Active profiling and polishing for efficient control of ... - CiteSeerX

Mechatronics 13 (2003) 295–312

Active profiling and polishing for efficient control of material removal from large precision surfaces with moderate asphericity Sug-Whan Kim

a,b,c,*

, David Walker b, David Brooks

b

a

c

Center for Space Astrophysics, Yonsei University, Sudamun gu, Shinchon dong, Seoul 134, Republic of Korea b Optical Science Laboratory, Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK Physics, Mathematics and Astronomy Division, Mail Code 405-47, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA Received 30 October 2000; accepted 5 November 2001

Abstract We present the development of an active fabrication technology for controlling material removal on large precision surfaces of moderate departure from a sphere. The underlying philosophy was established as an efficient solution to the challenging problem of fabricating secondary mirrors of up to nominally 2.5 m in diameter for modern 8 m class telescopes and beyond. The facility described comprises a CNC profiler, two contact profilometers, and a full size active polisher. The trial work-piece was a convex surface of 830 mm in diameter on a zero-expansion ceramic (‘Cervit’) blank – a 1/3 scale hyperbolic mirror for a proposed 2.5 m diameter f/7 secondary mirror for the 8 m Gemini telescope. Using software error-correction from profilometric metrology data, a factor of 2 improvement in generating the convex aspheric profile was achieved. An active loose-abrasive polishing process is also described, in which a full-size tool is configured to deliver variable, edgeless, sub-diameter removal-footprints. Real-time monitoring of process variables is described, and approximately 10% convergence in each polishing pass is reported. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Aspheric surfaces; Material removal; Active control; CNC grinding; Polishing

*

Corresponding author. Tel.: +1-626-395-2284; fax: +1-626-568-0285. E-mail address: [email protected] (S.-W. Kim).

0957-4158/03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 7 - 4 1 5 8 ( 0 1 ) 0 0 0 8 8 - 5

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S.-W. Kim et al. / Mechatronics 13 (2003) 295–312

1. Introduction Building the next generation of astronomical telescopes poses a significant technical challenge to the optics community worldwide. Surprisingly, it is the fabrication of the highly aspheric convex secondary mirrors (much smaller than the primaries) that are most difficult. These exhibit departures from the closest fit sphere (‘asphericity’) of a significant fraction of a millimeter, across diameters of up to, perhaps, 2.5 m for an 8 m primary. The problem will be exacerbated for the next generation of 30–100 m telescopes, now on the drawing board. Traditionally, fabrication of astronomical aspheric optics consists of two stages [1]. The first is to shape the blank, involving facing, edging, beveling and finally generating a closest fit spherical surface using bound diamond abrasives typically in a metal-matrix on a rotating cupped or peripheral wheel. The second is to polish the spherical surface through loose-abrasive lapping and fine polishing. Then the aspherization proceeds, using fine loose-abrasive polishing. The traditional technique of tedious step-cutting for profile-generation, followed by passive sub or full diameter lapping and polishing, has become obsolete. This is mainly due to the low form convergence-rate of craft processes, and the high overhead in producing specialized tooling to service iterative removal-cycles. The difficulty in testing such mirrors has also contributed greatly to the challenge. This paper is concerned with a new development in CNC grinding and active polishing for efficient fabrication of a sub-micron form accuracy surface using a Cervit blank of 830 mm in diameter. Section 2 deals with a new approach of active fabrication of large precision surfaces on brittle ceramic glasses. The discussion includes a summary of other relevant studies and their limitations of applicability in CNC machining large ceramic glasses. It also points to the shortcomings of polishing techniques used widely elsewhere. Section 3 is concerned with the details of a 2.5 m CNC grinding machine, the work-piece error compensation technique and necessary metrology facilities. A full size active polisher is summarized in Section 4, followed by the experiments and results in Section 5. The implications of the technology and the concluding summary are presented in Section 6.

2. New philosophy of active fabrication CNC machining including grinding, milling and turning have been widely used technique for producing precision work-pieces. Numerous investigations on different aspects of CNC machining have been made recently in the literature [2–21]. In particular, various techniques for improving work-piece error in CNC machining have been reported [4–18]. Insightful overviews and analysis on error sources and control methods of CNC machining are presented by Liu [4] and van Luttervelt [5]. Gao et al. [6] reported an active surface grinding technique using a micro-positioning work-piece table. The work-piece defects caused by dynamic behavior of


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machine spindle were studied by Kim et al. [7] and Segond et al. [8]. The cutting force effects on the work-piece error and the compensation techniques were investigated by several researchers [9–12]. Laser interferometry was used to decompose and quantify various error sources, and to develop compensation techniques [13–15]. Moreton et al. [16] studied a technique to compensate the 3D tool geometric error. Grinding burn and chatter vibration were investigated using micromagnetic sensor [17], and acoustic emission and power sensors [18]. Interpolation techniques relevant to CNC machine control were studied for simultaneous 3-axis control [19] and a better representation of measured data points on curved surfaces [20]. For optimization of cutting path plan, Lin et al. [21] used a neural network technique to relate the grinding variables to the surface quality of the machined work-piece. As demonstrated above, the CNC machining community worldwide has placed comparatively little attention to high precision machining of large zero expansion ceramic glasses such as Cervit and Zerodur. This is partly due to relatively small size of its application market which is mostly centered around academic research community such as astronomy, and classified work in some parts of the defense industry. The nature of one-off or small batch production, together with low profitper-project, have also played a significant role in repelling the research interests of the CNC machining community. Having witnessed the construction of, and plans for, a number of 8–10 m scale large astronomical telescope, we acknowledge an increasing need to exploit the results of our study in this small but yet rapidly growing field of CNC machining of large brittle materials ranging from 0.5 m to about 10 m in size. The aforementioned studies of error compensation techniques [4–18] are concerned with work-pieces that are mass-produced, small, less accurate and more complex (i.e. often 3D combinations of flat and curved surfaces) in shape. The workpiece used in our research is a one-off work-piece, of significant size (i.e. 830 mm in diameter), high precision requirement (i.e. sub-micrometer form accuracy) and relatively simple form with continuously changing curvature of radius (i.e. hyperbolic convex surface, of which sag exceeds 20 mm). The size and weight of such large brittle materials, together with the required surface form precision, have made it extremely difficult to utilize any machining techniques developed for smaller, less accurate and mass produced work-pieces. Consequently, there are many technical challenges to be overcome, until such techniques can be used readily for cost-effective machining of large brittle materials of few meters in diameter. This tends to call for a different approach for both the machining hardware and the processes used, compared with the common CNC machining centers and associated error compensation techniques used in those investigations above. Regarding approximate shaping of large ceramic glass, Wilson [22] described the spin casting technique that reduced greatly the amount of material removal required for large concave primary mirrors. However, it does not work directly when shaping large convex mirror blanks. It would in principle be possible to spin-cast convex surfaces using the ‘float glass technique’ where the molten glass is floated on tin.

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However, to our knowledge this has not been applied to convex mirrors. Even so, spin casting of concave mirrors still needed substantial additional material removal in shaping the work-piece surface. In our case, the direct generation of an aspheric surface from the bulk material by CNC bound-abrasive grinding was an efficient solution to shorten the time for surface fabrication. Such aspherization during grinding was a significant evolution from the traditional method of applying aspherization in only the final polishing. For improving the efficiency in generating an aspheric surface, the surface error produced in the previous grinding operation was measured and fed back to the next grinding pass to reduce errors. This process required off-line metrology calibrated to about 20 lm measurement accuracy, that could measure a generated surface-form having up to few centimeters in sag. Simple contact LVDT-based (linear variable displacement transducers) profilometers were preferred over a spherometer or other measurement techniques [9–15,17,18] mentioned above, due to the directness and the cost-effectiveness of the measurement. A 10:6 lm infrared interferometer could in principle have been used, but would have required a null lens larger than the workpiece, which itself would have been an extreme manufacturing challenge. There have been a number of technical developments, addressing final figuring of large optical surfaces over the last few decades. They include stressed lap polishing [23,24], computer-controlled optical surfacing [25], stressed mirror polishing [26], ion-ablation process [27,28], linear membrane polishers [29,30]. Whilst these methods have been used for controlling material removal in polishing large aspheric optics, they suffer from at least some technical limitations such as low removal rate, high spatial-frequency and zonal errors (‘waviness’), open-loop operation, lack of real-time process monitoring, absence of real-time control of removal-rate, etc. Fundamentally, a skilled optician is often the key to the process control algorithm. Realizing the shortcomings of other methods, the concept of ‘‘Full Size Active Polishing’’ was proposed [31]. For faster removal rate and smoothness over the entire sample surface in polishing, the polisher was made full size to cover the whole work-piece surface (i.e. 830 mm diameter in this study), yet sufficiently flexible to conform to the aspheric profile during relatively short machine strokes. Its flex plate, one of the main structural parts of the polisher, was a full size aluminum plate of 8 mm in thickness. This was to allow for the sag of about 22 mm (i.e. close to the sag of work-piece surface profile), when it is supported at the center. Of particular interest was the active control of the distribution of polishing pressure, as the lap traverses across the sample. This approach was fundamentally different from the 1/3 scale subdiameter stressed lap, where the first three Zernike terms of the lap shape were actively controlled during strokes across the diameter, in order for the tool-surface to conform to the target work-piece surface [23,24]. Classical optical figuring is open-loop in nature. No process control feed-back is available to an optician while the machine is running, other than the manual ‘feel’ of the tool. Part of the work described in this paper has overcome this by telemetering real-time process-data to the optician, and displaying it through a graphical user interface that can readily be interpreted.


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3. 2.5 m scale CNC grinding machine and contact profilometers 3.1. 2.5 m scale CNC grinding machine Due to the very limited availability of few-meter scale grinding/milling machines, a historic vertical boring machine was converted, with the addition of a modern grinding spindle, moire-fringe encoders, stepper motor drives and control software. The vertical borer was a 2.5 m diameter capacity machine shown in Fig. 1. This was previously used by the former Grubb Parsons to produce a number of astronomical optics including the 2.5 m Isaac Newton telescope primary mirror. Their technique used manual advancement of the slide-ways to generate steps, which were subsequently removed by loose-abrasive grinding with a tool covered with ceramic tiles. Fig. 1 shows a schematic diagram of the machine used. The rotating table on which the mirror blank is mounted is powered by a 14.914 kW electric motor and rotated at rates set by a mechanical gearbox (typically 43 s per revolution). Two

Fig. 1. 2.5 m ex-Grubb Parsons vertical borer, as used for manual generation of profile steps.

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vertical columns rise from the base-casting either side of the machine, and are linked with a fixed arch at the top. A horizontal bridge slides up and down the columns on lead screws either side to accommodate different thicknesses of work-piece, although the bridge is normally locked near its central position. The bridge carries the horizontal slide-way, on which is mounted a massive manual vertical angle stage. This carries the quill, which is usually left near-vertical, but which can be set between 45°. The drives for the quill and the horizontal sideway each retained their original lead-screws. However, the original lead-screw gear-boxes, driven from the main machine motor, were stripped out and replaced by geared stepper motors driving through toothed belts. One turn of each lead screw advances the corresponding slide-way by 6.35 mm, and individual stepper motor steps of a few microns can be discerned using a dial micrometer on the moving slide-ways. A 2000 rpm 3.728 kW grinding spindle, mounted on the vertical column was installed for use with a vertical or horizontal axis, and supports bonded abrasive tools such as a diamond cup tool. Machine renovation is shown in Fig. 2. The two moire fringe linear encoders were fitted, one on the horizontal sideway and the other on the quill, to monitor the X and Y coordinates of the grinding tool. The encoders were interfaced to a PC via a programmable digital I/O card. The two geared stepper motors ran in half step mode for finer stepping and minimum resonance. Motor driver controllers under software control generate all the requisite signals. A pair of micro switches – software halt, then hardware override – limit the X and Y travels. The machine status, such as the current tool location, limit switches, and stepping time interval are monitored before and after each cutting step, and then used to calculate the next target position of the cutting tool during profiling. Profile generation software was developed in-house, allowing the optician direct control over the cutting tool by sending series of low level command strings. More usually, the optician uses the program to define high level operating parameters instead. The program has two distinct elements. First, it uses the philosophy of a ‘‘Moving Reference Profile (MRP)’’ for moving the target surface profile in 3D space and thereby the CNC grinding tool on the sample surface. The program takes input variables defining the target surface and the 3D motion of the target surface profile. This concept enables the machine to complete multiple cutting operations without the need for redefining the subsequent CNC file each time. In this mode, the entire grinding operation is executed with no user intervention once commenced. Secondly, an error compensation routine utilizing profilometer data and localized polynomial interpolation was incorporated. The technique uses 4 sets of measured ðX ; Y Þ data close to the point of interest Xi along the X axis and applied the Lagrange formula [32] to calculate the corresponding Yi value at Xi. For each step movement of the cutting tool, the routine used the off-line metrology data and the theoretical target profile data to calculate the height error DYt at the next target location Xt of the tool and add the negative DYt (i.e. DYt) to the theoretical target Yt. Then the cutting motion profile between ðXi; YiÞ and ðXt; Yt DYtÞ is calculated and fed to the motor controller.


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Fig. 2. New CNC profiling machine controller.

3.2. Mark 1 and 2 contact profilometers The Mark I single probe profilometer shown in Fig. 3 used a rectangular optical flat of about 1 m in length, sitting on three mechanical pads. One edge of the flat was placed to cross the center of the sample surface. A 1 lm resolution LVDT (Type LDC 100C from RDP electronics) interfaced to a PC was used to measure distance between the flat and the sample surfaces along the diameter. The measurement resolution was adequate for assessing the machined profile, remembering that some 20 lm of ceramic material caused by sub-surface damage remained to be removed by loose-abrasive lapping. The probe was moved over the top surface of the work-piece, while the supporting platform was moved along one edge of the flat reference mirror that crosses the center of the work-piece surface. Active thermal stabilization of 0:5 K around the LVDT probe achieved the measurement accuracy of about 7 lm including repeatability. The LVDT was calibrated to an accuracy of 10 lm for the dynamic range 0–60 mm, using stacks of precision engineering slip gauges.

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Fig. 3. Mark I single-probe profilometer. Note that both surfaces of the 1 m optical flat have the form accuracy of 0:25k at He–Ne laser wavelength.

The calibration data showed residual non-linearity of 1:728 mm Peak-to-Valley (P-to-V) after a least squares fit over the dynamic range 0–60 mm. Localized polynomial interpolation was again applied to the data and a final residual error scale of approximately 10 lm was obtained for the final calibration. The Mark II multi-probe profilometer using 10 LVDTs (i.e. Schlumberger AG2.5) is shown in Fig. 4. It has one LVDT at the center of the work-piece and another at its edge. 7 LDVTs and one fiducial steel knife edge are separated at 50 mm intervals in between these two LVDTs, along a 20 mm diameter Invar rod. Another fiducial knife edge is located at the same radius as the first knife edge, but on the opposite side along the work-piece diameter. The final LVDT is positioned at 50 mm distance outwardly from this second knife edge. The profilometer was designed to rest on the mirror surface via these two knife edges, these being mounted along the rod at distances of 200 mm from the center. Although it is not shown in Fig. 4, a third leg is positioned next to the left-hand knife edge. It is a 200 mm long 8 mm diameter rod with a 10 mm diameter steel ball at the end. It is connected to the Invar bar using a close fitting ring and locked into place with screws. The device was first set up on an optical flat, and under each LVDT metric inspection grade steel gauge blocks (British standard BS4311:Part 1993) were as-


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Fig. 4. Mark II multi-probe profilometer. Note that the third leg is just behind the left-hand knife edge and not shown in this diagram.

sembled to take out the calculated sags at each corresponding point on the mirror. Each LVDT was then adjusted vertically in its holder so that it was at mid-range. The device was then placed on the mirror and radially centred using an adjusting screw at one end. The LVDT signals were consequently differential with respect to the slip-gauge stacks, and all near mid-range, circumventing most of the nonlinearity in response. This profilometer had a number of advantages over its predecessor. The probes had a repeatability of better than 0:15 lm. The LVDTs were AC-energized and all the electronic components were mounted on the PC interface card. Thus, the LVDT suffered very little from its own thermal characteristics. With the comparative thermal change of 1 K, the zero point change was less than 3 lm and the sensitivity altered less than 3 lm in the full scale of 2.5 mm. The disadvantages were of course the discontinuous sampling of the surface, the reliance on slips, and the minor inconvenience of producing a new invar rod for each mirror size. Since Mark II needs a time of less than about 30 s to sample the height data across the work-piece diameter, there is no substantial temperature change (i.e. larger than 0:5 K) in the room during the measurement. The thermal error is then within 3 lm. The total measurement error of the Mark II profilometer in the worst case is estimated to be about 5 lm. The portability of the device is such that it is easily placed onto the fabricated mirror surface while mounted on the polishing machine. It allows the profile to be measured over several diameters so that any asymmetry or astigmatism of the surface profile can be detected immediately. Because the profilometer is mounted on the surface to be measured, there is no tilt variation in successive measurements. As it gives no information between the LVDTs, the Mark I and II profilometers are considered to be complementary.

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4. Full size active polisher Fig. 5 shows an active polisher as built. Kim et al. [33] showed an exploded diagram of this polisher. The working surface comprised a thin shell of carbon-fiber reinforced epoxy formed, using the generated mirror as a mold, to support an array of square pitch tiles that provide the polishing action. The upper side of the shell had a grid of 65 hexagonal wedges of epoxy resin converting the curve of the pitch tiles to a flat plane interface with the active mechanism of the lap. The active structure consisted of two circular metal plates bolted together through a central spacer. 32 linear stepper motor units were attached to the upper ‘reaction plate’ and exerted variables forces via custom designed spring units on the lower ‘flexible plate’. The spring units each had a metal disk of about 4 mm in thickness that was sandwiched by two stacks of disk springs. Kim et al. [33] presented the details of the customdeveloped flat-line load cells for monitoring the 2D distribution of axial polishing force exerted onto the work-piece surface. A flat metal ring was mounted in bearings on the upper side of the lap. Three ‘global force actuators’, attached to a rigid test tower, pulled on the ring to vary the absolute polishing pressure and to tilt the pressure distribution across the mirror.

Fig. 5. Active polisher as built.


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Each global force actuator comprised a Duff-Norton mini-pac actuator (i.e. model HPD6405-6 from Power Jacks), a commercial off-the-shelf load cell (i.e. model T6001P-100 from Thames Side), a tension spring and a braided steel cable. The mechanism left the lap free-rotating independent of the lap location and tilt. As the lap strokes the work-piece, the tension on the wires was monitored by the load cells. A servo kept the global pressure to a pre-defined value. A central boss on the lap interfaced to two drive arms that pushed and pulled the tool through the traditional motor-driven eccentric mechanism. Electronics for load cell digitization, motor drivers, position encoding, and power conditioning were located on board the lap and controlled by an single-board computer. It provided (i) polling of the load cells, multiplexing and A/D conversion of their signals, (ii) reading the temperature sensors and encoders, (iii) serializing and triggering data transfer to a host PC, (iv) accepting the target pressure, computing the required adjustments for each stepper motor and updating the actuators. The host PC communicated with the on board processor via a custom developed bidirectional infra-red data link embedded within the central boss, which also had sliprings for power and an encoder for lap rotation. PC software provided (i) a graphic user interface, (ii) data input for pressure, lap location and rotation, temperature, etc. (iii) display of computed surface removal from a real-time ablation algorithm. The active lap design allowed for three different modes of operation; passive, semi-active and fully active modes. In the passive mode, the actuators were adjusted to produce a desired pressure map e.g. pressure hot spot and then locked so that there was no real-time servo update activated during a polishing run. However, polishing variables such as pressure, speed and dwell time were continuously monitored and therefore an ablation map was updated graphically, giving the optician realistic estimation of what was happening on the work-piece surface. The semiactive mode was designed to utilize a servo update cycle at slower interval e.g. one update per minute, altering the pressure map to increase or decrease ablation at a specific location on the sample surface. The full active mode was intended to update the servo cycles at higher frequency i.e. currently at 5 Hz but targeted at 20 Hz. In practice, all results presented in this study have been obtained in the passive mode.

5. Experimentation and results The 830 mm diameter (i.e. 820 mm useful diameter) work-piece was a hyperbolic convex surface with a conic constant of 1:8639, sag of 22.468 mm and aspheric profile departure of 212 lm from the sphere at the edge. The experiment objective was to investigate the controllability of differential material removal in generating and figuring the asphere. Table 1 summarizes the experimental conditions for both CNC-grinding and polishing. In machining this convex surface, the control action was entirely dependent on the current location of the tool within the global machine coordinate system. The machine monitored the current tool position and calculated the cutting step trajectory between the current and next target positions. It should be noted that, although

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Table 1 Experimental conditions for CNC grinding and polishing Experimental condition

CNC grinding

Polishing

Work-piece

830 mm diameter, convex hyperbolic mirror Zero expansion Cervit blank 2.5 m 2 axis CNC grinding machine 100/200 bronze bond cupped diamond grinding wheel

830 mm diameter, convex hyperbolic mirror Zero expansion Cervit blank 1 m polishing machine

175 mm 5 mm 100 lm 500 lm 1400 rpm 5 HP 10°

830 mm

Work-piece material Machine used Tool Tool parameter: Diameter Edge radius Nominal cutting depth Nominal cutting step Spindle rotation Spindle power Quill angle Stroke: off-set Grinding coolant or abrasive slurry

Coolant feed rate 10 l/min

Table rotation Control parameter or action

1.5 rpm Active control of tool coordinate

On-line monitoring parameter

Tool coordinate, limit switches

Full size active polisher with pitch tiles