Astronomical telescopes enable astronomers to see into deep space and unravel the mysteries of the universe. Freeform mirrors surfaces offer substantial benefits by providing additional degrees of freedom that make it possible to improve the optical performances of the instrument.
Freeform optical mirrors surfaces must be construct with nano-scale accuracy to produce clear images. Currently, freeform mirrors are usually produced by computer control optical surfacing and single-point diamond turning, which is expensive and requires long lead times. Researchers at the Laboratorie d’Astrophysique de Marseille are developing an innovative manufacturing process based on the plastic deformation of materials and the hydroforming process.
The hydroforming process is difficult to design and optimize because the mirror undergoes plastic deformation to provide a freeform optical surface. The analysis of material under stress in the plastic domain is much more difficult because it involves both material and geometric nonlinearities. Achieving these goals requires analyzing the global structural behavior of the substrate while taking into account work-hardening, anisotropy, contact conditions, boundary conditions and load cases applied during the hydroforming process.
“We selected Marc to analyze the hydroforming process because Marc has demonstrated the ability to provide accurate results in problems involving complex nonlinear changes in geometry and material properties,” said Zalpha Challita, in post-doctoral position at LA Marseille.
The materials used include stainless steel, aluminum, and titanium because they possess a large plastic domain, good elastic behavior and the ability to be optically polished.
FEA was performed with Marc to quantify the residual errors after the hydroforming process and to optimize the system. The optimized parameters are, for example, hydroforming parameters such as clamping and forming pressures and optical parameters concerning the overall geometry of the initial mirror and of the mold shape. Contact analysis between the mold and the back of the mirror is also performed. The final shape of the deformed substrate after the conclusion of the hydroforming process is then extracted from Marc and treated optically.
The simulation was very beneficial in terms of defining the limits of the process and the sensitivity of the final geometry to the various hydroforming parameters. Zalpha Challita said. “The highly complex material and geometrical nonlinearities involved in plastic deformation of materials make it essential that accurate and iterative modeling of the process be performed in advance to determine the required mold shape to achieve the desired optical form. Marc demonstrate the ability to accurately model the hydroforming process and will be used extensively going forward.”
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