Slow tool servo (STS) assisted ultra-precision diamond turning is considered as a promising machining process with high accuracy and low cost to generate the large-area micro lens arrays (MLAs) on the roller mold. However, the chatter mark is obvious at the cut-in part of every machined micro lens along the cutting direction, which is a common problem for the generation of MLAs using STS. In this study, a novel forming approach based on STS is presented to fabricate MLAs on the aluminum alloy (6061) roller mold, which is a high-efficiency machining approach in comparison to a traditional method based on STS. Based on the different distribution patterns of the discrete point of micro lens, the equal-arc method and the equal-angle method are also proposed to generate the tool path. According to a kinematic analysis of the cutting axis, the chatter mark results from the overlarge instantaneous acceleration oscillations of the cutting axis during STS diamond turning process of MLAs. Cutting parameters including the number of discrete points and cutting time of every discrete point have been experimentally investigated to reduce the chatter mark. Finally, typical MLAs (20.52-μm height and 700-μm aperture) is successfully machined with the optimal cutting parameters. The results are acquired with a fine surface quality, i.e., form error of micro lenses is 0.632 μm, which validate the feasibility of the new machining method.

A simplified calculation method is evaluated to calculate the static performance of an aerostatic journal bearing with multiple orifice-type restrictors. This method adopts a one-dimension flow assumption and is a fast calculation method to design journal bearings in engineering by directly linking the structural parameters and performance parameters affecting radial bearings with nonlinear equations. In addition, this method is verified with computational fluid dynamics by two actual case studies, and it is found that the LCC difference between those two methods is less than 5% for a 200 mm diameter spindle, and less than 10% for a 100 mm diameter spindle. Subsequently, the influence of a key parameter${\mathsf{\zeta }}_i$on the static performance of journal bearings is explained theoretically. This method is much easier and more intuitive compared with numerical computational methods. Furthermore, it promotes the application of aerostatic journal bearings.

This paper describes a method for measuring and compensating the roundness error of a larger mandrel manufactured by an ultra-precision diamond-turning lathe aimed to obtain a calibration cylinder with a roundness of less than 0.1 μm. The diamond-turning machine has a cross-stacked hydrostatic guideway, produces a cutting depth and feed movement direction, and a dual-spindle system that is firmly connected to the bed. Due to the good repeatability of aerostatic spindles, only in situ rather than online real-time measurements are required. To this end, three high-precision capacitance displacement sensors were utilized to detect the cross-section of the workpiece and the time domain via the three-point error separation technique to separate the roundness error from the rotation motion error. The slow tool servo (STS) cutting technique was employed to compensate for the roundness error, which did not require extra axes, only the excellent dynamic response of the feed axis; hence, the servo control parameters could be suitably adjusted. The experimental results reveal that the low-order harmonic error, often caused by aerostatic spindles, is almost removed completely. For this particular lathe, the experiments indicate that about 60% of the rotational error motion is compensated, and the roundness error is reduced to less than 0.1 μm, which is evaluated by the least-squares circle method.

In the interest of analyzing the effect of the structural deformation root caused by gas pressure on the static features of aerostatic bearings, a fluid–structure interaction (FSI) model based on orifice-type aerostatic bearings is proposed that can predict the characteristics of aerostatic bearings more accurately by using the direct-coupling method (DCM). By using COMSOL Multiphysics, the governing equation matrix of the finite element model of structural deformation and gas film pressure was solved with the integral solution method, and the orifice boundary conditions were calculated with the root iteration method. At the same time, the static performance of I-shaped orifice-type aerostatic bearing with various supply pressures was analyzed theoretically and tested experimentally. The results show that in comparison with the calculation results without taking account of structural deformation, the theoretical values from the model derived in this paper considering the FSI effect are closer to the experimental values. Finally, by using the orthogonal design method, FSI simulation was carried out to analyze how the key dimension factors influence the structural stiffness of the spindle, and it is concluded that the thrust bearing’s stiffness is strongly influenced by the thickness of the thrust plate.

The X-ray satellite “Einstein Probe” of the Chinese Academy of Sciences (CAS) was successfully launched on 9 January 2024 at 15:03 Beijing Time from the Xichang Satellite Launch Center in China with a “Long March-2C” rocket. The Einstein Probe is equipped with two scientific X-ray telescopes. One is the Wide-field X-ray Telescope (WXT), which uses lobster-eye optics. The other is the Follow-up X-ray Telescope (FXT), a Wolter-I type telescope. These telescopes are designed to study the universe for high-energy X-rays associated with transient high-energy phenomena. The FXT consists of two modules based on 54 thin X-ray Wolter-I grazing incidence Ni-replicated mirrors produced by the Italian Media Lario company, as contributions from the European Space Agency and the Max Planck Institute for Extraterrestrial Physics (MPE), which also provided the focal-plane detectors. Meanwhile, the Institute of High Energy Physics (IHEP), together with the Harbin Institute of Technology and Xi’an Institute of Optics and Precision Mechanics, has also completed the development and production of the structural and thermal model (STM), qualification model (QM) and flight model (FM) of FXT mirrors for the Einstein Probe (EP) satellites for demonstration purposes. This paper introduces the precision manufacturing adopted in China of Wolter-I X-ray mirror mandrels similar to those used for the EP-FXT payload. Moreover, the adopted electroformed nickel replication process, based on a chemical nickel–phosphorus alloy, is reported. The final results show that the surface of the produced mandrels after demolding and the internal surface of the mirrors have been super polished to the roughness level better than 0.3 nm RMS and the surface accuracy is better than 0.2 μm, and the mirror angular resolution for single mirror shells may be as good as 17.3 arcsec HPD (Half Power Diameter), 198 arcsec W90 (90% Energy Width) @1.49 keV (Al-K line). These results demonstrate the reliability and advancement of the process. As the first efficient X-ray-focusing optics manufacturing chain established in China, we successfully developed the first focusing mirror prototype that could be used for future X-ray satellite payloads.

Over the past 30 years, researchers have developed X-ray-focusing telescopes by employing the principle of total reflection in thin metal films. The Wolter-I focusing mirror with variable-curvature surfaces demands high precision. However, there has been limited investigation into the removal mechanisms for variable-curvature X-ray mandrels, which are crucial for achieving the desired surface roughness and form accuracy, especially in reducing mid-spatial frequency (MSF) errors. It is essential to incorporate flexible control in deterministic small-tool polishing to improve the tool’s adaptability to curvature variations and achieve stable, Gaussian-like tool influence functions (TIFs). In this paper, we introduce a curvature-adaptive prediction model for compliance figuring, based on the Preston hypothesis, using a compliant shaping tool with high slurry absorption and retention capabilities. This model predicts the compliance figuring process of variable-curvature symmetrical mandrels for X-ray grazing incidence mirrors by utilizing planar tool influence functions. Initially, a variable-curvature pressure model was developed to account for the parabolic and hyperbolic optical surfaces’ curvature characteristics. By introducing time-varying removal functions for material removal, the model establishes a variable-curvature factor function, which correlates actual downward pressure with parameters such as contact radius and contact angle, thus linking the variable-curvature surface with a planar reference. Subsequently, through analysis of the residence time distribution across different TIF models, hierarchical filtering, and PSD distribution, real-time correction of the TIFs was achieved to enable customized variable-curvature polishing. Furthermore, by applying a time-varying deconvolution algorithm, multiple rounds of flexible polishing iterations were conducted on the mandrels of a rotationally symmetric variable-curvature optical component, and the experimental results demonstrate a significant improvement in form accuracy, surface quality, and the optical performance of the mirror.