Stressed Mirror Polishing: Finite element simulation of mirror blank deformation

摘要

The theoretical principle of Stressed Mirror Polishing (SMP) is introduced, including the representation method of elastic deformation, the formulations of discrete bending moment and shearing force. A Finite Element Analysis (FEA) simulation model of has been set up by ANSYS software. The warping facility in this model is consisted of 36 aluminum alloy arms equally distribute on the ambit of mirror blank. Two forces are applied on each arm to provide bending moment and shearing force. Taking type 82 segment of Thirty Meters Telescope (TMT) primary mirror for example, a FEA simulation of mirror blank deformation has been performed. Simulation result shows that, the deformation error is 33um PV. The theoretical deformation PV value is 205μm and the simulation deformation PV value is 172μm, converging rate reaches to 0.84 in a single warping cycle. After three or four warping cycles, the residue error may converge into 1 μm.