Non-axisymmetric Aspheric Surfaces Research Articles

Machining control of non-axisymmetric aspheric surface based on piezoelectric fast tool servo system

Non-axisymmetric aspheric machining is increasingly important in photoelectric industry. The machining process requires an external feeding device mounted to a machine tool to achieve fast-tool servo (FTS) function. In this study, a piezoelectric (PZT, Lead zirconate titanate) FTS was used to perform non-axisymmetric aspheric machining by control methods. In the beginning, system identification of the PZT tool holder was conducted to obtain the mathematical model of the system and then the simulations were performed for various controllers, including the PID (Proportional-integral-derivative), sliding mode control (SMC), non-singular terminal sliding mode control (NTSMC), and adaptive NTSMC. The simulation results showed that the NTSMC and the adaptive NTSMC had excellent control performances with the tracking errors of 0.0 and 3.1 nm, respectively. Then, control practices without machining were performed with the PV (Peak-to-valley) tracking errors of 0.96 μm, 0.77 μm, and 0.95 μm obtained by the PID controller, NTSMC, and adaptive NTSMC, correspondingly. The large PV errors were found due to the low sampling rate of position commands. Finally, experiments of non-axisymmetric aspheric machining with the implemented controllers were performed for a workpiece of oxygen-free copper (OFC) having 5 mm diameter. The measured results of the machined surfaces were with the PV form errors of 7.2 μm, 2.8 μm, and 3.8 μm in corresponding to the usual machining, using NTSMC and adaptive NTSMC. The effectiveness of the implemented controllers was demonstrated, and the NTSMC showed the best performance. Future works are to examine the repeatability of various controllers with a large hardware memory size and improved environment.

Accuracy prediction of multi-axis simultaneous controlled ultra-precision machining of non-axisymmetric aspheric surface using a real-time position capture system

Accuracy prediction of multi-axis simultaneous controlled ultra-precision machining of non-axisymmetric aspheric surface using a real-time position capture system

Active Optics in Astronomy: Freeform Mirror for the MESSIER Telescope Proposal

Active optics techniques in astronomy provide high imaging quality. This paper is dedicated to highly deformable active optics that can generate non-axisymmetric aspheric surfaces—or freeform surfaces—by use of a minimum number of actuators. The aspheric mirror is obtained from a single uniform load that acts over the surface of a closed-form substrate whilst under axial reaction to its elliptical perimeter ring during spherical polishing. MESSIER space proposal is a wide-field low-central-obstruction folded-two-mirror-anastigmat or here called briefly three-mirror-anastigmat (TMA) telescope. The optical design is a folded reflective Schmidt. Basic telescope features are 36 cm aperture, f/2.5, with 1.6° × 2.6° field of view and a curved field detector allowing null distortion aberration for drift-scan observations. The freeform mirror is generated by spherical stress polishing that provides super-polished freeform surfaces after elastic relaxation. Preliminary analysis required use of the optics theory of 3rd-order aberrations and elasticity theory of thin elliptical plates. Final cross-optimizations were carried out with Zemax raytracing code and Nastran FEA elasticity code in order to determine the complete geometry of a glass ceramic Zerodur deformable substrate.

Active optics in astronomy – modeling of deformable substrates: freeform surfaces for FIREBall and MESSIER

Abstract Active optics techniques on large telescopes and astronomical instrumentations provide high imaging quality. For ground-based astronomy, the co-addition of adaptive optics again increases angular resolution up to providing diffraction-limited imaging at least in the infrared. Active and adaptive optics marked milestone progress in the detection of exoplanets, super-massive black holes, and large-scale structure of galaxies. This paper is dedicated to highly deformable active optics that can generate non-axisymmetric aspheric surfaces – or freeform surfaces – by use of a minimum number of actuators: a single uniform load acts over the surface of a vase-form substrate whilst under reaction to its elliptical perimeter ring. Two such instruments are presented: (1) the Faint Intergalactic Redshifted Emission Balloon (FIREBall) telescope and multi object spectrograph (MOS) where the freeform reflective diffraction grating is generated by replication of a deformable master grating, and (2) the MESSIER wide-field low-central-obstruction three-mirror-anastigmat (TMA) telescope proposal where the freeform mirror is generated by stress figuring and elastic relaxation. Freeform surfaces were obtained by plane super-polishing. Preliminary analysis required use of the optics theory of 3rd-order aberrations and elasticity theory of thin elliptical plates. Final cross-optimizations were carried out with Zemax raytracing code and Nastran FEA elasticity code in order to determine geometry of the deformable substrates.

Accurate spiral tool path generation of ultraprecision three-axis turning for non-zero rake angle using symbolic computation

An accurate spiral tool path generation method of ultraprecision three-axis turning free form surface is proposed based on symbolic computation in this paper. Many analytic optical free form surfaces often need to be machined to submicron in form error, such as optical nonaxisymmetric aspheric surfaces, but current mainstream CAM systems usually use nonuniform rational basis spline (NURBS) to describe the designed surface and generate tool path. If we want to use these systems, the analytical optical surfaces must be approximated using NURBS surfaces, but it will introduce approximation error and may be difficult to achieve the approximation error less than submicron. More importantly, there is no effective tool path generation method for the special three-axis turning machine tool in current mainstream CAM systems. In this context, we propose to calculate the tool path directly from these analytic surfaces by using symbolic math. The proposed method can be used to generate accurate spiral tool paths for zero/negative/positive rake angle in a unified way. Finally, several examples are given to prove its effectiveness.

Research on Measuring Path and Surface Fitting Algorithm for Non-Axisymmetric Aspheric

In accordance with the requirements and characteristics of non-axisymmetric aspheric surface measuring, three measuring paths were put forward and estimated. The applicant situations of the three paths were also analyzed. A data processing system was created for the measuring of non-axisymmetric aspheric surface. Levenberg-Marquardt method was adopted as the nonlinear least squares to fit the discrete data. The fitting result was assessed by the fitting residuals. The experimental results show that the fitting residuals was in the 10-3mm magnitude when convergence index parameter set as 1×10-10mm. Compared with the theory equation, it’s shown that the method can not only be used for non-axisymmetric aspheric surface quality evaluation, but also can generate compensation data to improve machining precision.

Study on Precision Machining of Glass Lens Mold with Minute Structures (2nd Report)

In recent years, the demand of optical devices with complicated and highly accurate shape such as Fresnel lens and f-q lens is growing up in terms of miniaturization and improvement of information equipments. Moreover, the demand of glass lenses increases for the purpose of improving its heat resistance and optical performances. The study proposes a machining process for non-axisymmetric aspheric cemented tungsten carbide mold with minute structures, aiming at high precision machining. In the proposed process, the non-axisymmetric aspheric surfaces except for minute structures are at first machined by the spiral form grinding tool path with a spherical resinoid bonded diamond wheel. The machined surface center is corresponding to the center of the rotation axis of ultraprecision machine tool. Afterwards, the surfaces are ground for compensation, based on allover shape measurement interpolated by cubic spline. Then, minute structures are created on non-axisymmetric aspheric surfaces by the grinding with a disk type metal bonded diamond wheel. As a result, it is found that the proposed machining method has the potential of producing a high precision non-axisymmetric aspheric glass lens mold with minute structures effectively.

3D simulation of arc envelope grinding of non-axisymmetric aspheric surface

A new simulation method for envelope grinding of non-axisymmetric aspheric surface was proposed by using 3D virtual curve grinding without complex mathematical calculations. The aim is to verify 3D distribution of envelop traces and form errors on ground curve surface. First, 3D objects of arc-shaped grinding wheel and workpiece were established in AutoCAD, then Boolean operation was conducted to simulate form grinding by AutoLISP program, finally tool path number and form errors were analysed. Grinding experiments proved the validity of this simulation method. It was shown that 3D envelope traces and form errors distribution can be displayed by simulation for tool path planning and form error compensation. It was confirmed that equal-envelope-height grinding can greatly reduce tool paths when precision grinding of very large curvature is conducted. In addition, form accuracy PV only increases 4.17 µm in the range of 200 × 20 mm² for wheel radial wear of 1 mm.

Arc Envelope Grinding of Non-Axisymmetric Aspheric Surface Using Equal-Envelope Height

An arc envelope grinding method for non-axisymmetric aspheric surface was proposed in order to achieve the mould core used for the precision injection molding of optic reflector. In grinding, the arc-shaped diamond grinding wheel trued on CNC grinder was used to envelope workpiece and generate curve surface, and the spacing distance between tool paths is controlled by the equal-envelope height between wheel and workpiece. In this paper, arc envelope grinding principle was investigated in connection with wheel coordinate calculation and tool path number. The theoretical analysis and grinding experiment showed that arc envelope grinding may improve form grinding efficiency especially for large curvature and smoothness of ground surface and a smooth curve surface can be produced when the equal-envelope height is less than a certain value.

Geometric Models of the Ultra-Precision Grinding for Large Non-Axisymmetric Optical Aspheric Surfaces

Geometric Models of the Ultra-Precision Grinding for Large Non-Axisymmetric Optical Aspheric Surfaces

An ultraprecision grinding machine for non-axisymmetric aspheric mirrors

For the purposes of grinding non-axisymmetric aspheric surfaces, a large five-axis controlled ultraprecision grinding machine has been developed for the first time in the world. As the machine is equipped with a profile measurement system, profile accuracy can be improved by feedback of profile error. A toroidal surface of 500 mm*100 mm made of CVD-SiC has been machined. It has always been hard to grind CVD-SiC in the ductile mode with metal-bonded grinding wheels because of its hard and brittle properties, but grinding in the ductile mode has been accomplished by an improved truing and dressing method. As a result, surface roughness of less than 5.0 nm RMS was attained. By correcting profile error with the profile measurement system, profile accuracy of about 0.5 mu m was obtained after four corrections.

オンマシン計測による斜入射Ｘ線ミラーの超精密研削

This paper deals with a machining method for making a large non-axisymmetric aspheric surface with a high accuracy. An electric micrometer has been set near a grinding head on 5-axis control ultra-precision grinding machine for measuring the shape error of ground surface in conformity with the machine movement due to the cutter location data. A series of the measured shape errors corrects the former cutter location data automatically and the next grinding operation will be performed by the new cutter location data. A large CVD-SiC sample 110 by 510 mm has been ground into a toroidal surface of 0.75 μm in shape accuracy by the fifth grinding operation with the fourth correction of cutter location data. The machine has been also installed in a constant temperature room of ±0.5K in variation.

斜入射Ｘ線ミラー用超精密研削加工機の開発

In order to fabricate grazing incidence X-ray mirrors made of hard and brittle CVD-SiC, a large 5 axis control ultra-precision grinding machine has been developed. The machine must be capable of generating non-axisymmetric aspheric surfaces by ductile grinding. So as to obtain precise profile accuracy, new mechanisms such as flexible coupling, guide rails with fine deformation mechanism and leveling blocks for correcting warp of guide rails are applied to hydrostatic linear slideways. As experimental results, excellent straightness of X axis slide of 0.05 μm in a 500mm traverse is obtained on the grinding machine. Non-axisymmetric aspheric mirrors have been ground within a profile error of 0.9μm with the machine.