SDSS 2.5-m primary support system measurements
Sloan Digital Sky Survey Telescope Technical Note
19981019
Walter
Siegmund, Larry Carey, Siriluk Limmongkol, Russell Owen and
Patrick Waddell
Contents
Introduction
The support of large optics in telescopes is complicated by the
extreme sensitivity of such optics to deformation. While such optics
may actually be quite rigid by normal engineering standards, their
deformations must be exceedingly small to be acceptable. A
satisfactory solution for monolithic optics is provided by separate
systems for defining the orientation and location of the optic with
respect to the telescope mount, i.e., the 6 rigid body degrees of
freedom, and supporting the weight of the optic. Typically, it is
called on to react to wind-induced forces of the optic at frequencies
higher than about 1 Hz. Such forces are generally less than 1% of the
weight of the optic. Since the definition system applies only small
forces to the optic, it cannot cause significant deformation of its
surface. The support system, on the other hand, must apply large
forces to the optic to support its weight. This is accomplished using
a large number of force actuators. Each force actuator need only
apply the relatively small force required to support the weight of
that portion of the optic that is near the actuator. Since each
portion of the optic is supported locally, bending stresses are small
as is the deformation of the surface of the optic.
In the case of the 2.5-m telescope primary mirror, the support
actuators are air pistons. The 48 axial and 18 transverse air pistons
support the axial and transverse components of the mirror weight
vector respectively. The pressure of the air that is supplied to the
pistons is controlled so that the forces applied by the definition
system (as sensed by load cells) are small.
Table 1: Air piston parameters.
Piston diameters are set so that the maximum pressure required is
similar for the two sets.
|
Axial
|
Transverse
|
Unit
|
Piston area
|
2299
|
3910
|
mm^2
|
Piston number
|
48
|
18
|
|
Piston force
|
156
|
416
|
N
|
Pressure
|
0.068
|
0.106
|
MPa
|
The air pistons are simple, high performance, reliable and
inexpensive (Figure 1 and Figure 2). They consist of an acetyl piston
(blue) that is captured in a machined aluminum housing (black). The
piston seal is made by a reinforced silicon elastomer formed into the
shape of a hat and folded as shown in the Figures (magenta). As the
piston extends and retracts, the elastomeric seal rolls in and out.
Since the seal is quite flexible, the force exerted by the piston is
to first order independent of its axial displacement ("Design of the
Apache Point Observatory 3.5 m Telescope III. Primary mirror support
system", E.J. Mannery, W. A. Siegmund and M.T. Hull, Proc. of
S.P.I.E., 628, 1986, p. 390). As reported by Mannery et al., axial
parasitic forces can be 1 N or even less depending on the diameter,
stroke and maximum pressure (which affects the strength of the seal
that is required and thereby its stiffness).
Figure 1: Axial air piston. The
piston consists of a two-part aluminum housing (black), an acetyl
piston (blue) and a reinforced silicon rubber seal (magenta).
Silicon rubber bumpers (cyan) support the mirror when the pistons
are not pressurized and prevent full compression of the pistons. A
cylindrical base (green) and washer (red) complete the
assembly.
Figure 2: Transverse air piston. The
piston consists of a two-part aluminum housing (black), an acetyl
piston (blue) and a reinforced silicon rubber seal (magenta).
Measurements
To measure the response of an air piston to transverse forces, a
transverse piston was loaded with 11 kg lead bricks and pressurized
using a syringe (Figure 3). To provide stable support for the bricks,
an aluminum plate was placed on the piston. It was supported at the
corners opposite the piston by two ø15 mm steel balls. A
spring scale was used to apply a transverse force. The transverse
displacement of the piston was measured using a dial indicator.
The data demonstrate that the piston behaves like a spring with
hysteresis (Figure 4). The spring rate is proportional to the load on
the piston (Figure 5). The data of Figure 4 were taken with the
piston extended 6 to 7 mm, i.e., about 50%. With the piston extended
3 mm (25%) and a load of 223 N, no significant change in the spring
rate or hysteresis behaviour was observed.
Figure 3: A spring scale was used to
apply lateral forces to the air piston as a dial indicator
measured its lateral displacement. The axial load was supplied by
lead bricks. The piston was pressurized with a syringe.
Figure 4: The air piston acts like a
spring with hysteresis in response to a side force. The spring
gets stiffer as the axial load increases from 111 to 445 N. The
data were taken with the piston extended 6 to 7 mm, i.e., about
50%.
Figure 5: The spring rates of Figure
2 are proportional to the axial load on the piston. The points at
0 N are much less reliable than the other data.
Conclusions
Measurements of the primary mirror transverse air pistons indicate
the following.
- In response to a sideways force, the piston behaves like a
spring with hysteresis.
- The spring rate is proportional to the load on the piston. As
the piston is decentered, the seal fold is squeezed higher on one
side and stretched lower on the opposite side. Thus the pressure
in the piston acts on more area on one side than the other. This
effect amounts to a spring rate of about 0.2 N/mm, much too small.
Instead, stress stiffening of the membrane of the seal fold may be
responsible, particularly in that part of the membrane that
deforms due to shear.
- If the transverse air pistons could be allowed to exert up to
+/-25 N axially on the mirror, then the mirror may be moved
axially up to +/-0.5 mm. It is likely that the mirror can be
positioned open loop to this accuracy. Finite element modeling
could be used to investigate the deformation of the mirror due to
these forces.
- Even if the air pistons are centered, their hysteresis is such
that they may exert up to 10 N axially, depending on their
history.
Acknowledgment
We are grateful to Jon Davis of Apache Point Observatory for
making the first measurements of the lateral stiffness of an air
piston.
Date created: 10/19/98
Last modified: 10/26/98
Copyright © 1998, Walter A. Siegmund
Walter A. Siegmund
siegmund@astro.washington.edu