Taking the Tianma Radio Telescope (TMRT) as an object, this paper focuses on the determination of temperature gradients and thermal deformations of the backup structure (BUS) with the finite element method. To this end, a modeling and analysis method, which consists of a simplified FEM and a four-component simulation process, is proposed. In the development, only solar radiation is considered and thermal convection is neglected. Based on the thermal time constant of the BUS, the simulations of temperature gradients are simplified as static analysis. The superposed temperature gradients agree well with the ones measured by thermometers with a 0.57°C root mean square (rms) error. In addition, the illuminated-weighted rms errors of the primary reflector surface calculated by the simulation and measured by the extended out-of-focus holography are in good agreement. The rms error increases approximately 170 μm when the Sun persistently illuminated the BUS for 3 hr. The optimized initial temperature of the antenna structure is 20°C by comparing the results between the finite element analysis and the e-OOF measurement. The thermal deformation database can support the real-time compensation of the active surface system if the traces of the radio telescope are known in advance.
Astronomical Instrumentation – Methods and Techniques – telescopes – methods: analytical
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