JCMT Technical Report TR/001/81/IP Flexural Analysis of the HARP K-Mirror assembly on the JCMT

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TR/001/81/IP



1



JCMT Technical Report

TR/001/81/IP


Flexural Analysis

of the HARP K
-
Mirror assembly

on the JCMT





Ian Pain

Senior Mechanical Engineer, JAC



07.Apr.00



Joint Astronomy Centre

660 N.A'ohoku Place,

University Park

Hilo, Hawaii.

96720 USA.

TR/001/81/IP



2

Flexural
Analysis of the HARP K
-
Mirror

assembly on the JCMT


Summary


This document describes a Finite Element Analysis performed on the JCMT Antenna as part of JAC support for the

HARP K
-
Mirror development project.


The analysis exploited models of the antenna a
vailable following work on the JCMT Surface Upgrades project,
modified by only the minimum required to add a simplified structure and load point for the K
-
Mirror.


The results were analyzed in FEA graphical format, by examination of deflection curves for s
elected K
-
mirror points
and by removal of best
-
fit parabola using dish fitting software developed as part of the surface upgrades project.


Movement of the K
-
Mirror mounting point due to flexure of the JCMT structure, is predicted a maximum of approx.
20
μm displacement (2 arc.sec angular offset). This appears acceptable within the K
-
mirror PDR specification, and
variations in error may be reduced to +/
-
10 μm halved by performing final alignment when tipped at 45°.


As far as impact on the JCMT antenna,
the K
-
Mirror mechanical loads should provide no significant problems for
pointing or surface quality which will not be corrected by normal alignment and pointing procedures.


Surface shape changes are predicted to occur, but below the level at which adjus
tments would be required. Thermal
isolation of the sub
-
frame structure and the receiver cabin environments are however a cause for concern, and a
specification target of no more than a 1°C change of tube temperature due to HARP K
-
Mirror heat loads should b
e
considered.


The likely error terms and methods of removal are summarized below. Although small, these effects will impact all
modes of observing for all instruments (not just HARP) so pointing model changes may need to be global
-

not just
HARP specif
ic.



Effect

Magnitude

Method of compensation

Surface error lobes close to surface base. Minor
variations thereof with elevation angle

<1μm

kot requiredK

mointing offsets, with elev~tion dependency

(offset 縠2K1 x cos(el))

1KR ~rcKsec ~t
㐵4

ooutine "~ll
J
sky pointing"
models; loc~l pointingK

Therm~l lo~d induced surf~ce errors


J
2μm/°C

Therm~l isol~tion, ~ctive
surf~ce controlK

Therm
~l lo~d induced pointing errors

縱 ~rcKsec/°C

Therm~l isol~tion, ~ctive
surf~ce control, loc~l pointing





TR/001/81/IP



3

Contents

SUMMARY
................................
................................
................................
................................
................................
................................
.....
2

CONTENTS

................................
................................
................................
................................
................................
................................
...
3

DISTRIBUTION

................................
................................
................................
................................
................................
............................
3

ACKNOWLEDGEMENTS
................................
................................
................................
................................
................................
...........
3

TABLE OF FIGURES

................................
................................
................................
................................
................................
...................
4

1.

INTRODUCTION

................................
................................
................................
................................
................................
...............
5

2. THE FE MODEL

................................
................................
................................
................................
................................
........................
5

2.1

M
ODELLING
A
SSUMPTIONS AND
S
OFTWARE

................................
................................
................................
................................

5

2.1.1

Antenna structure
................................
................................
................................
................................
...............................
5

2.1.2

K
-
Mirror structure

................................
................................
................................
................................
.............................
7

2.2

B
OUNDARY
C
ONDITIONS AND
L
OADS

................................
................................
................................
................................
.............

9

2.3

D
OCUMENT
&

F
ILE
C
ONTROL

................................
................................
................................
................................
........................

9

2.4

R
ESULTS
................................
................................
................................
................................
................................
.........................

10

2.4.1

Surface
................................
................................
................................
................................
................................
...............

10

2.4.2

K
-
Mirror
................................
................................
................................
................................
................................
............

16

3

CONCLUSIONS & RECOMM
ENDATIONS
................................
................................
................................
.............................

20

4

APPENDIX : DISHFIT R
ESULTS VS FEA DISPLA
CEMENTS
................................
................................
................................
.
I

5

APPENDIX : HARP K
-
MIRROR TECHNICAL DAT
A

................................
................................
................................
..............

V



Distribution


Dr.H.Smith

MRAO

R.Bennett

ATC

G.Rae


ATC

M.Ellis


ATC

P.Friberg

JAC

File copy

JAC : http://www.jach.hawaii.edu/JACdocs/JCMT/TR/001/81



Acknowledgements


Thanks are due to Dr.F.Baas for analysis of FEA results with 'dishfit', and for the images in Appendix A
TR/001/81/IP



4


Table of figures


F
IGURE
1

A
NTENNA
FEA

MODEL
.

1
ST

ORDER BEAMS AND SHEL
LS

................................
................................
................................
............

6

F
IG
URE
2

A
NTENNA
FEA

MODEL
.

R
EALISTIC PLOT
.
................................
................................
................................
................................
...

6

F
IGURE
3

K
-
M
IRROR MODEL SKETCH

................................
................................
................................
................................
..........................

7

F
IGURE
4

T
HE
K
-
M
IRROR SUSPENDED FROM

THE ANTENNA SUB
-
FRAME UPPER
.

................................
................................
.....................

8

F
IGURE
5

K
-
M
IRRO
R STRUCTURE AND LOAD

VECTORS FOR SIX LOAD

ANGLES
.

................................
................................
.......................

8

F
IGURE
6

V
ERTICAL DISPLACEMENT

OF THE SURFACE
,

ANTENNA AT ZENITH

................................
................................
.........................

10

F
IGURE
7

V
ERTICAL DISPLACEMENT
,

ANTENNA AT ZENITH
,

END VIEW
.

................................
................................
................................
....

11

F
IGURE
8

V
ERTICAL DISPLACEMENT

OF ANTENNA
,

REAR VIEW
.

................................
................................
................................
...............

12

F
IGURE
9

T
ILT OF THE ANTENNA D
UE TO TORQUE LOADING

................................
................................
................................
......................

13

F
IGURE
10

V
ERTICAL DISPLACEMENT
.

A
NTENNA AT
45°

RESTRAINED AT EL
EVATION RING
.

................................
................................

14

F
IGURE
11

A
NTENNA AT
45°,

RESTRAINED AT ELEVAT
ION RING
.

................................
................................
................................
..............

14

F
IGURE
12

S
URFACE VERTICAL DISP
LACEMENT
.

A
NTENNA AT
45°.

UNDERLYING LOBE STRU
CTURE JUST VISIBLE

.............................

15

F
IGURE
13

-

AS
F
IG
11

BUT WITH ALTERNATE S
CALE SELECTED TO ENH
ANCE LOBE
-
STRUCTURE
.

................................
........................

15

F
IGURE
14

D
ISPLACEMENT OF
K
-
M
IRROR OPTICS WITH EL
EVATION SLEW ANGLE
.

................................
................................
................

17

F
IGURE
15

R
OTATION OF
K
-
M
IRRO
R OPTICS WITH ELEVAT
ION SLEW ANGLE
.

................................
................................
.........................

17

F
IGURE
16

D
ISPLACEMENT OF
K
-
M
IRROR FRAME WITH ELE
VATION SLEW ANGLE
................................
................................
..................

18

F
IGURE
17

R
OTATION OF
K
-
M
IRROR FRAME WITH ELE
VATION SLEW ANGLE
.

................................
................................
........................

18

F
IGURE
18

-

S
URFACE DEFORMATIONS
IN MICRONS DUE TO A
1°C

RISE IN A SUB
-
FRAME UPPER TUBE
.

................................
................

19

F
IGURE
19

D
ISHFIT
-

Z
ENITH LOADCASE
(
COMPARE TO
F
IG
5,

MAIN BODY
)

-

REPRODUCED BELOW

................................
........................

I

F
IGUR
E
20

D
ISHFIT
-

A
NTENNA AT
75°

................................
................................
................................
................................
........................

II

F
IGURE
21

D
ISHFIT
-

A
NTENNA AT
60°

................................
................................
................................
................................
.........................

II

F
IGURE
22

D
ISHFIT
-

A
NTENNA AT
45°

(
NOT
-
RESTRAINED AT DRIVE
AXIS
)

................................
................................
..............................

III

F
IGURE
23

D
ISHFIT
-

A
NTE
NNA AT
45°

(
RESTRAINED AT DRIVE
AXIS
)


................................
................................
................................
.....

III

F
IGURE
25

D
ISHFIT
-
A
NTENNA AT
30°

................................
................................
................................
................................
........................
IV

F
IGURE
26

D
ISHFIT
-

A
NTENNA AT
30°

................................
................................
................................
................................
........................
IV

F
IGURE
27

D
ESIGN DISCUSSION OF
THE
HARP

K
-
MIRRO
R PER
RJB'
S EMAIL

................................
................................
............................
VI


TR/001/81/IP



5

1.

Introduction


1.1

This document describes a finite element analysis performed on the JCMT Antenna as part of the JAC work
package for the HARP K
-
Mirror. This analysis was performed at the JAC as a suitable
FE model of the antenna was
available following work on JCMT Surface Upgrades project.


1.2

The surface upgrades model is optimized to utilize data captured from a thermal sensor array on the JCMT antenna,
processing this and deriving the deformed dish shapes

which arise due to differential thermal expansion of the
structure.


1.3

For this study the model was modified by only the minimum required to add a simplified structure and load point for
the K
-
Mirror.


1.4

Four models were run as various additional parameters
were explored: all results here are from the final model (file
kmirr4.dbs). Results for antenna surface quality and pointing offsets, K
-
Mirror flexure and thermal deformations are
discussed.



2. The FE Model

2.1

Modelling Assumptions and Software

2.1.1

Antenna stru
cture


(a)

The Surface Upgrades FEA model, file mod20s.dbs is an EMRC NISA
-
II finite element model. It uses first order
beam element for computational speed, and as such contains many geometrical simplifications to force
convergence of elements at nodal points
, though these nodal points themselves are substantially as per the
JCMT design drawing set. Shell elements are used to model the sub
-
frame lower ballast mass, the sub
-
frame
upper fabricated ring zone and the secondary mirror spider. The receiver cabin and

bearing interfaces are not
modelled.

(b)

Additional shell elements, but with structural properties adjusted to provide no structural constraint, are
placed on the backing surface for visualization only
-

they provide a nominal dish surface for preliminary
dis
placement data analysis. For precise values only the dish nodal coordinates are used for off
-
line parabola
-
fitting analysis.

(c)

The model elements have density and mass properties, and mass elements are provided for applying point
loads from non
-
structural i
tems (ballast masses, equipment, nodal castings, adjusters, cables, etc). However,
the mass elements do NOT have the correct values, and time constraints currently prohibit a detailed survey to
update these. This implies that gravity
-
induced flexure analys
is is not possible and instead the only case
studied here is to consider telescope deflections with the additional load of the K
-
Mirror as compared to
without.

(d)

Modifications were made to the surface upgrades model, primarily:



the sub
-
frame tubes above the
elevation axis were broken, to insert additional nodes for placing the K
-
Mirror. (Mirror image tubes on LH of the antenna were similarly modified to retain symmetry).



Webs were added at the ends of the tubes (as on the actual antenna) as these areas were
found in initial
runs to appear significantly under
-
constrained.


TR/001/81/IP



6


Figure
1

Antenna FEA model. 1
st

order beams and shells


Figure
2

Antenna FEA model. Realistic plot.

TR/001/81/IP



7

2.1.2

K
-
Mirr
or structure


(a)

The HARP K
-
Mirror was modelled as a point load suspended below the elevation beam by very stiff links.

Figure 3, below, shows an end
-
on view (through the elevation tube) of the simplified K mirror model. O1 and
O2 are attachments to the sub
-
frame upper tube, M is master node at main body CoG, D is a node at the
rotating structure CoG. Very stiff elements (Young's Modulus at 10
3

times stiffer than steel) are applied to link
these units. Note that a virtual rigid constraint then exists between

01 and 02 as both are tied to the same point
by rigid elements.





Figure
3

K
-
Mirror model sketch


(b)

Although the vertical offsets of nodes M and D above were correctly modelled, less data was available for
the horizontal offset.

This was located in the final analysis (kmirr4.dbs) to match the K
-
Mirror PDR document
(23/9/99) data, which gives the K
-
Mirror optical centre at (0, 2268,250) (x,y,z) mm from the TMU. At the time of
writing (13/4/00) the CoG has been recently predicted t
o be at (15,2184,256)
-

see Appendix B for additional
details. This location is close enough for modelling of the effects concerned.

(c)

The attachments O1 and O2 were not as simple as sketched above and were in fact spread over several
nodes in the sub
-
frame
upper tubes, see below.

D

M

O1

O2

Fig 3

TR/001/81/IP



8


Figure
4

The K
-
Mirror suspended from the antenna sub
-
frame upper.


Figure
5

K
-
Mirror structure and load vectors for six load angles.

TR/001/81/IP



9


2.2

Boundary Condit
ions and Loads


2.2.1

The antenna was constrained at the two elevation bearings, allowing rotation and piston motion , but no forward or
vertical translation.

2.2.2

In addition the right elevation bearing axis was also constrained in rotation about the elevation axis

as the encoder
servo effectively locks this tube in place to a resolution better than 0.2 arc.seconds.

2.2.3

Rotation and lateral displacement at the tertiary mirror was constrained to ensure that sideways displacements
remain symmetrical. Though a more realist
ic assumption is that one bearing may be fixed and the other is free to
take up transverse expansion the fitting of parabolas to the data is considerably complicated if the structure is
allowed to expand non
-
symmetrically.

2.2.4

In displacement set 1 the elevat
ion drive constraint from friction on the drive ring was not modelled. It is
advantageous not to model this because by constraining the encoder alone we see any wind up of the structure
between the drive ring and encoder
-

and hence the pointing error term
. By constraining both the drive ring and
encoder we would not see these pointing errors.

2.2.5

At a later iteration, an additional displacement constraint set (set 2) was also applied to constrain the elevation
drive ring and eliminate pointing offsets from th
e model results. The constraint was such as to provide a tangential
restraint on the elevation drive at the approximate nodal location of the drive wheel at an antenna elevation of 45° .
This constraint was only run once, in conjunction with the 45° loadse
t.

2.2.6

Loads were applied to the K
-
Mirror nodes, by forces



1177N (120kg) at main body CoG, node M (250mm above axis).



589 N (60kg) at rotating mirror CoG, node D



Six load cases were modelled, using the correct vector components at angles from the horizon o
f : 90°, 75°, 60°,
45°, 30°, and 15°

2.2.7

Load combinations between the varying load and constraint sets were run in a number of load cases, as follows:

Table
1

Load combinations:

Load
Set

Displacement
Set


Load Case ID
for analysis

El
evation

Notes

1

1


1

90°

no elevation ring constraint


2

2

75°

3

3

60°

4

4

45°

5

5

30°

6

6

15°

4

2

7

45°

Elevation ring constrained at 45°


2.3

Document & File Control


FEA Control Document

JAC
-
FEA
-
20

-


archived on Ola
\
fea
\

FEA Report (this
)

fea_20_rep.doc

-


archived on Ola
\
fea
\
documentation

-


also raised as JCMT technical report (via
Ola
\
JACdocs
\
JCMT
\
tr
\
001
\
81)


Database files:


kmirr4.dbs

-

archived on Ola
\
fea
\
models

NISA file


kmirr4.nis

-

archived on Ola
\
fea
\
models

Output File


kmirr
4.out

-

not archived


TR/001/81/IP



10

2.4

Results

2.4.1

Surface


(a)

At Z
enith the z
-
axis displacements in the dish were a minima of
-
2.0μm near the K
-
Mirror and a peak of 0.8μm
on the opposite side. These effects caused primarily by warping the sub
-
frame upper 'ring' towards HARP and
the surface local to it. Removing a best
-
fi
t parabola from this data leaves maximum excursions as +/
-

0.5μm.
This is negligible given the overall ~5μm measurement error intrinsic in holography expected with RxH3, and
the 3μm minimum step of the surface adjusters.


Figure
6

Vertical displacement of the surface, antenna at zenith

TR/001/81/IP



11


Figure
7

Vertical displacement, antenna at zenith, end view.

TR/001/81/IP



12


Figure
8

Vertical displacement of antenna, rear view.

(b)

Away from zenith the surfac
e displacement is dominated by a rotation effect due to the torque load induced by
the K
-
Mirror. At 45° (see loadcase 4 result below) this is +/
-

60 μm of pure tilt, or a ~ 1.5 arc.second tilt on the
15m throw of the dish. This is not critical, as this ty
pe of pointing error is routinely removed. Unfortunately
though, this effect masks any underlying surface distortions in the raw FEA plots.

(c)

A crude analysis can be made by only looking at zenith effects and assuming only about 1/√2 of these effects
will o
ccur at 45°, with the torsion component producing only pure rotation of the dish.


TR/001/81/IP



13


Figure
9

Tilt of the antenna due to torque loading

(d)

For verification, the results of Load Case No.7 may be studied (below). Here the elevation driv
e wheel location
is restrained with the aim of investigating whether this will remove most dish rotation effects in the model and
allow a better first estimate of dish distortions. The results here are much better in terms of reducing pure tilt.
About +/
-
1
μm of tilt remains across dish (less than 0.1 arc.sec of throw), and some of this may be 'real' (i.e. due
to k mirror torque fed into dish, not just tip of whole antenna). By inspection the same kind of lobes as seen in
the zenith case are present, with ma
x amplitudes of about + /
-
0.8 μm. This fits the zenith/√2 value supposition
well, and is fully confirmed by the dish
-
fit data in Appendix 1.

(e)

Ideally we would adjust the surface at 45° elevation and then see only half the range of effects either side of
th
is elevation. It is fortunate that these effects are small as in practice holography is only available at 8.5°
elevation, so will see their full range.

TR/001/81/IP



14


Figure
10

Vertical displacement. Antenna at 45° restrained at elevation ring
.


Figure
11

Antenna at 45°, restrained at elevation ring.

TR/001/81/IP



15


Figure
12

Surface vertical displacement. Antenna at 45°. underlying lobe structure just visible


Figure
13

-

as Fig

11 but with alternate scale selected to enhance lobe
-
structure.

TR/001/81/IP



16


(f)

In addition to the above crude results, the JAC surface upgrades project's FEA "dishfit" routine can remove
the best fitting parabola from this form of data to reveal the effects on the sha
pe alone. Data reduction by
Dr.F.Baas with this technique confirms that overall magnitudes are as predicted above, and that no major
impacts are concealed in this analysis, see Appendix 1 for dish
-
fit data vs FEA plots comparisons.


2.4.2

K
-
Mirror


(a)

Motion of th
e K
-
Mirror optics themselves due to flexure of the sub
-
frame tubes to which they are attached is
of interest. These need to be combined with the internal flexure of the mechanism itself in assessing
acceptability. The table and charts below provide the app
ropriate data.

(b)

Note that vertical motion (z) of the frame and optics are essentially identical
-

as expected given their highly
rigid linking. Non
-
intuitively though the lateral (y) and forwards (x) motion of the frame is generally higher than
that of the

optical axis it supports. This is explained as the main motion seen is rotation about the elevation axis

of the entire antenna, with the frame being further from this axis.


Table
2

K
-
mirror nodal flexures




Displacement : micro
ns


Rotation : arc.sec



FEAL
oad
Case

Angle
from
Horizon

Node

x

y

z

x rot

yrot

zrot

max
spherical
displ.

1

90

205032

0.00

2.85

-
4.82

1.28

0.00

0.00

5.60

2

75

205032

-
7.05

2.75

-
4.65

1.24

0.84

-
0.95

8.88

3

60

205032

-
13.63

2.47

-
4.17

1.11

1.63

-
1.83

1
4.46

4

45

205032

-
19.27

2.01

-
3.41

0.91

2.30

-
2.58

19.67

7

45

205032

-
18.69

1.83

-
3.40

0.90

3.05

-
2.32

19.08

5

30

205032

-
23.60

1.42

-
2.41

0.64

2.82

-
3.17

23.77

6

15

205032

-
26.32

0.74

-
1.25

0.33

3.14

-
3.53

26.36

1

90

205033

0.00

1.29

-
4.82

1.28

0.00

0.00

4.99

2

75

205033

-
6.03

1.25

-
4.65

1.24

0.84

-
0.95

7.72

3

60

205033

-
11.66

1.12

-
4.17

1.11

1.61

-
1.83

12.43

4

45

205033

-
16.49

0.91

-
3.41

0.91

2.28

-
2.58

16.86

7

45

205033

-
15.00

0.74

-
3.40

0.90

3.03

-
2.32

15.40

5

30

205033

-
20.19

0.65

-
2.41

0.64

2.80

-
3.17

20.35

6

15

205033

-
22.52

0.33

-
1.25

0.33

3.12

-
3.53

22.56

1

90

4

0.00

n/a

-
0.39





2

75

4

-
0.20

n/a

-
0.38



Legend


3

60

4

-
0.38

n/a

-
0.34


Node ID

Description

4

45

4

-
0.54

n/a

-
0.28


4

Tertiary Mirror Location

7

45

4

-
0.75

n/a

-
0.25


205032

K
-
Mirror Frame

5

30

4

-
0.66

n/a

-
0.19


205033

K
-
Mirror Optical Axis

6

15

4

-
0.74

n/a

-
0.10






(c)

For flexure assessment purposes, motion of the K
-
Mirror optical axis alone is probably adequate. The
differential motion from zenit
h to 15° elevation of the K
-
Mirror optics are thus 23μm forward, 1.0 μm inboard
and 3.6 μm upwards, i.e. about 23 μm spherical. Half of this effect should be removed by fine tuning the
alignment of the K
-
Mirror optics when the antenna is tipped at 45°.

(d)

Not
e that JCMT antenna optical axis also moves, with the TMU moving by about 0.75 μm forwards and 0.25
μm downwards with respect to the elevation bearings. Although a small deflection, it should be borne in mind
that in practice a full payload of masses and i
nstruments may cause the TMU to move more than this, and in
TR/001/81/IP



17

other directions. Some of this is removed in homology
-
correcting motions of the secondary mirror, some by
pointing models and others by local
-
peak up on pointing sources. On
-
sky tests, rather than

further analysis,
would be the easiest way to quantify these effects if they are of any optical concern.




Figure
14

Displacement of K
-
Mirror optics with elevation slew angle.

Note the points loadcases 4 and 7 are both plotted
for the 45° point, giving an indication of errors due to
constraint variations.


Figure
15

Rotation of K
-
Mirror optics with elevation slew angle.

TR/001/81/IP



18


Figure
16

Displacement of K
-
Mirror frame with elevation
slew angle


Figure
17

Rotation of K
-
Mirror frame with elevation slew angle .


TR/001/81/IP



19

(e)

These errors may be compared with the PDR total specification of :



total pointing error (vector length): less than 10 arcsec



residual pointing error (
vector length) after subtraction of known error terms: less than 0.5 arc sec



the correction terms should be limited to constants plus sines and cosines of the telescope elevation and
the position of the K
-
Mirror or of combinations of these two, plus if ne
cessary similar functions involving
the temperatures inside and outside the cabin.

(f)

The predicted displacements here, of maximum value 23 μm over a 2268mm throw correspond to ~ 2
arc.seconds, which should allow an adequate remainder for the K
-
Mirror assembly's own flexure errors (though
note that these errors will be correlated and quadra
ture addition of error terms will not be appropriate).

(g)

Of greater concern is thermal expansion of the sub
-
frame tubes due to the K
-
Mirror heat loads, changes to
cabin insulation properties or conduction paths in the mount (between the tubes and the hotter
receiver cabin).

Insertion of isolation elements in the design to eliminate conductive links should be considered.

(h)

Heating effects have been modelled previously, producing approximately +/
-
2
μm of localized surface error per
1°C of tube temperature change
-

see below. Pointing errors will also occur
-

as an approximation the tubes
expand by ~ 64 μm for a 1°C change, producing yaw of magnitude 1 arc.sec. Active surface control will mitigate
bo
th these effects, but loads should be minimized if possible. A specification target of a 1°C maximum change
of the sub
-
frame tubes should be considered.



Figure
18

-

Surface deformations
1

in microns due to a 1°C rise in a sub
-
fra
me upper tube.




1

The figure is from JCMT TR/001/39 ("Technical Report No.39 FEA
-
Lookup table", Dr.F.Baas).

TR/001/81/IP



20

3

Conclusions & Recommendations


3.1.

The addition of the K
-
Mirror to the JCMT structure should provide no significant deflection problems for pointing
or surface quality.

3.2.

The likely error terms and methods of removal are noted below. Although sma
ll, the remaining effects will impact
all modes of observing for all instruments, not just HARP, so pointing model changes may need to be global
-

not
just HARP specific.


Table
3

Impact summary

Effect

Magnitude

Method of compensati
on

Surface lobes close to surface base. Minor
variations thereof with elevation angle

<1μm

kot requiredK

mointing offsets, with elev~tion dependency

(offset 縠2K1 x cos(el))

1KR ~rcKsec ~t
㐵4

oemove rem~ining effects vi~
routine "~ll
J
sky pointing"
modelsK

Therm~l lo~d induced surf~ce errors


J
2μm/°C

Therm~l isol~tion, ~ctive
surf~ce co
ntrolK

Therm~l lo~d induced pointing errors

縱 ~rcKsec/°C

Therm~l isol~tion, ~ctive
surf~ce control, loc~l pointing



3K3K

Flexure of the K
-
Mirror mounting point with respect to optical axis, will be ~ 20 μm (2 arc.sec) with an elevation
dependency. This may
be mitigated by fine
-
tuning the alignment when tipped at 45° and by modelling any
remaining terms.


3.4.

Thermal isolation of the sub
-
frame structure and the receiver cabin environments will be an important factor, and a
specification target of no more than a 1
°C change of tube temperature due to HARP K
-
Mirror heat loads should be
considered. This will impact the design work packages for the ATC mount design and the JAC cabin insulation.
TR/001/81/IP



i

4

Appendix : Dishfit results vs FEA displacements


The following data shows
surface displacements due to the K
-
Mirror loads, after removing the masking effect of elevation
tipping seen in the direct FEA data.



Figure
19

Dishfit
-

Zenith loadcase (compare to Fig 5, main body)
-

reproduced below




Repr
oduction (reduced size) of Fig.5

TR/001/81/IP



ii



Figure
20

Dishfit
-

Antenna at 75°


Figure
21

Dishfit
-

Antenna at 60°

TR/001/81/IP



iii


Figure
22

Dishfit
-

Antenna at 45° (not
-
restrained at drive axis)



Figure
23

Dishfit
-

Antenna at 45° (restrained at drive axis)


TR/001/81/IP



iv


Figure
25

Dishfit
-
Antenna at 30°


Figure
26

Dishfit
-

Antenna at 30°

TR/001/81/IP



v


5

Appendix : HARP K
-
mirror technical data


In addition to information in the HARP PDR document, the data below is of relevance to the design study


1.

Excerpts from Email with design details


From rjb@roe.ac.uk Tue Apr 18 14:14:50 2000

Date: Fri, 10 Mar 2000 13:53:08
-
0000

From: Richard Bennett <rjb@
roe.ac.uk>

To: 'Ian Pain' <i.pain@jach.hawaii.edu>

Cc: Maureen Ellis <mae@roe.ac.uk>

Subject: RE: JCMT solid model checks and telescope FEA


Hi Ian,


This is response to your email but there is an important action item from the PDR to be picked up by JAC,
FEA of
the effect of mounting the K
-
mirror on the telescope. The mass of the whole K mirror model at the moment is 120

Kg. This does not include the motor and worm assembly but it does allow quite a lot for the v
-
blocks/saddles
attaching the assembly to th
e sub
-
frame tubes. At the moment they're steel and I haven't light
-
weighted them at all.

The C of G is 250 mm above the optical axis (= elevation bearing axis). The rotating mirror assembly weighs 60 Kg
and has its C of G on the optical axis.



I have copi
ed the current HARP model to my ftp directory (ftp.roe.ac.uk/pub/rjb/). You need all the files (106 files
10Mb) in the sub
-
directory harp_proe. The model is in ProE 2000i commercial format.


I've attached a TIFF image of the model to this message.


Some

comments on the model:


I've addressed the issues arising out of the PDR (flexure, bearing arrangement, alignment on the telescope) but
some details are still a bit sketchy, in particular the mirror mounting, the motor drive and the balance

masses.


The
surface form tolerance on the mirror is quite tight: 5 microns rms, that includes manufacture and flexure due to
gravity and mounting. At the moment Zeiss seem to be the only manufacturer interested and of course their price

for the mirrors is more than th
e whole K
-
mirror project budget. The question of mounting hasn't been looked at
-

the

design will be something between simply bolting the mirror down with a 5/8" bolt in the back and UKIRT

secondary type flex pivots.



TR/001/81/IP



vi


Figure
27

Design discussion of the HARP K
-
mirror per RJB's email


For the motor drive I've assumed a worm driving a sector of a wormwheel (the green object at the inside end of the
mirror assembly).


The outer (as viewed from inside the receiver cabin) balance weigh
t is an embarrassment: it would have to be
removed to slide the K mirror along the guide rails (the removable extensions are coloured yellow in the picture)

and it might be a bit inaccessible to replace afterwards. Also it sticks up through the receiver c
abin roof. I haven't
had time to look at the effect of putting all the balance mass at the inside end. I'm sure it could be accommodated
but the mass of the trusses might increase a bit to maintain the same flexure.


I envisaged that the K mirror assy, f
rom the bearing housing (coloured pink) down, would be taken into the receiver
cabin, lifted up and turned round on a hoist on the rail extensions (yellow) and slid into position on the guide rails
(yellow).


Only one circumferential rail (shown in red in

the picture) of the receiver cabin structure absolutely needs to be
repositioned but it would ease installation and constrain the design less if the rail directly above the k
-
mirror were
to be moved too. Can that be done?


Regards


Richard


TR/001/81/IP



vii

2.


EMAIL with g
eometry details


Date: Thu, 13 Apr 2000 13:02:42 +0100

From: Richard Bennett <rjb@roe.ac.uk>

To: 'Ian Pain' <i.pain@jach.hawaii.edu>

Subject: RE: JCMT solid model checks and telescope FEA


The mass is 125Kg and the CofG is at (15,
-
2184,256) in the telescop
e co
-
ordinate system (origin at tertiary, Z
towards the secondary, Y towards SCUBA).


There is scope for reducing the weight of the saddles which mount on the JCMT sub
-
frame tubes. If these were of
ZERO mass the mass of the assembly would be 87 Kg and the
CofG would be at (0,
-
2156,95) so perhaps 105Kg and
(10,
-
2170,180) is achievable. I note that in your PDR submission you gave a guideline of 100mm offset of the CofG
from the optical axis, so we're only a factor of 3 out!


The attachment points are at y =
-
2064 and y =
-
2447 from the tertiary (intersection of the K
-
mirror truss members
and the sub
-
frame tube centrelines.


Hope this helps,


Richard