Recently, the research team in Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, has established a novel processing form of magnetorheological finishing (MRF) tool to realize ripple-free surface stably, besides, the detailed mathematical analysis is presented to obtain the magic angle-step precisely and explain the phenomenon mathematically. This work was published in International Journal of Machine Tools and Manufacture in February 2021.

Ultra-precision optical surfaces are the core components of high-end optical systems, such as high-power laser, astronomical observation and lithography systems. Optical polishing is an essential step to obtain the ultra-precision surface. The basic principle of the sub-aperture optical polishing is to eliminate the figure error deterministically by a polishing tool much smaller than the workpiece. However, the ripple error with tool path pattern is easy to remain during polishing (i.e., mid-spatial-frequency (MSF) error), and MSF error is difficult to be completely eliminated once it generates and severely affects the performance of the high-end optical systems which have the strict requirements for both the surface figure accuracy and MSF errors. Therefore, at present, MSF error has been the primary technical bottleneck that hinders the development of optical polishing.

Magnetorheological finishing is a precise, deterministic sub-aperture polishing process with the ability of fine figuring of flat, spherical, and aspheric optical components. Among various existing sub-aperture polishing tools, Magnetorheological finishing (MRF) is one of the few processes that can guarantee removal accuracy, surface quality, and processing efficiency at the same time. Compared with the small-tool with poor deterministic and the ion-beam tool with low efficiency and material limitations, solving the MSF error problem of MRF tools can directly realize the mass production problem of ultra-precision optical elements and promote the development of optical fabrication ability and the high-end optical systems.

Since the invention of MRF tools, 90° orthogonal processing method has been widely used and its correctness has never been questioned. However, the research team found that there is a magic angle-step state with only several tens of micron bandwidths for the MRF tool, under which a ripple-free surface can be stably achieved without affecting the convergence of other spatial frequency errors. Besides, it is first observed in experiments that the MSF error can be increased abnormally with the decrease of path step around the magic angle-step state, which further verified the existence of the magic angle-step. Compared with the traditional MRF orthogonal processing mode, the amplitude of MSF error generated under magic angle-step state can be reduced by several orders of magnitude, which is even smaller than atomic scale and submerged in noise.

Besides, the mathematical analysis shows that the MSF error is only related to the discrete value in a certain direction of the TIF spectrum. When the peak positions of the path spectrum all precisely fall on the positions of the extra-low valley point of TIF spectrum, the MSF error can be greatly suppressed. Moreover, through the two-dimensional (2-D) Taylor approximation analysis of tool influence function (TIF), the research team proved that the existence of the ultra-low valley in the TIF spectrum at a specific angle and step is mainly due to the shape asymmetry and the edge truncation effect of the TIF.

The magic angle-step gives a brand-new approach that is extremely simple but a high-effective method to eliminate the MSF error, which pushes the MRF to a higher extreme. Furthermore, the phenomenon of magic angle-step state is not limited to MRF tool theoretically, most of the polishing tools have magic step state and the tools with rotational asymmetry TIF have magic angle state, which makes that the existing processing technology can be widely updated by this discovery.

This work was supported by Key Project of the Joint Fund for astronomy of National Natural Science Foundation of China, Outstanding Member of Youth Innovation Promotion Association of Chinese Academy of Sciences and Shanghai Sailing Program.

fig.1 Schematic diagram of the traditional and magic angle step processing mode (Image by SIOM)

Article website:
https://doi.org/10.1016/j.ijmachtools.2020.103673