1. SCOPE OF WORK

This document reports on the structural analysis of the M2-f15 spider.

The model behavior has been studied from the static and the dynamic point of view, in two different configurations: the spider truss alone and the whole spider, including the rotation mechanism.

 

2. SPIDER TRUSS ANALYSYS

 

Model

The finite element model has been developed in accordance with the technical specification 401a005.

The material for both the spider and for the hub structure is steel:

mass density:	7850 kg/m³
Poisson ratio:	0.3
thermal coeff.:	16 e-6 1/K
Young mod.:	21 e10 N/m².

The mass of the M2 hub dummy is 550 Kg.

The overall weight is approximately 22414 N. A further concentrated mass of 100 Kg is added to the deployment mechanism (label "M" on figure 1).



Fig. 1. Spider FE Model and its beam’s groups.

 

Hereafter, with reference to fig. 1, the beam’s sections table is reported.

Beam’s group symbol	A [m²]	IX [m4]	IY [m4]	J [m4]	Shape [mm]
· ·	2.00 x10-3	3.65 x10-6	4.76 x10-7	1.03 x10-6	2 x (  ) 70x40x5
· · ·	2.40 x10-4	3.20 x10-10	7.20 x10-8	1.22 x10-9	(  ) 60x4
n	3.48 x10-3	5.41 x10-6	5.41 x10-6	1.08 x10-5	F 121 th. 10
o	9.76 x10-4	9.59 x10-7	2.56 x10-7	6.28 x10-7	(  ) 90x40x4
O	1.20 x10-3	1.44 x10-6	1.00 x10-8	4.00 x10-8	120x10
| |	3.48 x10-3	5.41 x10-6	5.41 x10-6	1.08 x10-5	F 121 th. 10
| | |	4.60 x10-3	3.53 x10-5	2.90 x10-6	1.49 x10-7	( I ) 120x236x10
| | | |	7.36 x10-4	1.02 x10-7	4.21 x10-7	2.56 x10-7	(  ) 70x30x4
D	2.12 x10-3	3.58 x10-7	3.58 x10-7	7.17 x10-7	F 52
< < < <	8.16 x10-4	2.04 x10-7	5.08 x10-7	4.43 x10-7	(  ) 70x40x4
	5.29 x10-3	7.38 x10-5	2.90 x10-6	1.76 x10-7	( I ) 120x319x10
C	3.85 x10-3	1.18 x10-6	1.18 x10-6	2.36 x10-6	F 70

Table 1. Beam’s sections (ref. figure 1 for coordinate system definition).

A pre-load is applied to the spider crosses to increase their bending stiffness. It is well approximated by imposing a negative temperature gradient (-6.21°) between the specified beams (•••) and the rest of the structure (T_ref=0°). In fact it has been verified that the thermal deformations are almost totally absorbed by the cross tie rods.

The pre-load value (5000 N) comes from a static-dynamic compromise that intends to increase the natural frequencies of the cross tie rods without affecting static performances.
If required, the pre-load can be increased up to 15 kN without causing static deformations of the structure comparable to the ones due to the hub gravity load.

 

Results

The bending of the spider alone is nearly symmetric and the max vertical deflection of the payload–spider interface is 0.30 mm when the telescope is pointing the zenith.

The dynamic analysis is run including the load stiffening effects of the truss elements.

The first global mode (piston + local crosses) results at 28.5 Hz, while the lowest frequency of 12.8 Hz is the bending of the largest cross tie rods.

In case that no pre-load is applied to the cross tie rods the lowest natural frequency drops to 4.14 Hz, again the large cross tie rods bending mode.

 



Fig. 2. Spider truss first global mode (28.5 Hz).

3. SPIDER AND ROTATOR MECHANISM

The 50 kN pre-load is modeled by imposing a positive temperature gradient equal to 11.6 C between the specified beams (D) and the rest of the structure (T_ref=0°).