As a flexible grinding method with high efficiency, abrasive belt grinding has been widely used in the machining of mechanical parts. However, abrasive belt grinding has not been well applied in the field of ultra-precision optical processing, due to the lack of a stable and controllable removal function. In this paper, based on the idea of deterministic machining, the time-controlled grinding (TCG) method based on the abrasive belt as a machining tool was applied to the deterministic machining of optical components. Firstly, based on the Preston equation, a theoretical model of the TCG removal function was established. Secondly, removal function experiments were carried out to verify the validity and robustness of the theoretical removal model. Further, theoretical and actual shaping experiments were carried out on 200 mm × 200 mm flat glass-ceramic. The results show that the surface shape error converged from 6.497 μm PV and 1.318 μm RMS to 5.397 μm PV and 1.115 μm RMS. The theoretical and experimental results are consistent. In addition, the surface roughness improved from 271 to 143 nm Ra. The results validate the concept that the removal function model established in this paper can guide the actual shaping experiments of TCG, which is expected to be applied to the deterministic machining of large-diameter optical components.

The aerostatic lubrication model with orifice restriction is built based on finite difference method. The model is solved by combination of flux-error feedback and optimization of grids parameter. The stiffness of aerostatic bearing can be improved by reducing the diameter of the orifice, but the optimum working gas gap is reduced and the processing difficulty of surface throttle is improved. The experiments of load and stiffness are carried out on the slider (50 × 50 mm) with the diameter of orifice at 50 µm. The experimental results and theoretical calculation are in good agreement; thus, the model is verified. The structural parameter of two, three, and four orifice gas-bearings is optimized, respectively, based on the proposed model, and the optimum positions of the orifices are obtained. According to the results, the aerostatic bearing guideways, made up of optical material (K9), are manufactured by some optical ways, and the lubrication of the small gas gap is guaranteed; meanwhile, the straightness accuracy of the aerostatic bearing guideways is 0.1 µm/200 mm. The analysis result verifies that the calculation method and the aerostatic lubrication model are significant to the design of high-precision aerostatic equipment.

The fast tool servo (FTS) technology has unique advantages in the machining of complex surfaces such as special-shaped targets and free-form surfaces. In view of the shortcomings in the performance of the existing FTS device, this paper puts forward a novel FTS which uses two piezoelectric ceramics instead of flexure hinges to provide restoring force. Firstly, the feasibility of the double-drive principle is verified theoretically, and the corresponding mechanism is optimized accordingly. Then, the system control hysteresis model is established and identified, and the appropriate control strategy is designed. Finally, the performances of the proposed FTS device are tested, and a typical microstructure is machined based on the device and ultra-precision lathe. The results indicate that the proposed device effectively improves the performance of the FTS system, which is useful for the processing of microstructures and free-form surfaces.