Introduction

The integrated study of the SRT reflecting surface is the purpose of this work. This work is developed in the frame of “SPECTR - R” program: high-sensitive centimeter-band parabolic space radiotelescope for extra-large interferometer. In mathematical model we took in to account:

The common space factor causing the distortions of the space structures is temperatures fields (Sun radiation). They are considered in computational modeling in an explicit form and allow us to model temperatures distortions.

The manufacturing and installation faults are also very important for telescopes with wave-length about 1 cm. Mainly the SRT is made of composite materials. Their behavior features in space are caused additional deviations of the reflecting surface. These deviations are specific for the researching structure.

To take into account the manufacturing faults and behavior features of the composite materials in space we use the additional loads (moments, forces and enforced motions) in the model. Thus we consider all factors causing the deviations of the reflecting surface in the same model and can use finite-element method.

Telescope manufacturing and installation faults, and deformations caused by features of composite materials behavior in space aren’t determinate.

Therefore the result deviations aren’t also determinate. To their analysis we use probabilistic model.

Structure description

SRT has the parabolic reflector, his diameter is 10 meters.

It consists of the central part and 27 petals.

The petals are collapsed around SRT long axis (focal arm) at take-off phase.

The petal is laminate composite shell, fixed on the frame.

The frame consists of the longitudinal composite pipe and the transverse titanic ribs.

The reflector is placed in the Central Module (CM).

The transition arm connects CM with space service module.

Finit-Elements Model

Software MSC.NASTRAN is used as a solver.

Brief model characteristic:

General view of the FE model shows at the fig. 1.

Fig. 1

FE model.

We verify the model by several tests:

Beside these tests we made the numerical modeling of the petal deformation and comprised it with the results of the thermo-vacuum test [1].

The analysis of the deviations.

The normal deviations of the reflector surface are defined relative to 3 bases. These bases are:

where

Temperature deformations

Because of the difficult form of the SRT antenna structure the definition of the temperature field is a difficult problem.

For the purpose of decreasing the temperature heterogeneity influence on the SRT function parameters of the petal frame pipes is using:

We use the same finite element model as for the main problem decision (distortions of SRT mirror) as for temperature field calculation.

For the heat calculations we use the monolayer shell of the single petal. This monolayer shell has the effective thermophysical characteristics conforming to honeycomb structure ((_eff = 8 W/(m((C)).

The effective heat conductivity along the frame pipes is 35 W/(m((C) (composite with aluminum foil)

For other metal element we use the thermophysical characteristics from the technical guide.

The results of the direct measurements give us the thermooptic characteristics of the petal shell for the calculation (A_S, ():

To detect the thermophysical characteristics of MLI we use guide and define them more exactly using the results of thermo-vacuum tests of the petal [1].

We use the software TERM to define the external heat loads on SRT structure elements.

The cases of modeling for two modes of functioning (orientation at the Sun) SRT are studying:

The main difference of these two variant is the temperature field of focal module arm.

Fig.2 is the results of the heat calculation for the single SRT petal. According to these results the petal shell temperature is located from –110 to –140°C, frame pipe temperature is located from 20 to –50°C.

Fig. 2

Temperature field on the petal shell.

The Central Module temperatures, focal module temperatures and other structure elements are defining in similar way.

The view of the deformed model for Load Set 2 is shown at fig 3.

Fig. 3

The view of the deformed model for Load Set 2.

The field of the normal displacements (for Load Set 2) is shown at fig. 4 (in mm, the rigid-body motions of reflector are excluded) and fig. 5 (in mm, for best-fit paraboloid).

Fig. 4

The field of the normal displacements (in mm, the rigid-body motions of reflector are excluded, Load Set 2)

Fig. 5

The field of the normal displacements (related to best-fit paraboloid, Load Set 2).

Manufacturing faults and the space influence

The manufacturing and installation faults are important not determinate factor, influencing on the deviations from theoretic profile. The technological experiments with single detail allow us to define these faults. Maximum values of the faults are describing in the specifications. The space influence consists in sublimation of composite components. This sublimation reduces to additional shell distortions and bending and torsion of composite frame pipes. Such distortions are determined during the thermo-vacuum tests [1].

The couple of enforced motions (card SPC of MSC.Nastran), prescribed in join points shell/frame take into account the technical deviations in model ((Tn_i, fig. 6). The enforced motion values are changed random in interval, prescribed in technical specification.

Fig. 6

The join points shell/frame and the enforced motion.

Such method allows getting the “smooth” deviation field. Special software is used for the MSC. Nastran input file creation. Load sets are created automatically and added to the based MSC. Nastran input file. Input file contains 50 load sets. In each load set the enforced motion value for all join points shell/frame is changing. Typical distribution of the normal displacements (in mm) caused by manufacturing faults and the vacuum influence on the petal shell is shown at fig. 7.

Fig. 7

The field of the normal displacements (the manufacturing and installation faults and the space influence).

Bending and torsion are used in the model as equivalent bending and torsion moments, applied at the end of the composite pipes of the frame (fig. 8).

Fig. 8

The equivalent bending and torsion moments

The equal moment values are also changed random in interval, prescribed in technical specification. The technological experiments with single pipe allow us to define these angles of bending and torsion.

Special software is used for the MSC.Nastran input file creation. Load sets are created automatically and added to the based MSC.Nastran input file. Input file contains 50 load sets. In each load set the bending and torsion moment value for all pipes for all frames is changing.

Typical distribution of the normal displacements (in mm) caused by vacuum influence on the frame pipes is shown at fig. 9.

Fig. 9

The field of the normal displacements (the space influence on composite pipes).

Result analysis

Special software is developed to analyze reflecting surface deviations, caused by the complex of the deformation factors. This software uses the results of the numerical modeling get from MSC.Nastran (files *.f06). It allows us to get the normal deviation fields at different bases (with exception of the rigid-body motion, relative to best-fit paraboloid, see fig. 3 and 4 for example) and carries out the probabilistic analysis of the deviations, caused by the all deformation factors. The distribution of the probability for normal deviations (caused by the all deformation factors for two orientation variants) is shown at fig. 9 and 10.

Fig. 9

The distribution of the probability for maximum normal distortions.

Fig. 10

The distribution of the probability for RMS distortions.

Conclusion

The complex analysis of the reflecting surface deviations is carried out.