wiley, New York (1974). 11. S. Ramalingam, Tool-life distributions--Part I. J. Engng Indust. Trans. ASME (Aug, 1977). 12. S. Ramalingam, Tool-life distributions--Part 11. J. Engng Indust. Trans. ASME (Aug. 1977). 13. A. O. Schmidt & J. Hain, Experimental and theoretical evaluation of tool wear. J. Mat. 4, (1969). 14. H. Takeyama a at, A study of adaptive control in an NC milling machine. Annals o[ CIRP 23 (1974), 15. F. W. Taylor, On the art of cutting metals. Trans. ASME 29~1119), 31-350 (1907). 16. J. Taylor, Tool wear-time relationship in metal cutting. Int. J. Mach. Tool Design and Res. 2 (1962). 17. V. A. Tipnis, Development of mathematical models for adaptive control systems. Numerical Control Society Proceedings, 13Ih Annual Meeting (1976). 18. J. G. Wager & M. M. Barash, Study of the distribution of the life of HSS tools. J. Engng Indust. Trans. ASME (Nov. 1971). 19. S. M. Wu & D. S. Ermer, Maximum profit as the criterion in the determination of the optimum machining conditions. J. Engng lndust. Trans. ASME 88, 81-92 (1966).
APPENDIX Tool-li[e considerations The expanded Taylor equation was employed here for illustrative purposes. Since tool life decay is measured, using the above equation as a function of the random variate-depth of cut, it expresses tool life as a random variable. The authors are aware that research continues to progress in defining tool life in a probabilistic framework[l 1, 12, 18]. However, a key issue in adaptive control is the ability to map tool life decay explicitly as a function of such random variates as depth of cut, material hardness, speed, feed, tool interface temperature; and further that, in an application context, these variates be measurable. Ongoing research on the probabilistic nature of tool life represents a major step in this direction but, as yet, has not produced definitive functional relationships for tool life as a random variable. Again, the tool life equation used here is intended to serve as an illustration--it may, or may not, be suitably accurate for a specific implementation.
SIMULATION OF ADAPTIVE CONTROLLED MACHINING R~cH,,3~ A. WvsK, DELBERTL. KIMBLERand ROBERTP. DAVIS Department of Industrial Engineeringand Operations Research,Virginia PolytechnicInstitute and State University,Blacksburg,VA 24061.U.S.A. (Revised October 1979;receivedfor publication 31 October 1979)
Abstr,et--Thispaperpresentsa basicdigitalsimulationstructureforadaptivecontrolledmachiningprocesses. The use of this approachto determinethe feasibilityof adaptivecontrolis discussedand illustrated in the context of a turningoperation. INTRODUCTION The term "adaptive control" has many meanings to users of control systems. These various meanings have in common the notion of sensing process state(s) and modifying process control parameters through some feedback mechanism. Interpretations differ primarily in the logical structures they assume for the relationship between modification and sensed process state. Adaptive control is defined here as the modification of process controlling parameters to optimize some measure of performance as the process state changes over time. The importance of control in machining has long been recognized, beginning with Taylor's tool-life experiments[l l]. The introduction of tool-life as a limited resource depending on machining parameters led to the idea of selecting speed, feed and depth of cut to achieve some optimal measure of performance, such as minimum time or cost of machining[7]. Tayior's mathematical model has been extended by several researchers[i, 2, 5, 13] to include limits such as machine tool power consumption and applied force, tool temperature, achieved surface finish and physical limits on the machining parameters themselves. Resultant advances in the control of machining processes have led to increases in efficiency and productivity, but the static nature of the control structure which they employ has limited effectiveness due to two implicit assumptions. This static control approach assumes that control is perfect and work-piece composition is homogeneous. In reality, control is imperfect and work-piece composition varies through the cutting path, especially in such characteristics as surface contour and material hardness. These variations lead to a consideration of the simplest form of dynamic control, the use of a feedback control loop. This control method monitors the process state and adjusts the process parameters according to specified functional relations between detected state and corresponding control parameter settings. This type of control is typically implemented through an analog control system. While analog control is an improvement over static control, it has its own limiting assumptions. Due to the nature of the analog control loop, the form of the functional relations between process state and parameter set are fixed. Furthermore, it is extremely difficult to incorporate the optimization of some objective performance measure in the control loop [8]. These difficulties can be overcome by the use of a digital control system. This system would sense the process state, determine the parameter values which optimize some objective performance measure, and adjust the process accordingly. Such a control system would be an adaptive control system from the definition above, yet would be controlled by a digital computer. Should an ideal adaptive controller exist, its use should result in further increases in machining efficiency. A realistic system, however, would be subject to the same delays as analog feedback controllers, as well as additional delay in determining the optimum process parameters. Research is proceeding in the technological development of the adaptive control loop[3, 6, 8, 17] and efficient optimization procedures [4, 8, 9]. As this research continues, on-line adaptive control of machining processes comes closer to reality. 69
70
R.A. WvsK et al.
Given an hypothesized adaptive control system, two questions need to be addressed. First, is the control system feasible? Second, how do changes in segments of the control loop affect its operation? These are central issues in determining a system's operational parameters and feasibility, as well as its economic utility. This research describes the development and use of a digital computer simulation model which addresses these questions. THE A D A P T I V E CONTROL SYSTEM
The adaptive control loop can be regarded as a collection of control processes, as shown in Fig. 1. The process begins by sensing changes in cutting conditions, such as tool forces, vibration and tool-chip interface temperature. These signals are quantified by an analog-todigital (A-D) converter and transferred to a digital optimizer. The optimizer, an optimization algorithm, determines values for machining parameters (typically speed and feed) which satisfy some measure of performance, such as minimum cost or machining time, subject to feasibility constraints due to the machining environment. Once the optimal machining parameters are determined, they are converted to analog signals which drive the modification process. The ensuing modifications in process parameters and changes in the workpiece since the last sensing result in new cutting conditions, and the entire process is repeated. The feasibility of this system depends on several related factors. Of prime importance is the total loop response time (i.e. time from sensor stimulation to completion of response). The modified machining parameters are based on a particular set of cutting conditions, and the machine adjustments must be made before these conditions change substantially. The response time must be as short as possible, while retaining sufficient fidelity in the sensing, conversion and modification process to their inputs. Thus, for a given fidelity of response, there will be a lower bound on response time. A further complication is that response time will vary with the magnitudes of change in machining parameters, primarily due to the modification process and machine inertia. From the nature of the process and the structure of the control system, the optimizer is expected to be the determining factor with respect to system feasibility. Some other important factors are sensing thresholds, sampling rates, sampling strategies and technological advances in conversion, modification servomechanisms, and machine design. Finally, the workpiece itself is part of the control loop, so workpiece geometry and composition must also be considered.
-ISonsin l J A-D I 7 .J 7 c°nv°rter Cutting Conditions
Machining Operation IMachining Parameters
I
Modification
Fig 1 Adaptive control loop.
Optimizer
Simulation of adaptive controlled machining
71
THE SIMULATION MODEL
The adaptive control loop is simulated using a combined continuous/discrete next-event timekeeping system in the GASP IV[10] language, according to the logic flowchart in Fig. 2. Major events are machining, optimizing and process adjusting. Clock advances are determined by the loop delay time for one cycle. The simulation cycle begins with generation of a depth-of-cut value from a random walk process. Sensing and A-D conversion are assumed to have perfect fidelity and require constant times. The depth-of-cut is input to the optimization routine, which determines the optimal speed and feed for the next cycle using a dynamic programming algorithm[4]. The time required for optimization is a random variable.
" Start
)
1
Initialize ]
Simulator
1 Next = Optimize
© Adjust
Machine
1
Accumulate
I
Adjust Delays
Sense
Depth-of-Cut I 1
Set Speed, Feed to Optimal Values
i Accumulate Optimizer Delays
'
Next = Machine
Remaining Tool Life
Determine
Yes
Optimal Speed, Feed
Next = Adjus t
© ]
Outpu~
Simulator
<5
Stop )
Fig. 2. Simulatorlogicflow chart.
Compute blachine Time For Previous Cycle
Optimize
6
R. A.
72
Once optimal of computing proportional
WYSK
et al
values of speed and feed are determined,
servomechanism
times, both of which are
to the magnitudes of changes in feed and speed. After the adjustments
and tool-life
reduced
depth-of-cut
by an amount
depending
on the previous
cycle
are made,
conditions,
a new
is generated and the cycle repeated.
This model allows delays in sensing and conversion, acceleration
times,
depth-of-cut
process could also be modified
to be modified
replaced by a cutting material hardness. The optimization alternative
an adjust event begins. This consists
response times and physical adjustment
to simulate
as well as servo response and machine
a particular
to correspond
machining
environment.
to a particular
force process which would include both surface profile routine can also be modified for real-time
procedures
to be evaluated.
feasibility evaluation. described below.
Accordingly,
The simulation
model is applied
interval
loop delay times and functions
SIMULATION
or
and changes in
measurement,
The emphasis of this particular
The
surface profile,
model,
allowing
however,
is
are chosen to be realistic,
as
RESULTS
to a turning operation
on a mild steel workpiece.
Each
workpiece is 1000 mm in length, with a turning diameter of 100 mm. The machine is limited to 47.5 kN in torque, 60 N in thrust and 2.25 kW in power. Tool-life (see Appendix) is assumed to be described by the expanded Taylor equation: f =
and is constrained
to be between
6
x
10”
c-J
75 d-0.75,
25 and 45 min. The machining parameters
speed:
5 mlmin (_ c 5 400 m/min
feed:
0.3 mm/rev cr f 5 0.75 mm/rev
depth:
1.2 mm I d 5 3.75 mm.
The speed and feed are initially
f-1
set to 100 m/min and 0.75 mm/rev.
and bounds are
respectively.
Tool changing
time is assumed constant at 1.5 min. The adaptive depth-of-cut.
control
loop simulation
This is a uniformly
surface roughness
distributed
of approximately
begins with the generation value between
of a value
for actual
1.2 mm and 3.75 mm, simulating
18 pm. Sensing and signal conversions
a
are assumed to
contribute 3.5 x 10e5set to the loop response time. The optimization time is normally distributed with mean of 0.2 set and standard deviation of 0.05. Servo response times are based on the absolute
amount
of adjustment
required,
with
feed response
at 0.1 mmlsec
and speed
response at 0.5 m/se?. The servo delay is the greater of the two response times. Machine adjustment is the sum of adjustments for speed and feed, and these adjustment times are also proportional
to absolute change. Speed is adjusted at a rate of 0.2 m/set* and feed at 0.05 mm/set.
The to!al loop response time is the increment generations.
for clock advances
between
During each cycle, statistics are collected on speed, feed, depth-of-cut,
depth-of-cut estimated
tool life and production time. Tool life expended during the cycle is computed from the calculated tool life in an interval (based on the above form of Taylor’s equation) and is expressed as a fraction of tool life expended over the cycle length. When remaining tool life is reduced to near zero, a tool change takes place and the clock is advanced by the tool changing time. Upon termination of the simulation, GASP generates statistical summaries for observations of speed, feed, depth-of-cut, tool life, tool-changing frequency and total production time per part. The simulation is validated by running it under a constant depth-of-cut condition. The optimization procedure used is the dynamic programming algorithm described in[4]. With depth-of-cut constant at 3.75 mm, the simulation statistics for machining parameters are speed of 108.1 m/min and feed of 0.75 mm/rev for a production time per part of 4.099 min, which is in agreement with the mathematical solution of the model in[4]. The effect of adaptive control in machining is shown in the comparison of results from simulation experiments under two sets of conditions. First. depth-of-cut is allowed to vary with
Simulation of adaptive
controlled
73
machining
surface roughness and the turning operation is adaptively controlled. The process is then repeated using steady-state optimal speed and feed based on maximum allowable depth-of-cut of 3.75 mm, but with surface roughness (and simulated depth-of-cut) varying as before. As expected, adaptive control results in a reduction of mean production time per part, as show in Table I. This reduction reflects both more efficient cutting, and a lower frequency of unnecessary tool changes per part. The behavior of tool-life in this process illustrates one effect of adaptive control on a more detailed level. The dynamic programming solution for optimal “steady-state” machining parameters is constrained by the lower bound of tool life, i.e. 25min. The adaptive control simulation and the steady-state control simulation both result in feasible tool lives. (Observed tool life in the adaptive control case is below the lower bound because the tool is replaced before beginning a part if the tool is expected to become worn out during cutting.) These tool life values differ because the steady-state machining parameters are selected to allow feasible operation at maximum depth-of-cut, while the adaptive control system modifies machining parameters based on detected depth-of-cut. The pattern of estimated tool-life depletion is also quite different, as shown in Fig. 3. Tool-life depletion in the adaptive control case is smooth, since every machine adjustment is an attempt to minimize cutting time while achieving a specified tool life. The steady-state simulation achieves a higher estimated mean tool life, and tool-life depletion varies with the instantaneous depth-of-cut, since speed and feed are held constant.
1.000
Steady-State --
Adaptive
Control Control
0.992
0.984
0.976
0.96s
U.9h0
0.962
0.944 0
10
20
30
Time
Fig. 3. Plot of remaining
(Seconds)
tool life vs time
40
50
60
74
R. A, WYSKel aL Table 1. Simulation results: mean operating parameters and process times
Depth-of-cut (ram) Feed (mm/rev) Speed (m/sec) Time per part (rain) Tool life (rain)
Adaptive control
Constant control
2.433 0.75 I 15.9 3.839 23.75
2.472 0.75 108.1 4.023 32.62
CONCLUSION
The simulation results presented here deal with two aspects of adaptive controlled machining--production time and tool life depletion. Based on these results, it appears that adaptive control is operationally feasible for this particular turning operation. This paper illustrates the use of simulation in analyzing a hypothetical turning operation. The simulation model described here is easily extended to the study of several important problems in adaptive control. In many cases simulation is the only viable approach for predicting the expected behavior of an adaptive-controlled machine, due to the empirical nature of many machining relationships and the difficulties inherent in the study of actual systems (e.g. cost and time in experimental replication), REFERENCES 1. M. M. Barash & P. B. Berra, Automatic planning of optimal metal cutting operations and its effect on machine4ool design. J. Engng lndust. Trans. ASME (May 1971). 2. G. Boothroyd & P. Rusek, Maximum rate of profit criteria in machining. ASME Paper No. 75-W?dPROI3-22 (1975). 3. B. Daives, J. W. Bruce & A. E. DeBarr, Technological forecast for the computer control of machine tools, Numerical Control Society Proceedings, 12th Annual Meeting (1975). 4. R. P. Davis, R. A. Wysk & M. H. Agee, Characteristics of machine parameter optimization models. AppL Math. Modelling (Dec. 1978). 5. R. P. Davis, R. A. Wysk & M. H. Agee, Optimizing machining parameters in a framework for adaptive control. Dept. o[ IEOR Tech. Rep. 78-02, Virginia Polytechnic Institute and State University (1978). 6. D. S. Ermer, A Bayesian model of machining economics for optimization by adaptive control.IJ. Engng lndust. Trans. ASME (Aug. 1970). 7. W. W. Gilbert, Economics of machining. Machining Theory and Practice. American Society for Metals (1950). 8. M. P. Groover, Adaptive control and adaptive control machining. MAPEC, Purdue University (1977). 9. D. L. Kimbler, R. A. Wysk & R. P. Davis, Alternative approaches to the machining parameter optimization problem. Comput. & lndust. Engng 3, 195-202 (1978). 10. A. A. B. Pritsker, The GASP IV Simulation Language. Wiley, New York (1974). 11. S. Ramalingam, Tool-life distributions--Part I. J. Engng Indust. Trans. ASME (Aug, 1977). 12. S. Ramalingam, Tool-life distributions--Part 11. J. Engng Indust. Trans. ASME (Aug. 1977). 13. A. O. Schmidt & J. Hain, Experimental and theoretical evaluation of tool wear. J. Mat. 4, (1969). 14. H. Takeyama a at, A study of adaptive control in an NC milling machine. Annals o[ CIRP 23 (1974), 15. F. W. Taylor, On the art of cutting metals. Trans. ASME 29~1119), 31-350 (1907). 16. J. Taylor, Tool wear-time relationship in metal cutting. Int. J. Mach. Tool Design and Res. 2 (1962). 17. V. A. Tipnis, Development of mathematical models for adaptive control systems. Numerical Control Society Proceedings, 13Ih Annual Meeting (1976). 18. J. G. Wager & M. M. Barash, Study of the distribution of the life of HSS tools. J. Engng Indust. Trans. ASME (Nov. 1971). 19. S. M. Wu & D. S. Ermer, Maximum profit as the criterion in the determination of the optimum machining conditions. J. Engng lndust. Trans. ASME 88, 81-92 (1966).
APPENDIX Tool-li[e considerations The expanded Taylor equation was employed here for illustrative purposes. Since tool life decay is measured, using the above equation as a function of the random variate-depth of cut, it expresses tool life as a random variable. The authors are aware that research continues to progress in defining tool life in a probabilistic framework[l 1, 12, 18]. However, a key issue in adaptive control is the ability to map tool life decay explicitly as a function of such random variates as depth of cut, material hardness, speed, feed, tool interface temperature; and further that, in an application context, these variates be measurable. Ongoing research on the probabilistic nature of tool life represents a major step in this direction but, as yet, has not produced definitive functional relationships for tool life as a random variable. Again, the tool life equation used here is intended to serve as an illustration--it may, or may not, be suitably accurate for a specific implementation.