National Radio Astronomy Observatory
, Tucson, USA
Copyright 1998 Society of Photo-Optical Instrumentation Engineers. This paper was published in SPIE and is made available as an electronic reprint with permission of SPIE. Single print or electronic copies for personal use only are allowed. Systematic or multiple reproduction, or distribution to multiple locations through an electronic listserver or other electronic means, or duplication of any material in this paper for a fee or for commercial purposes is prohibited. By choosing to view or print this document, you agree to all the provisions of the copyright law protecting it.
Jingquan Cheng and Jeffrey Kingsley
National Radio Astronomy Observatory, Tucson, USA
The prospect of a joint Millimeter Array development effort between the US and Europe has led to various antenna designs. This paper describes a new 12-m antenna design that has many new features which are not widely used among existing millimeter wavelength antennas. These include: light-weight machined aluminum panels; feedlegs with triangular roofing for reflecting scattered rays to the sky; double-layered carbon-fiber reinforced plastic (CFRP) trusses on large radius supports; rotating counterweight for reducing the moment of inertia; a yoke incorporating CFRP trusses and a steel beam structure; and a displacement-measuring metrology system. A design incorporating these features could achieve a combination of high performance and reasonable overall cost. The paper also discusses in detail a number of key issues of interest for future millimeter wavelength antenna development. The design is influenced by the large number of antennas required for the Millimeter Array.
Keywords: Antenna, millimeter wavelength, radio astronomy
After a decade of preparation, the US astronomy community will formally begin the design and development (D&D) phase of the Millimeter Array (MMA) project in 1998. Although the final choice of antenna diameter and number of antennas is still under discussion, one possible option for the diameter is 12 meters, with specifications as listed in Table 1.
| Diameter | 12 meters | Elevation range |  to  |
| Surface error |  r.m.s. | Temperature range |  to  |
| Pointing error | 0.69 arc.sec r.m.s., 50 % time | Frequency range | 30 to 800 GHz |
| Phase error |  r.m.s., 50 % time | Dynamic performance | Allow rapid fast switching |
| Working condition | 6 m/sec wind, all temperatures | Close packing | 1.19 diameter |
| Site altitude | 5,000 m | Solar observation | Yes |
As can be seen from the above specifications, the high precision of the antenna surface and its phase and pointing characteristics must be maintained over a wide range of ambient conditions. The dish design also influences the counterweight, the yoke, and the base design. Important aspects of the design include: panel type, adjusters, feedlegs, truss structure and sub-dish support structure. In the present design, the whole dish is supported at four points on top of the receiver platform. This arrangement eliminates or minimizes dish distortion caused by the deformation from the receiver cabin loading. The dish structure can be seen in Figure 9.
A prime requirement of the surface panels is that their accuracy be maintained under
gravitational loading and varying environmental conditions. Lamb[8] studied
various panel types for millimeter wavelength antennas, including:
aluminum skin with
aluminum ribs epoxied on the underside (e.g., panels made by Electronic Space System Co.); aluminum honeycomb with aluminum
facings (e.g., panels of James Clerk Maxwell Telescope (JCMT)); aluminum honeycomb with CFRP facings (e.g., panels of the Heinrich Hertz Telescope); cast, machined
aluminum panels (e.g., panels of the Berkeley-Illinois-Maryland-Association
Millimeter Array antennas (BIMA)) and CFRP honeycomb with CFRP facings. Due to the poor
thermal conductivity of epoxy and CFRP material, panels involving these materials will have
serious thermal gradients under solar loading. Lamb's conclusion is that a cast machined
aluminum panel (BIMA) would be thermally good for the MMA. These panels have a
thickness of 8 mm with stiffening ribs arranged to be parallel to both sides of the panel. The
height the of ribs is about 80 mm. The panels are machined on computer numerical controlled
(CNC) machines. Independent of Lamb's study, Delannoy[6] 
[7] studied a light-weight machined aluminum panel for the Institut de Radio Astronomie Millimetrique (IRAM) 15 m
antenna resurfacing project. These panels are extremely light in weight. Their cross section is
shown in Figure 1.
The thickness of the face skin is only 2.5 mm; the honeycomb size is about 100
mm; its wall thickness is 1.5 mm and the height is about 30 mm (plus 20 mm wide top). The back of the panel is spherical to
accommodate the surface machining. The study showed
that the light-weight panels of the new IRAM surface have a gradient-induced deformation of
only 0.1 
under the sun when the center of the panel is fixed. However, if we
compare the surface with a fixed paraboloid surface, the error due to absolute temperature
difference is larger. It could be 4 for 25
C change. With these studies, the
only panels which could be chosen for the 12 m dish are either the cast BIMA style or the
light-weight machined IRAM style. These panels are equally good in surface stability. The
main differences between the BIMA and IRAM panels are listed in Table 2. In the table, panel size, surface error, and cost are more important in panel selection.
| Items | unit | BIMA panels | New IRAM panels | Notes |
| Maximum size |  | 0.55 | 1.70 | Outer ring panel size |
| Support points | 4 | 5 | ||
| Density |  | 28.0 | 14.0 | |
| Stiffness |  | 56. | 2. | Lifting a corner when it is fixed |
| Surface r.m.s error | | 8. ( Welch et al ) | 15. (
Plathner ) | |
| Cost |  | 1.8 | 3.0 |
The choice of panel type affects other aspects of the antenna design. The weight, size, and stiffness of the panels affects the backing structure design; the panel stiffness affects the adjuster design; and the overall weight of the surface affects the counterweight design and fast switching performance of the antenna. Cost is obviously an issue. The design procedure for the backing structure results from consideration of two main loadings: a) the weight of the panels and backing structure; and b) the wind loading. There are two aspects for the wind loading - maintaining specifications in normal operation and survival. Considering the performance of the structure under varying gravitational loads, the dish surface nodes must remain within a tight tolerance from a best fit paraboloid. This design procedure is not easy and needs a number of iterations. However, when the dish is under the survival wind loading, the design process is straightforward. It requires that all structural members are stressed within their elastic limits. Experience shows that for millimeter wavelength antennas, if the deformation requirements are satisfied, then survival stresses are not usually an issue. Since the deformation of a structure is a linear function of the load applied, by using lighter weight panels the absolute deformations of the truss structure will be smaller. This will lead to a quick convergence in the iteration process if the dish design uses the homologous principle. The light weight panels plus high modulus CFRP trusses also make the dish design possible by using a non-homologous approach[14]. Obviously lighter panels generally lead to a lower overall cost. Panel size is another factor in dish design. Small panels require more joints in the truss structure. These joints are complex in shape and their cost is a significant part of the whole dish cost. Small panels also affect the tube member number and length (IRAM panel has 5 support points, but the middle support point brings only one additional tube for each panel as shown in Figure 4). Small panels require more and short tubes. For CFRP tubes with steel ends, the thermal expansion coefficient will be a problem if the tubes are very short. Therefore, the larger panel size is always preferred in the dish design. Larger, light-weight panels are less stiff, but this may not be a serious issue.
An important aspect of the antenna performance is the ability to switch to a nearby calibration
source, perhaps 1.5 degrees away, within 1 second. This requirement implies a low moment
of inertia for the telescope and its counterweight. The mass of the panels combined with the
necessary contribution of the counterweight is the major component of the moment of inertia.
For this 12 m antenna, the surface area is about 125 and the center of gravity of all
panels is about 2 to 3 m above the elevation axis. A simple calculation shows that if the
panel weight is reduced by half, the counterweight required will be reduced by as much as 30
%. The moment of inertia about the elevation axis will
be reduced by as much as 40 % by reducing the panel weight 50 %. This decreases the azimuth moment of inertia which is dependent on elevation angle. Furthermore, lowering the overall antenna weight will
result in lower costs for the foundations, the transporter, and the service roads.
The panels for the proposed 12 m antenna are the same size as the IRAM panels. The properties of these panels are summarized in Table 3. There are five rings in the design. There are 16 panels in the first and second rings and 32 panels in the outer rings. The total panel number is 128. The performance is more than adequate for our requirements (Table 7). From Table 2, the most important factor in panel manufacture error is the size of the panel.
Absolute temperture load ( ) | 4.0 | | Data from Delannoy[6] |
| Solar thermal gradient load | 0.1 | | Data from Delannoy[7] |
| 6 m/s wind load at 5000 m altitude | 1.9 | | Calculated from data of Plathner[13] |
| Gravity load | 5.0 | | Data from Plathner[13] |
| Surface manufacture error |  | | Estimated number for the 12 m antennas |
| Total |  | |
The adjusters for the surface panels are a critical issue. Most millimeter wavelength antennas use adjusters which permit a differential thermal expansion between the trusses and the panels. Detailed study on the thermal problem of panels were conducted by Lamb[8]. In this design, the selected adjusters will be soft so that unexpected surface errors or stresses will be minimal and amenable to computer analysis.
By supporting the feedlegs at the edge of the dish could completely eliminate spherical wave blockage. The overall blockage and antenna ground
pickup would be minimal[11]. However, recent studies by Cheng and Mangum[5] and Lamb[10] suggest that this is not necessarily true.
Because the feedleg stiffness (in a torsional direction about dish axis) is a function of the
feedleg length, for a given stiffness the feedleg width can be smaller when their support
radius is reduced. Therefore, the minimum aperture blockage does not necessarily happen at
the feedleg edge support. The feedleg bending effect of the edge support and the support
point stiffness are other issues for which it is desirable to reduce the support radius. The
study also shows that, for the background noise pickup issue, the feedleg scattered ray
termination is not the best for the feedleg edge support if a rectangular feedleg cross-section
is assumed. The feedleg scattered ray terminations for different feedleg support radii (In the
figure, 
is the ratio between the feedleg bottom radius and the dish radius, and the feedleg
top radius at the primary focus plane is assumed as 0.125 of the dish radius.) are shown in Figure
2 and are a result of the computer ray tracing. The figure includes four
regions of curves: A) The straight parallel lines at the left bottom of the figure are direct
feedleg scattered rays of plane wave blockage. As the support radius becomes larger, the rays
may go to warm ground directly; B) The second group of curves run from top left to bottom
right. These are plane wave rays which hit the primary dish twice. This group has four curves
starting from the feedleg relative radius 
to 
; C) For , there is
a small curve which is above curves of Region B. This represents the plane wave ray which
hits the primary dish three times in total; and D) These curves are all at the top right corner
and are spherical wave rays termination. From a noise pickup point of view, the figure shows
that the situation of an edge feedleg support is worse than a number of inner radius supports.
Moreira et al., Satoh et al., and Lawrence et al.[5] have made an extensive
study on the issue of the ground spillover pickup and feedleg shaping
or baffling. There are a number of ways in reducing the ground spillover pickup for antenna
feedlegs. However, this analysis is based on diffraction theory and existing examples are
available only for a relatively low frequency range (4-50GHz). For a shorter wavelength
range, ray tracing studies and diffraction theory (Lamb[10] and
Cheng[5]) also show that by adding a triangular roof baffling on the inner side
of the feedleg, the scattering rays can be terminated on cold sky for any feedleg angle 
with the dish axis. This is true for all scattered rays. The formula for the termination angle
above the aperture plane 
is:
where 
is the half angle of the triangular roof. For a larger angle,
the required half roof angle should be small as in the 
relationship (Figure 3). For spherical wave scattering, the roofing of the
feedleg will reflect the rays outwards in radius. This makes the incident angle on the dish
approach the incident angle of a ray which would hit the same location if the feedleg were
removed. Therefore, the spherical rays will have an even higher termination angle.
The edge feedleg support may also have a poor wind pointing performance. Cheng studied the relationship between the dish pointing error and feedleg support location for an 8 m model antenna. This is a design where the four feedlegs are all supported at the edge of the dish. For a 6 m/s wind at 5000 m altitude, the various contributions to pointing error at the zenith are listed in Table 4.
| Error source | Error | Error source | Error |
| Secondary mirror translation | 0.708 arc sec | Primary mirror translation | 1.109 arc sec |
| Secondary mirror tilt | -0.180 arc sec | Primary mirror tilt | -0.854 arc sec |
| Feedhorn translation | 0.009 arc sec | TOTAL | 0.792 arc sec |
| Support location | X | Y | Z |
| Front |  0.0 | -13.5 | -11.8 |
| Back | 0.0 | 11.4 | -12.0 |
All these errors are calculated using a best fit paraboloid to the deformed dish surface. The
data show that the total dish pointing error is 0.8 arc sec for the edge feedleg support. From
the table, although there is a significant contribution from the primary mirror tilt and
translation, the net contribution of the primary mirror is very small. This is understandable since
the translation of the vertex of the dish is closely related to the tilt of the dish. The most
significant contribution is from the translation of the secondary mirror. Careful study shows
that the translation of the secondary mirror is related to the movement of the feedleg support
points. Under the wind loading, the two support points of the feedlegs along the wind
direction are significantly moved in both the wind (-z) and vertical (y) directions. The
displacements are listed in Table 5,
while the z displacement of the secondary mirror point is -19.7 for 6 m/s
wind. The number is very large. When using the same loading conditions and fixing the
feedleg support points, the resulting secondary mirror z displacement would be only -1.05
. The new secondary mirror tilt contribution is now -0.17 arc sec; a change of only
8 %. Applying the new number to Table 4, the total pointing error would be
0.14 arc sec; six times smaller than the edge support case. This example shows that the
stiffness of the edge feedleg support is inadequate, and that a better location would be at
stronger support points.
In the present design, the feedleg is at four strong points on the steel sub-dish ring structure. The support radius is about 3.9 m at the sub-dish plane. On top of the dish the support radius is about 3.4 m: 0.56 of the dish radius. The feedlegs will be sharply angled towards the dish. These feedleg support points are at the same radius as those for the dish truss support. If the feedleg support points are not in the same ring as the truss support points, the temperature difference inside the steel sub-dish ring structure will bring significant secondary mirror axial movement. By arranging the feedleg support points away from the truss support, the truss homologous design is simpler. The preliminary design of the feedleg has a cross section of 4 cm x 24 cm including the roof. The very low aperture blockage is 2 % when 11 dB tapping is applied.
Cheng[2] has studied the thermal performance of the BIMA 6 m steel dish. The
study was based on finite element analysis using the measured dish temperature data by Lamb
and Forster[9] in 1993. A TIW dish model was used in the analysis[15]. The
temperature of the dish trusses was measured with and without the BIMA fan and sun-shield
system. The analysis showed that the BIMA fan and sun-shield system is among the most
effective in existing dish temperature control systems. However, even with this cooling
system, analysis suggested significant surface errors within a
6-hour period every morning. The component of the surface r.m.s. error caused by thermal
differences within the backing structure was 18 and the component due to
temperature differences between the dish and the cabin was 14 . During the day solar
heating can produce pointing errors. The temperature measurements of the backup structure
suggest a pointing error of 0.4 arc sec rms over a 30-minute period, while the feedlegs
contribute an additional 1.4 arc sec. The steel feedleg contributes most of the pointing error in
this all-steel system. The rate of pointing change is 2.5 arc sec/hour. The steel dish also
produces phase error at a rate of 40 to 200 /hour r.m.s.. The study suggested that
even for an 8 m dish, an all-steel structure with fan and sun shield system will not be
sufficient in meeting the MMA specifications for 6 hours every morning. CFRP feedlegs will
help the pointing performance, but the problem with the surface accuracy will remain.
Moving the antennas to a high site of 5000 m above sea level exacerbates the thermal
problems as the fan cooling efficiency diminishes. The air density on site is about 54 % that at
sea level. The study suggests that CFRP material is very attractive for the dish backing
structure for millimeter wavelength antennas, especially in an outside environment. This
agrees with the prediction of Lamb[8] [9]. Measurements done on the
JCMT dish also confirmed that the thermal distortion of a steel backing structure is complex
and significant even for a well protected in-dome antenna (R.E. Hills, private
communication).
A radio telescope normally has a homologous truss structure to support the surface panels.
To achieve this homologous effect, the support ring, which is at the rear of the dish, should
be small and the dish load should be axially symmetrical. It is better to support the feedlegs
separately from the dish structure as is the case in many existing antennas. For a
multi-frequency millimeter wavelength antenna, the required size of the receiver room effects
the size of the support ring. In this case, a strong center cone structure is necessary to prevent
the surface points within the support ring from being distorted in undesirable directions when
the dish is either pointing to the horizon or to the zenith. If the feedlegs are connected to the
backing structure, the backing structure has to be thick in order to reduce the effect of bending moment on the
cone caused by the weight of the feedleg and secondary mirror mechanism. A thick backing
structure brings problems in close packing and other structural design. Also the central cone,
whether it is tall or short, is a significant cost in the dish budget if constructed from CFRP
material. To avoid these difficulties an alternative approach in the dish design is to use CFRP
plates as the basic element. This could produce a thin dish structure as the plates provide
more stiffness in the design. However, this approach has not yet been used for larger antennas
in astronomy. There are only a few companies where the structure could be
manufactured. By using this approach, there are still problems of stress concentration, cost,
competition in the bidding process, future dish maintenance, and accuracy in computer
modelling. ( Note: In finite element analysis software, it may be difficult to represent
accurately the bending displacements of a structure by using plate elements. Most plate elements are capable of
representing only linear behavior, which may not be realistic in practice.) The plate structure
of CFRP has a limiteded allowable stress under cyclical loading. The allowable stress for
steel under a 
cycles loading is 108 MPa (15.12 ksi); for CFRP tubes is 128 to 343 MPa (18 to 48 ksi); and for plate
CFRP structure is only 13 to 52 MPa (1.8 to 7.3 ksi)[3].
The requirements of the dish lead to designs with either a tall central cone or complete plated structure. Both of these are undesirable in cost and performance. An alternative is to support the dish at a much larger ring (the support ring is equal to or larger than half of the dish diameter) as used in the Bonn 100 m, JCMT 15 m, or SMT 10 m dishes. (Strictly speaking the Bonn 100 m and JCMT 15 m dishes are supported at two on-axis points: one in front and the other behind.) In 1997 Plathner[14] proposed a dish design of this type for a 15 m antenna. Anderson[1] and Cheng[4] have shown that light-weight panels plus CFRP double-layer trusses supported at a larger radius will produce a more cost-effective design. By moving the support radius from the center outwards, the dish backup structure design is now a deflection-driven rather than homologous approach, and obviously lighter panels will ease the design problem. For the present design, the truss is supported by 16 equal softness points which are on a ring of about 7.8 m in diameter (0.66 of dish diameter). This is near the optimum support diameter. By using 16 points instead of 6 points in the dish support, the surface error will be reduced for a given backing structure. Figure 4 shows the truss structure. It is very simple compared to a design using smaller panels. The tube numbers of one sector are: 18 on top, 15 on bottom, and 43 in between. The total number of beams in the backing structure is 1216. In the truss design, the lower inner part is below the truss supporting plane (shown in the Figure 9). The truss stiffness is improved without lifting up the dish structure.
The preliminary design criteria are fairly simple. Firstly, the structure must meet the survival
wind condition. All the members have to be under the safe stress limit for CFRP tubes.
Taking the survival wind speed at 65 m/s, resulting in a pressure of 
, trusses
of 600 kg CFRP material will survive if CFRP tubes are used at the strength limit of
1.2x
. However, this is insufficient to meet the surface r.m.s. requirement of
8 to 10 . Calculations indicate that 2200 kg CFRP material has to be used if the
modulus is 1.2x
and the panel density is 
. Although CFRP material has a
very low thermal coefficient, thermal problems may arise when the member length is short
relative to the steel end plus joint. With the larger panels in this design, the CFRP tubes are
relatively long, resulting in low overall thermal errors.
The purpose of the steel sub-dish ring is to provide 16 equal softness points for the dish truss support and 4 strong points for the feedleg support. All these points are on the same ring with a diameter of 7.8 m. The sub-dish ring then transfers the dish loads to the four points above the receiver platform. The sub-dish ring also provides additional torsional stiffness to the dish trusses. The sub-dish ring is shown in Figure 5. The design is a compromise between the best dish performance and the consideration of a spacious and easy-to-access receiver cabin. From the dish performance point of view, this steel sub-dish ring is not as good as the JCMT inverted conical truss design. The steel sub dish would bring some errors in pointing. However, it allows a larger and accessible cabin space under the ring and it is easy to connect the dish to the elevation axis. These are both difficult for the JCMT-type structure. The design idea of this ring is to provide equal softness support points. Starting from the 4 hard points which are connected with the four corners of the receiver platform (shown as circles in Figure 5), the ring provides 16 equal-softness points at the outer ring radius. The structure uses all straight plate members as the load bearing components. The feedleg support points are directly extended from the 4 hard points at 45-degree angles. There is no connection between the feedleg support and the dish support at the outer ring radius. Joints between the sub-dish ring and the truss structure are designed to take the thermal expansion differences between CFRP and steel.
The most important consideration in the sub-dish ring design is to keep all the support points
at the same diameter. In this way, any radial or axial temperature gradients within the
sub-dish will not affect the dish surface error, the pointing error, or the distance between the
primary and the secondary mirrors. These linear temperature gradients are the dominant form
for this ring-shaped structure. However, there is a special gradient which will affect the
pointing error of the dish. This gradient is from one side of the diameter to the other. The
estimated effect is about 0.2 arcsec per C temperature difference. This temperature
pattern is rare for this ring structure, and the effect is a slow one which could be cancelled by
pointing calibration. Displacement sensors are provided to monitor this pointing effect. The
details of these sensors will be discussed in a later section. Insulation and fans can help in
reducing the thermal gradient effect. Since the ring structure is flat in shape, the phase error
due to temperature change is small. The sensors would also correct this phase error.
The purposes of the elevation structure in this design are: to provide four support points for the dish structure; to provide a strong platform for the receiver and instruments; to balance the dish weight; and to provide drive and angle measurements. Featured in this part of the design are: four points of dish support over the elevation platform; open receiver space (or simple removable receiver cabin) for receiver and instruments; rotating counterweight inside the yoke; and side drive systems from both elevation axes.
Under the dish there is a strong receiver platform extended to two elevation axes. The
platform itself is a double layer steel-box structure with a square outer shape and a circular
interior hole (Figure 6). The dimensions of the square are 3.6 m x 3.6 m. The circular hole for the
receiver is stiffened by a conical shell above the platform. This shell ensures the stiffness of
the receiver platform. In both elevation axes sides, the platform is stiffened by the couterweight
plates. In the other direction, short stiff ribs are located as in
Figure 6. Between the counterweight plates and stiffening ribs, the platform
provides a space of 3 m x 3 m x 2 m. In the center, the height could be 2.5 m for equipment and a cabin. The counterweight plates on
both sides of the platform will hold a mechanism for moving the counterweights. This will
be addressed in a later section. Outside of the counterweight plates, drive wheels (each is a half wheel) are
arranged. Above this receiver platform, four points are used to support the dish structure. This
is a point contact support system. It would reduce the effect of the platform distortion on the
dish structure. The antennas will be required to support a wide range of frequencies resulting
in appreciable weight of the receiving equipment . This loading may result in
distortions of hundreds of s. The penetration of these deformations on the dish would
significantly affect the surface accuracy.
A receiver cabin needs to be integrated into the design. One extreme idea is to support the dish from the four corners of the cabin through a number of plates inward to a ring not much smaller than the cabin size. To enable movements of equipment in or out, a door is required on one side. Using a bull gear, opposite the door, the cabin wall remains. It is also stiffened by the bull gear. This arrangement is asymmetrical. Analysis shows that this cabin and its dish supporting points do not have any symmetry about the elevation axis even when the dish is at zenith pointing. The plate thickness has to be optimized to assure the dish bottom deforms evenly on its support. However, using this asymmetrical cabin for dish support, the dish load may not distribute evenly over all support points as designers hope. Soft points will take less load, while hard points will take more. Distortions of the dish are difficult to avoid. And for this asymmetrical structure, any additional loading inside the cabin will bring additional asymmetrical deformations over the dish support points. These may penetrate the dish and will appear in its surface. Some existing radio telescopes using an asymmetric cabin support show serious dish surface distortion, even though the dish and support ring are both stiff (TIW[15]).
In the present design, an open cabin space is provided. This would require that the receiver packages be developed as a limited number of self protected modules. The only work needed at the site would involve module replacement. All repair work would be performed in a lab at a lower altitude. By removing the cabin altogether, the wind-dragging, thermal-inertia related problems and modules assembly or disassembly would be simplified.
The elevation axes of all existing large antennas lie below the center of gravity of the dish
itself, except for the very early Jodrell Bank design. For balancing the structure, a
counterweight is necessary. For a 12 m antenna, the panels weigh about 1.75 tonnes using the
14 kg/ light-weight panels; the trusses weigh between 3 to 5 tonnes; and the sub-dish
weighs 4 tonnes. The counterweight required ranges from 3 to 5 tonnes depending upon the
distance between the counterweight and the elevation axis. This is much greater than the weight
of the receiver equipment and the protective cabin combined. Replacing the
counterweight with a heavier cabin is less effective in terms of materials and cost. The material used for the cabin stiffness should be on top of the cabin but it does very little in counter-balancing the structure. In an
MMA memo, Cheng[4] suggests putting the counterweight far behind the
elevation axis. However, for a fixed product of mass and distance, the moment of inertia
produced is a linear function of the distance. To save the counterweight mass in balancing the antenna will increase the moment of inertia of the structure. This is contrary to the fast
switching requirement of this design. The fast switching requirement is one of the most challenging in this design. By moving the antenna from one object to a nearby calibrator(1.5 degrees away) within 1 second, the antenna should have an acceleration larger than 10 degrees/
; a few times greater than that for existing antennas. To achieve this, it is necessary to minimize the structural moment of inertia and avoid structural vibration. The rotating counterweight design is for the minimization of the moment to avoid structual vibration. Higher structural frequency, optimized switching routine, and structural damping may be necessary. This is a field needing further study.
In the present design, a new rotating counterweight arrangement is proposed as shown in Figure 7. The mechanisms are located at both inner sides of the yoke structure. Each mechanism involves a quarter gear which is fixed on the yoke and a floating counterweight gear on the counterweight plate. The required ratio between the fixed gear and the counterweight gears is 2:1. The counterweight is connected to the counterweight gear and will rotate inside a circular rail on the counterweight plate as the antenna elevation angle changes. When the antenna is pointing at zenith, the counterweight is located at the top of the platform (shown left, Figure 7). As the zenith angle increases, the counterweight will have an angle twice that of the zenith angle from the dish axial plane. The system will remain balanced about the elevation axis in the vertical direction. The mechanism is easy to design. The counterweight position is at a zenith angle of 45 degrees (shown right, Figure 7). The counterweight is perpendicular to the dish axis as the counterweight gear rotates twice the angle that the dish rotates. The fixed gears bear no loading at all and they are well guided by the counterweight plates when the dish moves. The guiding mechanisms are not shown in the Figures.
If the dish has a mass of 
and the distance from its center of gravity
to axis is 
, we assume the counterweight mass to be 
and the
rotating radius to be 
. The equation of the first order moments about the axis in
the vertical direction will be zero as:
The second order moment of inertia about the elevation axis, I, is:
From this equation, Figure 8 shows the moment of inertia as a
function of the dish zenith angle. The moment of inertia about the elevation axis is equal to
the moment of inertia of the dish only for zenith pointing, which is one third of the maximum
number. The maximal moments of inertia happen in the horizon pointing. Even for zenith
angle at 60 degrees, the moment is still one third smaller than its maximum. The drive
torque T required is a product of acceleration 
and the moment of inertia
I. The fast switching rate could be greatly increased for a fixed drive torque when the
antenna is near the zenith direction. When the source is near to the horizon, the atmosphere
will change rapidly in the direction of elevation. The desirable fast switching direction will be
in the azimuth direction rather than in the elevation direction. By fixing the fast switching
rate, the drive torque required at the elevation axis could be reduced as well by introducing
this rotating counterweight device. In summary, the advantages of using the rotating
counterweight are: a) the moment of inertia
could be reduced for most observing directions; b) the structure frequency could increase
for most of the observing directions; and c) the switching rate could be improved near the zenith. However, as the counterweight location is inside the
yoke structure, the counterweight rotating radius is limited. One alternative is moving the
rotating center down and making the rotating arm stronger. When the antenna is at horizon
pointing, the counterweight will be out of the counterweight plate. Or we could use a
combination of the fixed and the rotated counterweight arrangemet. The rotating counterweight is a new idea in this design driven by the fast switching requirement. The detailed arrangement and mechanism is very important to ensure the performance of the moving counterweight part. This idea may be incorporated with a fixed counterweight design in the beginning to achieve the best performance.
Most large antennas today use a bull gear drive but recently many optical telescopes and smaller radio telescopes have been built using a friction wheel drive in which the gear cutting cost is eliminated, and the drive performance remains the same or better. However, for small antennas, where a large Cassegrain receiver cabin space is required, the drive wheel will seriously block the entrance to the cabin area. To overcome the bull wheel problem, some antennas use a single screw-nut drive for the elevation structure. For a well-balanced structure, using a screw-nut drive is feasible. However, the drive system should be in the center of the yoke structure to compensate for wind moment on the dish thereby blocking space needed for the receiver cabin. For this reason, a side-drive system would be a better choice. The side-drive system involves two sets of drive motors from both sides of the elevation axes as shown in Figure 6. The system shown is a wheel-type one. However, screw-nuts or direct torque motors may be alternatives. The wheel-type side-drive system requires space for the drive system. Using the direct torque motor drive resolves the space problem. However, direct drive requires larger torque. This is a field which needs further study. The screw-nut drive has the same advantage as the direct motor drive.
The elevation encoder suggested for this design should have an accuracy of 23 bits and have a resolution better than 24 bits. The encoder will be fixed on top of the yoke structure. To fully utilize the encoder accuracy, two points are important: a) avoiding any bending or compressing loads on the encoder shaft and b) to shorten in torsional stiffness the connection between the encoder and the structure to be measured.
The proposed yoke structure involves four parts: CFRP truss structures for both sides; a steel beam structure over the azimuth bearing; steel protective covers on top of the CFRP structure; and a reference platform under the steel beam structure. The steel cover parts, together with the elevation bearings, are fixed on top of the CFRP truss and the bottom of the covers is connected to the horizontal beam by expansion joints. Since the CFRP truss structures are supported from the bottom of the beam structure, there is no thermal problem in the vertical direction which may affect the pointing and phase. The reference platform under the beam structure is supported from the same azimuth bearing. The reference platform is used for the yoke deformation measurement. The reference platform itself is also monitored by three displacement sensors from the outer ring of the base to correct the wobbling of the azimuth bearing. The yoke provides basic stiffness for pointing and phase accuracy. The measurements of the sensor system will be used for further improvement of the structure phase and pointing accuracy.
The base part of the antenna is under the azimuth bearing. This cylindrical structure is mounted directly on top of the foundation. Inside the base structure is the cable wrap mechanism. A unique feature of this design involves three displacement measuring devices near the support screws for measuring the wobbling of the azimuth bearing.
A steel yoke structure can introduce serious pointing problems due to thermal effects. Cheng[2] studied this problem in 1995 by analysing a typical millimeter-wave antenna yoke structure using the parameters given in Table 6.
| Maximum solar loading | 1260 |  | Upper limit |
| Absorption of shiny sunshade | 0.04 | Lower limit including foam effect | |
| Radiation factor to steel yoke | 0.5 | Another reduction | |
| Structure wall thickness | 0.025 |  | very heavy thick wall structure |
| Steel density and specific heat | 7800 |  | |
| Specific heat of steel | 418 |  | |
| Area factor | 3.0 | Heated steel area over area under the sun | |
| Conduction loss factor | 0.5 | For long time period only |
The study calculates the heat required for a 1 C temperature increase
per yoke plate and the heat transferred to the plate from the sun. The calculation also takes
care of the heating of nearby plates and the conduction loss once the temperature difference
builds up. If the yoke height is 3 m and its width is 0.4 m, the maximum pointing error due to
heating one side of the yoke arm will be about 8 arc sec (about 3 arc sec r.m.s.) in 2.73
hours. The short time pointing error is calculated by ignoring the conduction loss factor. The
pointing error is as large as 2.6 arc sec (that is 0.9 arc sec r.m.s.) for every 30-minute time
period. This result is calculated for a yoke wall thickness of 0.025 m (1 inch thick). If the
wall thickness is reduced, the pointing error will be larger. As a result, the yoke or alidade
design for a millimeter antenna is critical.
Based on the above thermal calculations, the proposed yoke structure applies CFRP trusses in the vertical direction. The CFRP trusses and the horizontal beam will carry all the load of the antenna. The steel cover is a protective component. The reference platform under the horizontal beam is a calibrating part. The horizontal beam is a double-layered steel box supported on the azimuth bearing. On the front and rear sides of the beam, there are lifting hooks for the antenna transportation. The stiffness of this beam determines the lowest number of structure natural frequency. On both sides of the beam, the CFRP trusses are set to carry the elevation axis. They are also load bearing structures. They are supported from the bottom of the beam structure. The trusses on each side include two A-frames with connecting members between them. The trusses support the encoder and bearing systems through the steel cover structures. The cover structure is made of thin steel plate. The bottom of the cover structure is connected to the horizontal beam by expansion joints. The cover structure supports only part of the antenna loading. It provides a platform for the fixed gears of the counterweight, the motor support when the wheel type drive is adapted, and for the brake system if a direct drive is used. However, the main purpose of the cover structure is to protect the CFRP trusses inside. The CFRP material has to be protected from UV radiation. The cover also provides protection from possible collision loads with equipment during installation and maintenance service. The reference platform under the beam structure is supported from the same azimuth bearing, but there are no other connections with the load bearing beam. The reference platform is used for yoke displacement measuring purposes. The reference platform is also covered by protective skins (details described in later section). The target of the yoke design is to achieve a pointing error of 0.6 to 0.8 arc sec r.m.s.. Further improvement can be made using the data recorded by the sensor system.
The base part is a cylinder with thick steel plate walls supporting the azimuth bearing and providing room for cable wrapping. The base has a ring of screws connecting the structure to the foundation. Three of them are main support screws. Near these screws, there are three vertical calibration bars which extend from the bottom of the base to near the top of the calibration platform of the yoke. The calibration invar bars will not touch the inner part of the platform. The gaps between bars and the inner part of the platform are measured by laser displacement devices. The information will indicate the wobbling of the azimuth bearings relative to the foundation. One important point in the base design is the position of the screws connecting to the foundation. If the base is supported by screws away from the cylinder base body, as used in some existing antennas, the cantilever beam effect will significantly reduce the natural frequencies in both elevation and azimuth directions (Wright [18]).
The distinctive feature of this design is to minimize the thermal problem by using lower expansion CFRP material from top to bottom. The feedlegs, the dish trusses, and the vertical parts of the yoke are all CFRP. There are components which are not made of CFRP material between these parts. These components are monitored by the sensor system of the antenna. There are two groups of sensor systems in the proposed design. One is a quadrant detector for monitoring the relative displacement of the secondary mirror to the primary dish and a group of four displacement capacitance sensors on top of the invar bars to measure the absolute thickness variation in the steel sub-ring structure. The second group of sensors includes: azimuth bearing tilt sensors between the foundation and the reference platform and the yoke deformation measuring system between the reference platform and the CFRP yoke truss structure.
The quadrant detector has proven to be effective in practice. By using the quadrant detector
on the dish, the thermal and wind pointing errors caused by secondary mirror lateral
movement could be corrected. The accuracy of the quadrant detector is about 10 (Payne[12]). This is equivalent to 0.1 arc sec r.m.s. in pointing error. Another pointing
error is caused by the distortion of the steel sub-dish ring. The top surface of the sub-dish
ring may have an angle with its bottom surface when the temperature of one side is different
from the other. By using the four displacement sensors at the sub-dish ring support points,
this error can be compensated for.
The second set of sensors is more important in the 12 m antenna design. This set of sensors plus CFRP truss structures will provide nearly all the information of the shape change from elevation axis downwards. Starting from the foundation, the system includes three laser displacement measuring devices which measure the tilt and distance change of the azimuth bearing. This eliminates the structure expansion-induced dimensional change of the base. It will also correct all the deformations over the bearing surface, including the bearing runout and the wind- or thermal-induced bearing deformations. The other set of the measuring devices include two CCD systems and a number of displacement sensors. The CCD systems are located on the bottom of the horizontal beam. Each is at the center line of the CFRP truss structure and will provide most of the information regarding the yoke tilts and lateral displacements. Another alternative of these CCD systems is using lasers to monitor the elevation bearing supports directly. The displacement sensors on CFRP truss bottom ends will provide redundant information of the local deformation of the yoke beam. Together these will provide accurate information on yoke deformation and will be used for correcting the pointing and phase errors up to elevation axis.
| Performance items | Error sources | Error before | Error after | Notes | ||
| calibration | calibration | |||||
| Surface r.m.s. error | panel part | 15.52 | | Ref. Table 3 | ||
| dish gravity | 8. | | ||||
| dish thermal | 0.2 | | ||||
| secondary | 5. | | ||||
| homology | 10. | | ||||
| TOTAL | 20.73 | | 20.73 | | ||
| Pointing r.m.s. error | wind on dish | 0.2 | arc sec | 0.1 | arc sec | 6 m/s |
| thermal on dish | 0.4 | arc sec | 0.2 | arc sec | ||
| wind on yoke | 0.6-0.8 | arc sec | 0.2 | arc sec | 6 m/s | |
| thermal on yoke | 0.4 | arc sec | 0.2 | arc sec | ||
| bearing | 0.3 | arc sec | 0.2 | arc sec | ||
| TOTAL | 0.9 | arc sc | 0.45 | arc sec | ||
| Phase r.m.s. error | thermal | 25. | | 5. |
|  |
| wind | 22. | | 5. | | 6 m/s | |
| TOTAL | 33.3. | | 7.1 | |
| Items | Quantity | Cost/unit | Cost(k$) | Items | Quantity | Cost/unit | Cost(k$) |
| Panels | 120. | 3.0 | 360. | Adjusters | 600. | 0.02 | 12 |
| CFRP truss | 2200. kg | 0.2 | 440. | Feedleg | 4 | 25. | 100. |
| Secondary | 1 | 130. | Sub-dish | 3000. kg | 0.006 | 18. | |
| Elev platform | 3000. kg | 0.006 | 18. | Yoke(steel) | 2000. kg | 0.006 | 12. |
| Yoke(CFRP) | 700. kg | 0.2 | 14. | Base | 8000. kg | 0.006 | 48. |
| Bearings | 35. | Encoders | 2 | 17. | 34. | ||
| Metrology | 50. | Cabling | 30. | ||||
| Assembly | 250. | TOTAL | 1,551. |
The 12 m antenna structure is shown in Figure 10. This design is not finalized yet, but a good estimation of its performance is possible as shown in Table 7. The table includes numbers of the three most important parameters of the antenna performance. These are the surface error, pointing error, and phase error either before or after calibration.
The cost of the design is estimated in Table 8. The costs of the transporter and foundation are not included. When producing a cost budget, we have to keep in mind that all antenna components are closely related. A change of one component may affect other components. A cost saving in one component may increase costs elsewhere.
Jennifer Neighbours has helped in English editing.
T effects through aluminum
panels, W.R.213, IRAM, France, 1992.
