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Design of a six-axis high precision machine tool and its application in machining aspherical optical mirrors Hao-Bo Chenga, Zhi-Jing Fenga, Kai Chengb,*, Ying-Wei Wanga aDepartment of Precision Instruments, Tsinghua University, Beijing 100084, China bSchool of Engineering, Leeds Metropolitan University, Leeds LS1 3HE, UK Received 23 September 2004; accepted 19 November 2004 Available online 11 January 2005 Abstract The paper presents the design of a six-axis machining system and its application in fabricating large off-axis aspherical mirrors with sub- aperture lapping techniques. The new system is based on computer-controlled optical surfacing (CCOS), which combines the faculties of grinding, polishing, and on-machine profi le measuring, has the features of conventional loose abrasive machining with the characteristics of a tool having multiple degrees of freedom moving in planar model. And a novel dual touch-trigger probe profi ler is designed, which is composed of a probe, model METRO-MT60 made by HEIDENHAIN Co., is integrated into the system for measuring the shape accuracy of the tested aspherical surface, another probe modeled METRO-MT12 is designed as a calibrating device for minimizing the cosine error caused by assembly inaccuracy. The new CNC machining system with two kinds of moving coordinate systems, dual tool activities and on- machine measuring is presently developed basedon the new concept. The general material removal function during machining is analyzed on the basis of the Preston hypothesis. Further, an alignment test of the measuring profi ler is carried out using a leveling rule as a specimen. The accuracy of the optical surfaces measured by the dual probe profi ler is found to be within 1 mm PV after removing cosine error and error compensating, achieves to the resolving power of the profi ler is about 0.20.5 mm, so the developed system can be applied to the shape accuracy measuring of aspheric fabrication with micro precision during fi ne grinding process according to the calibrating results. Finally, the manufacturing experiments are carried out by virtue of an off-axis oblate ellipsoid mirror with rectangular aperture as 770 mm!210 mm and centered 127 mm. The accuracy of the aspherical mirror improved from the initial form error of 17.648 mm rms to the fi nal one of 0.728 mm rms after grinding for 200 h. q 2004 Elsevier Ltd. All rights reserved. Keywords: Sub-aperture lapping; Off-axis aspheric; Touch-trigger probe; Profi ler 1. Introduction In the classic fi nishing process, after a cutting machine makes a very low-precision cut to get the components close to the desired size, an expert optician performs most of the work manually, the optician usually uses a precisely shaped lap, a conventional rigid lap, made of pitch or polyurethane 1. The transfers pressure through an abrasive slurry to the entire surface material of the components. Material is then removed by chemical and mechanical interactions between theabrasiveandthecomponents.However,ithasarelatively slow removal rate and so takes a long time to fabricate high- precision optical elements 2. Recently, in order to attain higher resolution and wide FOV (Field of View), many optical designers have preferred to choose the TMA (Three Mirrors Asphere) off-axis confi guration for the next generation of space telescope. However, the designs had not been made applicable until the signifi cant progress recently taken place in optical design, computer controlled optical manufacturing, and testing 3. In particular, the signifi cant progress taken place in computer controlled optical surfacing (CCOS), as proposed by Rupp (Itek Com, USA) in the early 1970s 4,5, has made a large contribution toopticalmanufacturing.Bynow,asphericalopticalsurfaces are usually fi nished by computer-controlled polishing with sub-aperture pads 68. Computer-controlled polishing 0890-6955/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.11.018 International Journal of Machine Tools fax: C44 113 283 3110. E-mail address: k.chengleedsmet.ac.uk (K. Cheng). appliesthetraditionalfi nishingprocessoflooseabrasiveload controlled polishing 9. This is a three-body process in which abrasive particles (suspended in a fl uid) are pressed against the optical surface by use of a deformable polishing tool (pad), and material is removed by a chemo-mechanical process 10. Alternatively, minimizing the contact area betweenpad and surface, elastic emission machining (EEM) 11 is a fl oat polishing process 12 in which the tool is fl oatingonetheliquidlayercontainingtheabrasiveparticles. Thethicknessofthisliquidlayeramountstoamultipleofthe diameter of the abrasive particles 13, and the processs determining parameters include the hydraulic pressure generated by the tool and the hydraulic pressure generated by the tool and the kinetic energy of the abrasives. With surface roughness requirements ofbetter than 1 nmcommon in supersmooth optics, component specifi cations often exceed the capabilities of commercial high-speed optical- fabrication equipment 14. Toward that end, Kordonski, Prokhorov and coworkers initiated a novel technique, i.e. magnet-orheological fi nishing (MRF) 15,16, as an out- growth of the work with intelligent fl uids for shock absorbers, vibration isolators, which especially fi ts for rapid polishing of medium or small size optical elements 17.However,astothefabricationoflargeoff-axisaspheric mirrors with high shape accuracy for space telescopes and some relative industrial fi elds, the said techniques are still primarily an arduous, labor-intensive process. In this paper, forthepurposeofimprovingthecapabilityofCCOSonlarge aspheric mirrors, a function-expanded facility for manufac- turing of on- and off-axis aspheric components is presented with which it is possible to fabricate and test on the same machine. Experiments are then carried out to confi rm the theoreticalanalysisresults,andthesuccessfullymanufactur- ing on the off-axis oblate ellipsoid mirror with rectangular aperture as 770 mm!210 mm and centered 127 mm is also verifi ed the validity of the new CCOS facility. 2. Development of the machining system with sub-aperture lapping and on-line testing capability 2.1. Design principles In order to fabricate high accuracy aspherical and conformal (freeform surface shapes and geometry) optics, Tsinghua University has been pursuing for advanced fabricating techniques since 1995. Figs. 1 and 2 show an overall structure photograph and movement schematic view of the CNC machining system developed in house, respectively. The system arranged as gantry structure, two pillars, a crossbeam and a base form the main frame of the machine. Taking machining and measuring stability and performance into consideration, Chinese TSQ marble blocks, as the selected material, are shaped into parts of the machine frame. Based on the idea of deterministic manufacture, the tools self-rotation axis should always trace the normal line of the aspheric surface across the whole working area in order to achieve the required accuracy with high material removal effi ciency. Therefore, the system is designed to be controlled on six axes: (1) The tools self-rotation around its axis at a rotational speed of W2, (2) The tools swing around X-axis, (3) The tools motion in Y-axis, (4) The tools motion along its axis, (5) The turntables rotation around its axis at a rotational speed of W1, (6) The turntables motion in X-direction. Further, a profi ler equipped with dual touch-trigger probe (Heidenhain Co., Ltd, Germany) is installed in the system for on-machine profi le measurement during grinding process, which is also an innovating issue of the system. The system combined the faculties of grinding, fi ne grinding, polishing and on-machine profi le measuring. The sub-aperture tool is driven with two motors. One is for the tools swing around X-axis, and another is for the self- rotation of the tool around its axis. Meanwhile, a workpiece Fig. 1. Photograph of the new CNC machine tool. H.-B. Cheng et al. / International Journal of Machine Tools qj ZdKS1xi;qjKxi,tga ZdLxi;qjCdHxi;qj KS1xi;qjKxi,tga8 where, q is the rotate angle of the rotary table, S(xi, qj) is the theoretical sag of the workpiece. To resolve the tilt error Fig. 7. Calibrating linearity error of the sliding guide with the dual probe. Fig. 8. Geometrical relationship between the rotary table and translation stage. H.-B. Cheng et al. / International Journal of Machine Tools qjKaxicosqjCbxisinqjCc?g2ZFa;b;c (10) Resolve the equation (vF(a,b,c)/va)Z0, (vF(a,b,c)/ vb)Z0, (vF(a,b,c)/vc)Z0, we can easily deduce three coeffi cients a,b,c of the least square plane. Then, the fi nal surface sag errors removal matrix of the workpiece can be expressed as follows: Exi;qjZSxi;qjKaxicosqjKbxisinqjKc(11) 3. Software for scanning control For the purpose of automatic measurement, the motion control unit, the data processor of profi ler and personal computer (PC) must be integrated. Multi-axis motion control board bought from the National Instruments, which delivers accurate, high-performance motion for servo applications, can be utilized as the motion control unit in the measurement system. Integrated solutions and a line of easy-to-use plug and play motion controllers make the board good performance for PC-based motion control. The motion boards can be programmable from LabVIEW, Bridge VIEW, LabWindows/CVI, Visual Basic and C or CC C for windows NT/98/95 and other major operating systems. The ValueMotion servo controller implements trapezoidal point-to-point motion based on target position, maximum velocity and acceleration. A move in progress may be preempted by new parameters, and motion will continue following the new profi le. A trigger signal is sent from the counter card, which receives the impulses from the position measuring unit, whenever an interval is passed by the predefi ned distance. The trigger event is also the signal for the sensor to take a measurement, so that all coordinates of the measured location are exactly known. After the measured data in the PC are processed, NC-data sets can be generated and sent directly to the controller via the serial interface. An automatic measuring program written in Visual CC C was developed to measure the profi le of an aspherical surface by using this informational integration. The software integrates motion control, data acquisition, data processing and error compensation. Any resulting patterns can be performed, including circular, rectangular or linear pattern and the discrete points can be specifi cally customized by different acquisition density. 4. Experimental trials 4.1. Error removal tests on the dual touch-trigger probe profi ler The measuring experiment was performed by means of the proposed dual probe profi ler. The typical method used to verify the effect of error removal matrix is by measuring the sag of a single line of a leveling rule as a calibrating specimen fi xed on a rotary table with l/70 rms fi gure accuracy which high enough to meet the demand for contact mechanical measuring. To calibrate the linearity of the sliding guide on which translation stage built, we measured the sag of the same line on the specimen for fi ve times. The calibrating result before and after compensation for linearity error of sliding guide is shown in Fig. 9(a) and (b), respectively. Before error compensation, although the fi ve measuring fi gures present high repeatability, the measuring peak to valley value up to 8.5 mm, considerably larger than the actual accuracy of the specimen (consider the fi gure error is zero), and the asymmetric feature of error distribution is also very obviously. By virtue of calibrating probe A, these fi ve measuring results can convergent to 1.0 mm of peak to valley which has achieved to the limitation of the measuring probe. 4.2. Process tests based on Preston hypothesis From Preston hypothesis, the grind machining is a complex process, besides pressure and relative velocity Fig. 9. Calibration results before and after the linearity error compensation. H.-B. Cheng et al. / International Journal of Machine Tools & Manufacture 45 (2005) 108510941091 between workpiece and tool, one of the most important parameters affect material removal rate should be constant K. To get effective material removal rate and relative stable removal feature, K should be no much change during the grinding process. The material removal rate and changing rate of K experiments are performed on the proposed machine. The experimental conditions are shown in Table 3. The grinding tools are made of polyurethane pad, pitch and aluminum plate (with 0.25 mm thickness, 1 mm diameter of small holes and 5 mm distance between holes) separately, Fig. 10(a) and (b) show the removal rate curves and changing rate of K, respectively. In the experiment, the material removal rates correspond- ing to three kinds of tools were analyzed: for a tool made of aluminum plate (according to curve C in Fig. 11), removal rate is the largest, and K intents to be stable after grinding for 20 min, its even value is 0.00639, changing rate of K less than 5%. That of a tool made of polyurethane pad increases steadily at the fi rst 60 min (according to curve B in Fig. 10), and coeffi cient K almost no changing occurred, however, after grinding 60 min., the surface wearing of polyurethane pad decreases the size and quantity of mini poles on the surface, which results in its removal rate decreases gradually, and the even value of K decreases from original 0.00258 to 0.0012, changing rate has achieved to 50%. For pitch (according to curve D in Fig. 10), its removal rate is the least, although its working surface would not change remarkably as that of polyurethane pad, the aging phenomenon is also changing the grinding features greatly, after grinding 75 min, its even value decreases from 0.00149 to 0.00095, changing rate is about 36%. 4.3. Fabrication of an off-axis rectangular ellipsoid mirror By virtue of the proposed technique and machining system, an off-axis oblate ellipsoid mirror with rectangular aperture as 770 mm!210 mm and centered 127 mm is fabricated. Our purpose is to discover the relationship between the residual errors and the process parameters, and to optimize the CCOS process in order to remove these errors effi ciently. Figs. 11 and 12(a)(f) show the fi gure error convergence curve and distribution map in different machining stages based on the data measured using the profi ler. In the experiment, the residual errors were found to be sensitive to four parameters: diameter of tool, speed of tool, contact pressure and the abrasive size. First, a tool with diameter of 60 mm, a contact pressure of 300 g/cm2, speed Table 3 Experimental conditions Workpiece materialLoose diamond abrasive nominal size Relative speedTemperaturePressureWorking time K9 glass280#50 mm/min20 8C400 g/cm20100 min Fig. 10. Experimental curves of material removal rate (a) and changing rate of K (b). Fig. 11. Figure error convergence curve and processing parameters during grinding. H.-B. Cheng et al. / International Journal of Machine Tools & Manufacture 45 (2005) 108510941092 of tool ranging from 80 to 120 rpm, and an abrasive size of 280# was used to grind the workpiece. After 40 h of pre- grinding, as shown in Fig. 12(a) and (b), the form error has been quickly reduced from 17.648 to 8.547 mm rms. To reduce the subsurface damage, adjusting the contact pressure to 200 g/cm2, continue to carry out pre-grinding for 60 h, the form error can decrease to 3.612 mm rms as shown in Fig. 12(c). However, continuing to grind the workpiece without changing the parameters did not signifi cantly improve the surface fi gure, and the form errors were still very high. Therefore, resetting the parameters as contact pressure in the range of 150200 g/cm2, speed of tool 80 rpm and abrasive size 320#, after 50 h of fi ne grinding, the form error reduced to 1.969 mm rms as shown in Fig. 12(d), to smooth the surface of the workpiece, using a relative small tool with diameter of 30 mm, under the contact pressure of 150 g/cm2 to fi ne grind continually for 30 h, the form error reduced to 0.958 mm rms as shown in Fig. 12(e). Finally, after 20 h uniform fi ne grinding, as shown in Fig. 12(f), the shape accuracy has improved to 0.728 mm rms, which met the requirements of the Zygo GPI interferometer (working wavelength lZ0.6328 mm). 5. Conclusions A new machining facility, i.e. loose abrasive sub- aperture lapping system, by virtue of CCOS (computer- controlled optical surfacing) technique for a large aperture on- and off-axis aspheric with micron precision is presented in this paper. The material removal function and rate were studied theoretically and experimentally with respect to the novel tool designed to move in planar model enlightened from the traditional hand polishing. By virtue of a leveling rule as a calibrating specimen, the basic structure and measurement accuracy of the on-machine dual probe Fig. 12. Figure error distribution map in different grinding stages. H.-B. Cheng et al. / International Journal of Machine Tools & Manufacture 45 (2005) 108510941093 profi ler were studied theoretically with respect to the infl uence of error parameters such as the linearity error of sliding guide with dual probe, non-perpendicularity between the translation stage and rotary table after assemble, and tilt error between the actual measuring surface of workpiece and the theoretical surface, then established the error compensation matrix for improving the measurement accuracy at a level of micron. Based on the guide obtained theoretically, grinding experiments invol- ving an off-axis oblate ellipsoid mirror with rectangular aperture as 770 mm!210 mm and centered 127 mm were designed a