A.

Vibration isolation design

The main vibration sources on the satellite bus has been determined as the Control Moment Gyro (CMG). The perturbation frequency is 158 Hz (due to 9000 rpm) and 66 Hz (due to 0.4 rotating speed), the 1^st frequency of the satellite with bus directly connected to telescope is about 42 Hz. On the other hand, the 1^st frequency of the vibration system should be designed to avoid the 1^st frequency of solar array’s bending mode, which is 1 Hz.

According to these conditions, the 1^st frequency of the vibration isolation system connected to telescope is designed to locate in 5~12 Hz, while the amplify ratios at 66 Hz and 158 Hz should be less than 0.2. The vibration isolation connector is designed as a parallel spring guide flexure [2], as shown in Fig.1, to satisfy the confined space and thermal stress releasing requirements.

Fig. 1.

Parallel spring guide flexure

The stiffness of parallel spring guide flexure at the end of the cantilever along with the motion direction (which is y direction) is given by

Where K_y is the stiffness of the flexure along with the moving direction, d is the translation motion, L₀ is the blade width, t is the blade thickness, L is the blade length, E is elastic modulus of the flexure material and n is the number of flexure blades.

The stiffness of the flexure at the direction perpendicular to both moving and blade width direction (which is z direction) is given by

And G is the shear modulus of the flexure material. The stiffness of the flexure at the blade length direction (which is x direction) is given by

Vibration isolation connecters are equally spaced along with the primary mirror mount outer edge. The stiffness of the vibration isolation system is determined as

where K̃_x is the stiffness in x direction and K̃_y is the stiffness in y direction. With above equations, the fundamental frequencies of the flexure-mounted telescope can be estimated by

where f̃_x, f̃_y are the fundamental frequencies in x and y directions, respectively, and m is the telescope mass.

B.

Damping design

Considering the in-orbit environment, such as vacuum, extremely high or low temperature, space radiation, and the reliability of the connecter, metal damping material are the most ideal material to provide damping to the connector ([3], [4]).

Two types of metal damping elements are made to apply in the connecter system. Ring metal rubbers are used between the end of flexure and the telescope mount, as shown in Fig. 2.

Fig. 2.

Damping design

Sheet metal damping elements are combined with flexure blades to provide damping effect when the flexure blades bend.

Due to the damping system requirements, the damping ratio of the damping system should be no less than 14 Ns/m. Experiments are conducted in the future section to validate the effectiveness of the damping system.

C.

Thermal deformation releasing design

The parallel spring guide flexure is also used as the device for releasing the thermal deformation. As shown in section 3.1, the stiffness of the flexure along with motion direction is given by

And the stiffness of the flexure at the blade width direction is given by

where i is the Poisson ratio of the flexure material. The entirety stiffness of the connecter system is given by

In most condition, which means L is much larger than t, and t ≪ L, so

And

It is shown that: when t and L₀, L, is determined, thermal release feature improves with the thickness of blades: t decreases and the number of blades: n increases. Meanwhile, the entirety stiffness of the connecter system is maintained with little changes in K_z.

However, the thickness cannot be limitless thin due to the reliability and manufacture issue. With all this conditions considered and simulation conducted, n is chosen to be 3, and t is 2 mm.

A.

Vibration isolation simulation

In this section, the connecter system’s effectiveness for vibration isolation is validated though simulation using both rigid body model and satellite entirety model.

For preliminary analysis, telescope and satellite bus are modeled as rigid body. The finite element model is shown in Fig. 3 and the first 6 modal frequencies are given in Table. 1.

Fig. 3.

Point mass model

Table. 1.

The first 6modal frequencies

The requirement that the fundamental modal frequency must be in 5~12 Hz is satisfied. The amplify ratio at 66 Hz and 158 Hz at Rx-Rx and Ry-Ry directions are shown in the Fig. 4.

Fig. 4.

The transfer function at Rx-Rx and Ry-Ry directions

Since Rx and Ry directions are the most concerned directions, which the transfer ratio at these two directions effect the image quality most. It is shown that the amplify ratios at both sensitive direction are less than 0.2 and satisfied the vibration isolation requirements.

The finite element model of the connecter system connected to telescope is shown in Fig. 5.

Fig. 5.

Telescope finite element model

The finite element model of the satellite bus and telescope combined with connecter system is shown in Fig. 6.

Fig. 6.

The finite element model of the whole satellite Proc. of

The transfer function from CMG to the primary mirror mass point (of both Rx and Ry direction) is shown in Fig. 7.

Fig. 7.

The transfer function from CMG to the primary mirror mass point

The transfer ratio from CMG to the primary mirror mass point (of both Rx and Ry direction) is given in Table. 2.

Table. 2.

The transfer ratio from CMG to the primary mirror mass point

The simulation shows that: on the most concerned directions, i.e. Rx and Ry, the transfer ratios of perturbation are most below 0.3, even on those not so satisfied directions, future analysis proved that the vibration at the mirror mass point is much smaller than other directions.

B.

Damping experiment

Though many researches have been conducted to study the damping force of metal rubber, still it is difficult to determine metal rubber’s damping force theoretical. Thus, specified experiments are conducted to measure damping ratio of the ring metal rubber. The whole measure system is shown in Fig. 8.

Fig. 8.

Damping measure system

The ring metal rubber are fixed to measuring force platform at one end and at another end to vibration exciter. The damping ratio of metal rubber can be calculated with the measured response force, exciting force and metal rubber velocity. The experiment result shows the damping ratio of the damping element is up to 53 Ns/m, satisfies the required damping ratio 14 Ns/m.

C.

Thermal deformation releasing simulation

The RMS of the satellite primary mirror deformation under extremely temperature condition are calculated to validate the effectiveness of the connecter system thermal releasing feature. The finite element model of primary mirror is shown in Fig. 9.

Fig. 9.

Primary mirror finite element model

Temperature gradient of 60K (from 263K to 327K) on three directions: x, y, z are applied on the satellite finite element model. The RMSs of mirror surface deformation before and after deformation released are given in Table. 3.

Table. 3.

The RMSs of mirror surface deformation

The thermal releasing simulation result shows that: the connecter system functions well to release the thermal deformation applied on the primary mirror from satellite bus.