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A controller architecture for integrating a fast tool servo into a diamond turning machine
A controller archit ure for integrating a fast tool servo into a diamond turning machine Michele H. Miller, Kenneth P. Garrard, Thomas A. Dow, and Lauren W. Taylor Precision Engineering Center, North Carolina State University, Raleigh, NC, USA
Diamond turning has become an important fabrication technique for p r o d u c ing reflective optics. However, the generation of a genera/optical surface requires the capability to fabricate nonrotationally symmetric surfaces. Current commercial diamond turning machines cannot perform this task at production rates because of the fimited bandwidth of their axis motions and the limited update speed of their controllers. Although a fast too/servo overcomes the bandwidth limitation, the problem of integrating a fast control process (for the servo axis) and a slower control process (for the slide axes) remains. This article describes the computer hardware and software required to integrate a high-speed, Iow-ampfitude fast tool servo into a conventional T-based diamond turning machine. This system can machine e-dependent features, synchronized to the radial and axial position of the tool, up to the displacement range of the servo. ,4 set of interface boards have been designed and built that pass the position feedback data from the laser interferometer to both a high-speed servo controller and a slower sfide axes controller. This design allows the fast tool servo to be an independent add-on accessory to the diamond turning machine and successfully incorporates nonrotationally symmetric fabrication capability. As an example of the surfaces possible with this system, an off-axis segment of a parabolic mirror has been machined on-axis. The peak-to-valley figure error of this 125-mm optic is tess than 1. ! waves (0. 7 i~m).
Keywords: diamond turning; nonrotationally symmetric surfaces; high. speed controller design; fast tool servo; piezoelectric actuator
Introduction The technique of machining optical quality finish on a diamond turning machine (DTM) has revolutionized the fabrication of reflective and transmissive optical components. 1This technique allows the optical designer to specify aspheric shapes and provides a method of integrating the optical surface into the mechanical structure. Machining the optical surface and contact surfaces on the same machine eliminates most of the alignment procedures so costly in optical assemblies. By adding the possibility of fabricating nonrotationally symmetric surfaces with a fast tool servo (FTS), an even more dramatic expansion in the capability of optical components and reduction in their cost can be foreseen.
Address reprint requests to Michele H. Miller, Precision Engineering Center, North Carolina State University, Raleigh, NC 27695-7918, USA. © 1994 B u t t e r w o r t h - H e i n e m a n n
42
Current diamond turning machines are i~mited in the bandwidth of their slides as well as the speed of the controller processor. Most DTM controllers operate at an update rate of 10 msec, and the closed loop bandwidth of the slides is on the order of 10 Hz, This bandwidth is not sufficient to produce nonrotationally symmetric features on the surface, except at low rotational speeds, ~ Several efforts are under way to improve the capability of machine tool controllers. An Air Force sponsored program to develop an intelligent machining workstation :~' has been completed by Cincinnati Milacron, and the Next Generation Controller program 4 is under way at Martin Marietta. The scope of each of these programs is to improve the capability of machine tool controllers with a concentration on the commu., nication from the cell level and higher. The emphasis of the control system described in this article is below the cell level at the tool/workpiece inter-face. The objective is to describe the benefits to be gained from a high-performance computer control system, JANUARY 1994 VOL "16 NO i
Miller et aL : Controller architecture
+X
+ Z -"~ X sfide
Figure 1 Schematic of T-based diamond turning machine with fast tool servo
The limitations of the currently available commercial controllers revolve around the processors and the openness of the architecture. High-speed I/O is required for the large volume of data and the fast data rate necessary for a nonrotationally symmetric part. Current controllers are not fast enough to generate the reference positions, to accomplish the control algorithms necessary for the machine axes, or to provide correction of the geometric errors. In addition, the closed architecture does not allow additions of new inputs or outputs or major changes in the control algorithms. A new controller design is proposed with the capability to extend the potential of current DTMs. The architecture of this design is presented, as is a demonstration of the potential for error correction and shape generation.
Description of D T M and FTS This research was conducted on a Pneumo ASG2500 DTM, which is a T-base design. The slide defined as the Z axis carries the workpiece spindle. The diamond tool is mounted on the cross slide or X axis. In its three-axis orientation shown in Figure 1, an FTS is mounted to the tool post on t h e X s l i d e and parallel to theZaxis. The servo used in this work consists of a piezoelectric actuator with a range of 20/zm and bandwidth of 2 kHz. A complete description of its design and performance characteristics has been reported. 5
Evolution of high-speed controller architecture A series of controller architectures has been developed at the Precision Engineering Center to improve the capability of diamond turning and grinding machines. The first, a slide axes controller, is based on a PC-AT and a Motorola 68020 processor. 6 Important features are a 1-msec update time, realtime reference point generation capabilities for conic surfaces, and flexible control algorithm implementation. However, this controller is limited in data transfer rate as a consequence of its reliance on the PC bus for I/O and in computational power by the 68020 processor. Although this design significantly improved DTM performance, it could not be extended to more computationally intensive applications. PRECISION ENGINEERING
To solve this problem, a digital signal processor (DSP) was added to the slide axes controller. A performance comparison between the 68020 processor and DSPs has been described. ~ Depending on the type of computation performed, DSPs can be up to 20 times faster than a 68020 processor. An additional advantage is their I/O capability. The combination of greater computational speed and I/O capability makes it possible to control an FTS at a 10-kHz rate. DSP-based controllers have previously been developed for FTS applications that operate independently of the slide axes controller. 5'7'8 Independent FTS control has accuracy limitations, however, because the FTS motion cannot be perfectly synchronized with the X and Zslide motions. Interfaces were developed so that the DSP can monitor the slide positions and communicate that information to the slide axes controller.
Slide axes controller The slide axes controller architecture is shown in Figure 2. The master processor handles the user interface and checks for machine faults. The computation processor generates reference points for the slides and makes the feedback control calculation. All of the analog and digital I/O passes through the master processor, which then communicates with the computation processor. This slow I/O path limits the performance of this architecture. The slide axes controller does have the processing speed to implement sophisticated control algorithms for the slide motions as well as slideway error corrections.
Slideway error compensation Computer control allows in situ compensation of slideway errors. 9-11 Implementation of a scheme to correct repeatable slideway errors is an example of how this slide axes controller has been used to improve DTM performance.
Straightness errors. The X and Zstraig htness errors were mapped using a Zerodur straightedge and the reversal technique. Based on these error measurements, X straightness errors can be compensated by the Z slide, and Z straightness errors by the X slide. Error tables were created for each axis. These tables consist of a list of slide positions where the straightness error changes one laser count (2.5 nm).
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Thus, despite the small error resolution, the error tables for both slides are short. For example, on the X slide the straightness error was 200 nm, and this could be approximated by 156 X positions where the error stepped up or down one laser count. Linear searches through the error tables are avoided by noting that on each controller cycle the array index of the correct cumulative error is at most one table entry away from its position on the previous cycle. Thus, the geometric error compensation procedure is independent of the size of the error tables and can be calculated in constant time. To test the algorithm, axis straightness was measured with and w i t h o u t compensation. Figure 3a and b shows the results: the X straightness improved from 200 nm to 40 nm peak-to-valley (P-V) error, whereas the Z slide straightness improved from 60 to 40 nm P-V. The repeatability of the straightness measurements is approximately40 nm. Yaw errors. The angle of the workpiece spindle axis with respect to the X axis is another repeatable error that can be corrected by the controller. Although both slides exhibit yaw error, for facing cuts the Z yaw is the most important (cosine error on X). If a flat were machined at a specific Z position, any deviation from perpendicular causes a cone to be superimposed onto the machined surface. In addition, Z slide yaw causes an error in the measured position due to an Abbe offset. (When machining flat surfaces, this offset is constant and introduces no form error. However, for surfaces requiring Z slide motion, the Abbe offset w o u l d introduce figu re error if left uncorrected.) These two errors, depicted in Figure 4, can be compensated by modifying the Z slide reference point. Based on measurements of the Z slide yaw, a model of the form Craw = 8raw(Z) was derived. The correction algorithm modifies the Z reference point by (AZ)ref = (X 44
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Because they are easy to measure, flats were machined at a series of Z slide positions to test the effectiveness of the yaw compensation. Coneshaped figure error was reduced by nearly two thirds--from a range of 100-250 nm without compensation to 30-100 nm with compensation.
Error correction scheme implementation. The slide axes controller executes the correction algorithm at each controller cycle after the reference coordinates for each slide are calculated but outside the feedback loop as shown in Figure 5. Reference point modification consists of 1. looking up straightness errors f(Xuref) and g(Zuref), 2. calculating the yaw error h(X,,e~, Z,r~), and 3. calculating corrected reference points,
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Nonrotationally symmetric surfaces can be machined using the FTS to generate small perturbation Z axis motions synchronized to the rotation of the workpiece spindle (0) and the radius (X). The remainder (or base) surface may be either flat or the best-fit aspheric surface of revolution. Because it is independent of 0, this base surface can be machined using the standard control system on the DTM. The piezoelectric actuator in the FTS is driven by a high-voltage amplifier that receives commands from a DSP. Servo position feedback via a capacitance gauge is also interfaced to this processor. The FTS feedback control loop is independent of the X and Z slide control; however, generation of the nonsymmetric reference signal requires access to the spindle encoder and the laser interferometer. Making interferometer data available to both controllers was the primary obstacle in integrating FTS control with X and Zcontrol. It was not feasible to connect the two controllers directly to the interferometer interface output ports because they would both attempt to drive the measurement board sampling signals. The interfaces required to overcome this obstacle are represented in Figure 6. In the original configuration, the laser interferometers are read directly by the slide axes controller. In the new configuration, the FTS controller intercepts the instantaneous slide position via a laser input interface and communicates these data to the slide axes controller via a position feedback interface. The laser input interface* maps the bits of the interferometer interface connectors into one
*The specific implementation depends on laser interface design. Both parallel and multiplexed laser outputs can be accommodated using this concept.
45
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eight-bit control input port, one eight-bit control output port, and two 16-bit data input ports. The control input and output ports synchronize the transfer of the 32 bits of position data from the interferometers to the data ports of the input interface. This gives the FTS controller timely access to the current X and Z axes positions. The position feedback interface replicates the signals that the slide axes controller expects during communication cycles with the interferometer measurement boards. It also provides one level of data buffering, which permits the FTS controller to communicate current axis position information to the slide axes controller without synchronization delays. The only requirement is that the F-FS controller supply current X and Z values to the interface board at a frequency higher than that of the slide axes controller update cycle (i.e., 1 kHz). For the current implementation the update rate is 10 kHz. An additional interface, the angular feedback interface, provides access to the spindle encoder. This interface provides the FTS controller with the current value of 0 expressed as the number of 46
encoder pulses since the last once-per-revolution index pulse. The maximum resolution of the encoder is 0.0015 radians per count. The direction of rotation can also be determined. The once-per revolution index pulse is available externally to facilitate angular alignment of the workpiece fixture Figure 7 shows the integrated controiter, ;r~ cluding the three interfaces The FTS controlle~ includes a DSP (current system uses a Texas Instruments TMS320C30 DSP) and node controller The three interfaces connect the FTS controller to the DTM. In switch position a, the FTS controller reads the interferometers; in switch position b, the FTS is disconnected from the system With this architecture, the X/Z and FTS controi processes execute in parallel. Figure 8 shows a flowchart of the two control processes, which run at different rates. During a control cycle, each processor reads inputs, makes reference point calculations, and sends outputs. The inputs to the FTS control process are the X and Z laser data, the spindle angle 0, and the FTS position (provided by a capacitance gauge). A reference point is calculated based on the desired nonaxisymmetric shape and then adjusted by an integral controt law. The corresponding reference voltage is output to the amplifier that drives the FTS. The inputs to the slide axes control process are the X and Z laser data (provided by the position feedback interface). X and Z reference points are calculated based on the desired axisymmetric shape. After making dynamic and geometric error corrections, control signals are output to the axes servo ampii~ tiers,
Reference surface generation for off-axis conics An important application for ttle FTS is to machine off-axis conic sections on axis. With this capability, sections of large conic mirrors could be fabricated on small DTMs. The decomposition of the general aspheric optics equation into off-axis segments and their (X)-dependent and (X, /))-dependent components suitable for on-axis machining has been described. 7,12-14 The best-fit asphere is generated off-line and loaded into the slide axes controller memory while the nonrotationally symmetric modification is made by the FTS with respect to the actual position of the slides. By using the actual slide positions in the reference calculation, the FTS can also compensate for any high-frequency Z slide vibrations as well as the tow-frequency positioning error of the slide axes controller. The integrated FTS controller calculates the Z axis reference position (as a function of X and 0) on the fly and subtracts the current Zaxis position to obtain the small pertur~ bation component. Nonaxisymmetric surface capability was demo onstrated by machining a 125-mm diameter section ,JANUARY t994 VOL 16 NO
Miller et aL : Controller architecture
Figure 11
(a) Interferogram and (b) phase plot of off-axis parabolic surface
of a 1,080-mm focal length parabola 300 mm from the center. The best-fit aspheric component of this off-axis segment (Figure 9) has a sagitta of 1 mm. The nonrotationally symmetric component is shown in Figure 10. The range of the FTS required for this surface is less than 20/~m. This parabolic section was machined with closed-loop FTS control at a spindle speed of 200 rpm. Figure 1 la shows an interferogram of the surface measured in its off-axis position. 15 Straight, parallel fringes would indicate a perfect parabolic surface. Figure 1 lb is the phase plot generated from this interferogram. The P-V error of the machined surface is less than 1.1 waves (0.7/zm), which was within the specification of 1.5 waves required for the optical performance. While machining this surface, the servo cycled twice per part revolution as indicated in Figure 10. The phase plot shows a similar pattern with two high and two low regions, indicating that some error remains at the frequency of the FTS motion. Much of this error could be due to nonlinearity in the servo's piezoelectric stack. The following error for a linear system could be compensated by a slight angular shift of the part. However, for an actuator with some nonlinear hysteretic response (such as a high-voltage piezoelectric material), the phase lag varies with input amplitude and requires a nonlinear control scheme to compensate.
Conclusions A high-performance controller has been designed and built to add advanced features to an existing PRECISION ENGINEERING
DTM. These features include correction for repeatable errors and integration of FTS and slide axes controllers. The system was used to produce an offaxis parabolic section that requires coordination of the slide and servo axes to produce a nonrotationally symmetric optical surface. The figure error was less than 1.1 waves. Because further improvements in the accuracy and repeatability of fabricated components may be achievable by upgrading to faster processors, an architecture that incorporates two DSPs is the next step of development being undertaken. However, the intermediate controller configuration described here achieves FTS integration and has the advantage of portability to commercial DTMs with a variety of different axes controllers.
Acknowledgments This work was supported in part by the Office of Naval Research University Research Initiative Program in Precision Engineering and the corporate affiliates of the Precision Engineering Center. We thank Oak Ridge National Lab for measuring the off-axis optic.
References 1 Saito,T. T. "Precision machining application and technology: an overview and perspective," Proc SPIE 1983, 433, 48- 53 2 Schenz,R. F., Patterson,S. R. and Saito,T. T. "Direct machining of a non-axisymmetric phase corrector," Proc SPIE 1988, 966, 43-59 47
Miller et aL: Controller architecture 3 "intelligent machining workstation final report," Cincinnati Milacron Government Systems Operations, September, 1990 4 "Next generation workstation/machine controller architecture definition document," Document No. NGC-ADD-001, Martin Marietta Astronautics Group, June 1991 5 Dow, T. A., Miller, M. H. and Falter, P. J. "Application of a fast tool servo for diamond turning of non-rotationally symmetric surfaces," Precision Eng 1991, 13, 243-250 6 Fornaro, R. J., Garrard, K. P. and Taylor, L. W. "Architecture and algorithms for computer control of high precision machine tools," in Proceedings of ASPE Annual Conference, 1990 7 Luttrell, D, E. "Machining non-axisymmetric optics," in Proceedings of the ASPE Annual Conference, 1990 8 Weck, M. and Pyra, M. "Diamond turning of non-symmetric laser optics," in Proceedings of the ASPE Annual Conference, 1990 9 Bryan, J. B. "Design and construction of an ultraprecision
48
10 11
12
13 14
84 inch diamond turning machine," Precision Eng 1979, 1, 13-17 Donaldson, R. R. "Error budgets," Technology of Machine Tools: Machine Tool Task Force Report 1980, 5 Donmez, M. A., et al. "A general methodology for machine tool accuracy enhancement by error compensation," Precision Eng 1986, 8, 187-196 Thompson, D. C. "Theoretical tooi movement requirea [o diamond turn an off-axis paraboloid on axis," Proc SPIE 1976, 93, 23-29 Douglass, S. S. "A machining system for turning nonaxisym. metric surfaces." Ph.D. diss., University of Tennessee, Knoxville 1983 Gerchman, M, C. "A description of off-axis conic surfaces for non-axisymmetric surface generation," Proc SPIE 1990, 1266
15 Maxey, L. C. "Novel technique for aligning paraboioids. Oak Ridge National Laboratory, t991
JANUARY
1994 VOL !6 NO !
Diamond turning has become an important fabrication technique for p r o d u c ing reflective optics. However, the generation of a genera/optical surface requires the capability to fabricate nonrotationally symmetric surfaces. Current commercial diamond turning machines cannot perform this task at production rates because of the fimited bandwidth of their axis motions and the limited update speed of their controllers. Although a fast too/servo overcomes the bandwidth limitation, the problem of integrating a fast control process (for the servo axis) and a slower control process (for the slide axes) remains. This article describes the computer hardware and software required to integrate a high-speed, Iow-ampfitude fast tool servo into a conventional T-based diamond turning machine. This system can machine e-dependent features, synchronized to the radial and axial position of the tool, up to the displacement range of the servo. ,4 set of interface boards have been designed and built that pass the position feedback data from the laser interferometer to both a high-speed servo controller and a slower sfide axes controller. This design allows the fast tool servo to be an independent add-on accessory to the diamond turning machine and successfully incorporates nonrotationally symmetric fabrication capability. As an example of the surfaces possible with this system, an off-axis segment of a parabolic mirror has been machined on-axis. The peak-to-valley figure error of this 125-mm optic is tess than 1. ! waves (0. 7 i~m).
Keywords: diamond turning; nonrotationally symmetric surfaces; high. speed controller design; fast tool servo; piezoelectric actuator
Introduction The technique of machining optical quality finish on a diamond turning machine (DTM) has revolutionized the fabrication of reflective and transmissive optical components. 1This technique allows the optical designer to specify aspheric shapes and provides a method of integrating the optical surface into the mechanical structure. Machining the optical surface and contact surfaces on the same machine eliminates most of the alignment procedures so costly in optical assemblies. By adding the possibility of fabricating nonrotationally symmetric surfaces with a fast tool servo (FTS), an even more dramatic expansion in the capability of optical components and reduction in their cost can be foreseen.
Address reprint requests to Michele H. Miller, Precision Engineering Center, North Carolina State University, Raleigh, NC 27695-7918, USA. © 1994 B u t t e r w o r t h - H e i n e m a n n
42
Current diamond turning machines are i~mited in the bandwidth of their slides as well as the speed of the controller processor. Most DTM controllers operate at an update rate of 10 msec, and the closed loop bandwidth of the slides is on the order of 10 Hz, This bandwidth is not sufficient to produce nonrotationally symmetric features on the surface, except at low rotational speeds, ~ Several efforts are under way to improve the capability of machine tool controllers. An Air Force sponsored program to develop an intelligent machining workstation :~' has been completed by Cincinnati Milacron, and the Next Generation Controller program 4 is under way at Martin Marietta. The scope of each of these programs is to improve the capability of machine tool controllers with a concentration on the commu., nication from the cell level and higher. The emphasis of the control system described in this article is below the cell level at the tool/workpiece inter-face. The objective is to describe the benefits to be gained from a high-performance computer control system, JANUARY 1994 VOL "16 NO i
Miller et aL : Controller architecture
+X
+ Z -"~ X sfide
Figure 1 Schematic of T-based diamond turning machine with fast tool servo
The limitations of the currently available commercial controllers revolve around the processors and the openness of the architecture. High-speed I/O is required for the large volume of data and the fast data rate necessary for a nonrotationally symmetric part. Current controllers are not fast enough to generate the reference positions, to accomplish the control algorithms necessary for the machine axes, or to provide correction of the geometric errors. In addition, the closed architecture does not allow additions of new inputs or outputs or major changes in the control algorithms. A new controller design is proposed with the capability to extend the potential of current DTMs. The architecture of this design is presented, as is a demonstration of the potential for error correction and shape generation.
Description of D T M and FTS This research was conducted on a Pneumo ASG2500 DTM, which is a T-base design. The slide defined as the Z axis carries the workpiece spindle. The diamond tool is mounted on the cross slide or X axis. In its three-axis orientation shown in Figure 1, an FTS is mounted to the tool post on t h e X s l i d e and parallel to theZaxis. The servo used in this work consists of a piezoelectric actuator with a range of 20/zm and bandwidth of 2 kHz. A complete description of its design and performance characteristics has been reported. 5
Evolution of high-speed controller architecture A series of controller architectures has been developed at the Precision Engineering Center to improve the capability of diamond turning and grinding machines. The first, a slide axes controller, is based on a PC-AT and a Motorola 68020 processor. 6 Important features are a 1-msec update time, realtime reference point generation capabilities for conic surfaces, and flexible control algorithm implementation. However, this controller is limited in data transfer rate as a consequence of its reliance on the PC bus for I/O and in computational power by the 68020 processor. Although this design significantly improved DTM performance, it could not be extended to more computationally intensive applications. PRECISION ENGINEERING
To solve this problem, a digital signal processor (DSP) was added to the slide axes controller. A performance comparison between the 68020 processor and DSPs has been described. ~ Depending on the type of computation performed, DSPs can be up to 20 times faster than a 68020 processor. An additional advantage is their I/O capability. The combination of greater computational speed and I/O capability makes it possible to control an FTS at a 10-kHz rate. DSP-based controllers have previously been developed for FTS applications that operate independently of the slide axes controller. 5'7'8 Independent FTS control has accuracy limitations, however, because the FTS motion cannot be perfectly synchronized with the X and Zslide motions. Interfaces were developed so that the DSP can monitor the slide positions and communicate that information to the slide axes controller.
Slide axes controller The slide axes controller architecture is shown in Figure 2. The master processor handles the user interface and checks for machine faults. The computation processor generates reference points for the slides and makes the feedback control calculation. All of the analog and digital I/O passes through the master processor, which then communicates with the computation processor. This slow I/O path limits the performance of this architecture. The slide axes controller does have the processing speed to implement sophisticated control algorithms for the slide motions as well as slideway error corrections.
Slideway error compensation Computer control allows in situ compensation of slideway errors. 9-11 Implementation of a scheme to correct repeatable slideway errors is an example of how this slide axes controller has been used to improve DTM performance.
Straightness errors. The X and Zstraig htness errors were mapped using a Zerodur straightedge and the reversal technique. Based on these error measurements, X straightness errors can be compensated by the Z slide, and Z straightness errors by the X slide. Error tables were created for each axis. These tables consist of a list of slide positions where the straightness error changes one laser count (2.5 nm).
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Thus, despite the small error resolution, the error tables for both slides are short. For example, on the X slide the straightness error was 200 nm, and this could be approximated by 156 X positions where the error stepped up or down one laser count. Linear searches through the error tables are avoided by noting that on each controller cycle the array index of the correct cumulative error is at most one table entry away from its position on the previous cycle. Thus, the geometric error compensation procedure is independent of the size of the error tables and can be calculated in constant time. To test the algorithm, axis straightness was measured with and w i t h o u t compensation. Figure 3a and b shows the results: the X straightness improved from 200 nm to 40 nm peak-to-valley (P-V) error, whereas the Z slide straightness improved from 60 to 40 nm P-V. The repeatability of the straightness measurements is approximately40 nm. Yaw errors. The angle of the workpiece spindle axis with respect to the X axis is another repeatable error that can be corrected by the controller. Although both slides exhibit yaw error, for facing cuts the Z yaw is the most important (cosine error on X). If a flat were machined at a specific Z position, any deviation from perpendicular causes a cone to be superimposed onto the machined surface. In addition, Z slide yaw causes an error in the measured position due to an Abbe offset. (When machining flat surfaces, this offset is constant and introduces no form error. However, for surfaces requiring Z slide motion, the Abbe offset w o u l d introduce figu re error if left uncorrected.) These two errors, depicted in Figure 4, can be compensated by modifying the Z slide reference point. Based on measurements of the Z slide yaw, a model of the form Craw = 8raw(Z) was derived. The correction algorithm modifies the Z reference point by (AZ)ref = (X 44
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Figure 6 Interferometer interfaces. (a) Original configuration. (b) New configuration ,.JANUARY 1994 VOL 16 NO
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Flowchart of parallel FTS and axes control
processes
Because they are easy to measure, flats were machined at a series of Z slide positions to test the effectiveness of the yaw compensation. Coneshaped figure error was reduced by nearly two thirds--from a range of 100-250 nm without compensation to 30-100 nm with compensation.
Error correction scheme implementation. The slide axes controller executes the correction algorithm at each controller cycle after the reference coordinates for each slide are calculated but outside the feedback loop as shown in Figure 5. Reference point modification consists of 1. looking up straightness errors f(Xuref) and g(Zuref), 2. calculating the yaw error h(X,,e~, Z,r~), and 3. calculating corrected reference points,
Xr~ = Xuref + g and Zr~~ = Z,,~ + f + h. PRECISION ENGINEERING
Nonrotationally symmetric surfaces can be machined using the FTS to generate small perturbation Z axis motions synchronized to the rotation of the workpiece spindle (0) and the radius (X). The remainder (or base) surface may be either flat or the best-fit aspheric surface of revolution. Because it is independent of 0, this base surface can be machined using the standard control system on the DTM. The piezoelectric actuator in the FTS is driven by a high-voltage amplifier that receives commands from a DSP. Servo position feedback via a capacitance gauge is also interfaced to this processor. The FTS feedback control loop is independent of the X and Z slide control; however, generation of the nonsymmetric reference signal requires access to the spindle encoder and the laser interferometer. Making interferometer data available to both controllers was the primary obstacle in integrating FTS control with X and Zcontrol. It was not feasible to connect the two controllers directly to the interferometer interface output ports because they would both attempt to drive the measurement board sampling signals. The interfaces required to overcome this obstacle are represented in Figure 6. In the original configuration, the laser interferometers are read directly by the slide axes controller. In the new configuration, the FTS controller intercepts the instantaneous slide position via a laser input interface and communicates these data to the slide axes controller via a position feedback interface. The laser input interface* maps the bits of the interferometer interface connectors into one
*The specific implementation depends on laser interface design. Both parallel and multiplexed laser outputs can be accommodated using this concept.
45
Miller et al.." Controller architecture . --
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Figure 9 Rotationally symmetric component of an off-axis parabolic mirror
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Figure 10 Nonrotationally symmetric component of an off-axis parabolic mirror
eight-bit control input port, one eight-bit control output port, and two 16-bit data input ports. The control input and output ports synchronize the transfer of the 32 bits of position data from the interferometers to the data ports of the input interface. This gives the FTS controller timely access to the current X and Z axes positions. The position feedback interface replicates the signals that the slide axes controller expects during communication cycles with the interferometer measurement boards. It also provides one level of data buffering, which permits the FTS controller to communicate current axis position information to the slide axes controller without synchronization delays. The only requirement is that the F-FS controller supply current X and Z values to the interface board at a frequency higher than that of the slide axes controller update cycle (i.e., 1 kHz). For the current implementation the update rate is 10 kHz. An additional interface, the angular feedback interface, provides access to the spindle encoder. This interface provides the FTS controller with the current value of 0 expressed as the number of 46
encoder pulses since the last once-per-revolution index pulse. The maximum resolution of the encoder is 0.0015 radians per count. The direction of rotation can also be determined. The once-per revolution index pulse is available externally to facilitate angular alignment of the workpiece fixture Figure 7 shows the integrated controiter, ;r~ cluding the three interfaces The FTS controlle~ includes a DSP (current system uses a Texas Instruments TMS320C30 DSP) and node controller The three interfaces connect the FTS controller to the DTM. In switch position a, the FTS controller reads the interferometers; in switch position b, the FTS is disconnected from the system With this architecture, the X/Z and FTS controi processes execute in parallel. Figure 8 shows a flowchart of the two control processes, which run at different rates. During a control cycle, each processor reads inputs, makes reference point calculations, and sends outputs. The inputs to the FTS control process are the X and Z laser data, the spindle angle 0, and the FTS position (provided by a capacitance gauge). A reference point is calculated based on the desired nonaxisymmetric shape and then adjusted by an integral controt law. The corresponding reference voltage is output to the amplifier that drives the FTS. The inputs to the slide axes control process are the X and Z laser data (provided by the position feedback interface). X and Z reference points are calculated based on the desired axisymmetric shape. After making dynamic and geometric error corrections, control signals are output to the axes servo ampii~ tiers,
Reference surface generation for off-axis conics An important application for ttle FTS is to machine off-axis conic sections on axis. With this capability, sections of large conic mirrors could be fabricated on small DTMs. The decomposition of the general aspheric optics equation into off-axis segments and their (X)-dependent and (X, /))-dependent components suitable for on-axis machining has been described. 7,12-14 The best-fit asphere is generated off-line and loaded into the slide axes controller memory while the nonrotationally symmetric modification is made by the FTS with respect to the actual position of the slides. By using the actual slide positions in the reference calculation, the FTS can also compensate for any high-frequency Z slide vibrations as well as the tow-frequency positioning error of the slide axes controller. The integrated FTS controller calculates the Z axis reference position (as a function of X and 0) on the fly and subtracts the current Zaxis position to obtain the small pertur~ bation component. Nonaxisymmetric surface capability was demo onstrated by machining a 125-mm diameter section ,JANUARY t994 VOL 16 NO
Miller et aL : Controller architecture
Figure 11
(a) Interferogram and (b) phase plot of off-axis parabolic surface
of a 1,080-mm focal length parabola 300 mm from the center. The best-fit aspheric component of this off-axis segment (Figure 9) has a sagitta of 1 mm. The nonrotationally symmetric component is shown in Figure 10. The range of the FTS required for this surface is less than 20/~m. This parabolic section was machined with closed-loop FTS control at a spindle speed of 200 rpm. Figure 1 la shows an interferogram of the surface measured in its off-axis position. 15 Straight, parallel fringes would indicate a perfect parabolic surface. Figure 1 lb is the phase plot generated from this interferogram. The P-V error of the machined surface is less than 1.1 waves (0.7/zm), which was within the specification of 1.5 waves required for the optical performance. While machining this surface, the servo cycled twice per part revolution as indicated in Figure 10. The phase plot shows a similar pattern with two high and two low regions, indicating that some error remains at the frequency of the FTS motion. Much of this error could be due to nonlinearity in the servo's piezoelectric stack. The following error for a linear system could be compensated by a slight angular shift of the part. However, for an actuator with some nonlinear hysteretic response (such as a high-voltage piezoelectric material), the phase lag varies with input amplitude and requires a nonlinear control scheme to compensate.
Conclusions A high-performance controller has been designed and built to add advanced features to an existing PRECISION ENGINEERING
DTM. These features include correction for repeatable errors and integration of FTS and slide axes controllers. The system was used to produce an offaxis parabolic section that requires coordination of the slide and servo axes to produce a nonrotationally symmetric optical surface. The figure error was less than 1.1 waves. Because further improvements in the accuracy and repeatability of fabricated components may be achievable by upgrading to faster processors, an architecture that incorporates two DSPs is the next step of development being undertaken. However, the intermediate controller configuration described here achieves FTS integration and has the advantage of portability to commercial DTMs with a variety of different axes controllers.
Acknowledgments This work was supported in part by the Office of Naval Research University Research Initiative Program in Precision Engineering and the corporate affiliates of the Precision Engineering Center. We thank Oak Ridge National Lab for measuring the off-axis optic.
References 1 Saito,T. T. "Precision machining application and technology: an overview and perspective," Proc SPIE 1983, 433, 48- 53 2 Schenz,R. F., Patterson,S. R. and Saito,T. T. "Direct machining of a non-axisymmetric phase corrector," Proc SPIE 1988, 966, 43-59 47
Miller et aL: Controller architecture 3 "intelligent machining workstation final report," Cincinnati Milacron Government Systems Operations, September, 1990 4 "Next generation workstation/machine controller architecture definition document," Document No. NGC-ADD-001, Martin Marietta Astronautics Group, June 1991 5 Dow, T. A., Miller, M. H. and Falter, P. J. "Application of a fast tool servo for diamond turning of non-rotationally symmetric surfaces," Precision Eng 1991, 13, 243-250 6 Fornaro, R. J., Garrard, K. P. and Taylor, L. W. "Architecture and algorithms for computer control of high precision machine tools," in Proceedings of ASPE Annual Conference, 1990 7 Luttrell, D, E. "Machining non-axisymmetric optics," in Proceedings of the ASPE Annual Conference, 1990 8 Weck, M. and Pyra, M. "Diamond turning of non-symmetric laser optics," in Proceedings of the ASPE Annual Conference, 1990 9 Bryan, J. B. "Design and construction of an ultraprecision
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12
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84 inch diamond turning machine," Precision Eng 1979, 1, 13-17 Donaldson, R. R. "Error budgets," Technology of Machine Tools: Machine Tool Task Force Report 1980, 5 Donmez, M. A., et al. "A general methodology for machine tool accuracy enhancement by error compensation," Precision Eng 1986, 8, 187-196 Thompson, D. C. "Theoretical tooi movement requirea [o diamond turn an off-axis paraboloid on axis," Proc SPIE 1976, 93, 23-29 Douglass, S. S. "A machining system for turning nonaxisym. metric surfaces." Ph.D. diss., University of Tennessee, Knoxville 1983 Gerchman, M, C. "A description of off-axis conic surfaces for non-axisymmetric surface generation," Proc SPIE 1990, 1266
15 Maxey, L. C. "Novel technique for aligning paraboioids. Oak Ridge National Laboratory, t991
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1994 VOL !6 NO !