USSKA Antenna Development - Cornell...

Status Report

USSKA Antenna Development

Conducted for CALIFORNIA INSTITUTE OF

TECHNOLOGYPO# 67L-1065091

[email protected] Alamo, California USA Tel: 925 820 2151

SCHULTZ ASSOCIATES USSKA antenna development Status as of 6-30-05 Page 2 of 23

Figure 1 Allan Telescope Array 6.1 meter antenna

ANTENNA OVERVIEW

Most of the effort on this contract has been devoted to the design of the USSKA reflector. It will bediscussed first, then the pedestal and a cost estimate will be presented.

REFLECTOR

Work on the USSKA reflectordevelopment started after initial phases ofthe 12 meter JPL deep spacecommunications array development andefforts by developers of the ATA radiotelescope.

The Allen Telescope Array (ATA) hasfielded a radio telescope array made of onepiece reflector shells that are made byhydroforming. See Fig. 1. The shell hasbeen found to be structurally very rigidand effective when it is utilized as astructural part of the reflector. This has seta cost per square meter of aperturemilestone at $1,500. It operates initiallyup to 11 GHz. Structurally it is supportedby rim spars and center diaphragm thatconnect it to a gimbal structure.

Some work was done on a 12 meterhydroformed reflector design during theDSNAA task but it faded whenprogrammatic development stopped at thepoint of generating the funding for a 12 meter hydroforming facility and when it began to doubt itsability to achieve the required performance in view of thermal distortion issues. It will be shown bythe USSKA work done to date that there are designs available which produce the required accuracyAND the economies already demonstrated for large shell reflectors.

USSKA reflector development began by adjusting the F/D from 0.35 to the shallower dish at 0.5 for12 meters to accommodate the prime focus feed angle. Also, the requirements were found to bedivergent in that the availability rates for radio astronomy are significantly less than for deep spacecommunications. For example, accurate operation for the DSNAA is being specified up to 30 MPHwind but only 15 MPH for SKA yielding a 4 times lesser load for SKA deflection consideration.


Figure 2 JPL breadboard 6 meter antenna

Figure 3 USSKA strawman 12-16 meterantenna

The first USSKA reflector effort was directedto intuitively designing a “strawman”reflector for the purpose of demonstratingfeasibility for early SKA planning. This wasin no way to be confused with an optimizeddesign. That will come when appropriatefunding and schedule arrives.

The 12 meter strawman is scaled up from 6meter concepts. See Fig 2. However thereare difficulties that arise from only scalingthe design concept upward. These difficultiesand a first solution are enumerated as follows. Spar lengths become structurallyunmanageable from the perspective of lengthover radius of gyration, the measure ofcolumn stability (Euler).

ATA and the JPL breadboard antennas had all therim supporting spars terminated in two work pointsbehind the reflector which straddled the mount.These points were so far behind the reflector suchthat opposite pairs of spars generally made a rightangle between each other at these rear work points.The 12 meter reflector could not be shipped downhighways in most parts of the world as the 6 metercould.

The strawman utilizes a design that can alleviate allof the above problems. See Fig, 3. Spars arereplaced by radial truss structures emanating froma center hub with manageable span lengths. Theseradial truss are integrated into the shell in the sensethat the truss members closest to the reflector shellare formed and stabilized partly by that shell. Thereflector is split for shipping at least along a planethru the RF axis and the center plane transverse tothe elevation axis. With this split and the radialtruss depth set as it is, one half of a 12 meterreflector can go down the highway thruunderpasses with a permit in many parts of theworld. See Fig 4, next page . It remains to be seenhow much disassembly of the back structure can be


Figure 4 Half of the 12 meter reflector on a truck going thru a 15'underpass

achieved for volume reductionfor reflector shipping whileachieving fast, simple, noalignment assembly at theinstallation sight. On the onehand, reflector halves wherethe full reflector frame isfactory assembled to preservethe reflector shape, will belittle affected by a simple onplane split. On the other,stacks of reflector halvescould be stacked on a flatbedtruck, as they are for the ATA,with the back structuredisassembled. There will bemore loss of factory surfaceaccuracy with disassembly tothis degree but design andtesting may show this to bethe better economic solutionwhile providing the requiredsurface accuracy. If it is foundthat the reflector half needs to be shipped in one piece, it will go thru underpasses.

The outer 2 meters of mesh that complete the 16 meter dish (F/D = 0.375) will be disassembled inpie panel segments that can be stacked for shipment. Their assembled condition requires far lessaccuracy but need to be implemented so as not to significantly degrade the inner 12 meter highfrequency dish.

STRAWMAN DETAIL DESCRIPTION, inc. fabrication methods, tooling

-central 12 meter shell

The high frequency, high surface accuracy, 12 meter center part of the reflector is formed by a 12meter hydoroformed shell with the same design as for the 6 meter symmetric and offset with theusual outer ring beam formed by the hydroforming cone section and flat flange which is closed intoa beam by a flat section being intermittent welded to the hydroformed rim. This ring beam is bothrigid for bending and torsion and makes an excellent mounting for the 2 meter mesh extension,forming the 16 meter low frequency aperture.Reflector shell and all back structure is 3 mm thick except a few plates that are thicker at the


Figure 5 Zig-Zag dish split proprietary to Anderson Mfg.

connection to the three point pedestal connection details.

All vendors that inelastically form reflector shells use aluminum, for example 3003 alloy.

From a structural performance standpoint this center section could be made by hydroforming asingle sheet or by joining stretch formed pie shaped pieces. It remains to be seen which method willprevail from a cost standpoint.

-back frame structure

Six radial trusses were chosen to support the outer ring of the 12 meter solid dish. This is divisibleby three to allow connection to a tripod and divisible by two to provide side to side symmetry. Ifmore ribs were indicated by poor performance, 12 ribs or 6 intervening lesser rib structures couldbe considered. At this point no such need is anticipated.

The back frame structure was chosen with relatively deep per portion compared to many antennasto increase the accuracy of the surface. In addition to rigidifying the radial trusses, the longerseparation -front to back- causes there to be less large scale surface distortion caused by thedifferential thermal growth from sun to shade members by diluting the thermal differential distortionover a longer base line.

These free standing frame members are formed by aluminum square tubes to keep Euler stability,aluminum to match reflector shell growth as the average ambient temperature varies over the widerange of operating temperatures. Casting of joint details will be investigated in future work to findthe most economical method for fabrication of this framework.

-dish splitting

There are two dish splittingdetails and methods beingstudied. For the Z cutmethod two curved strips ofsheet metal are clampedradially over the cutlocation. A radial row ofholes is carefully drilledthru both the dish shell andthe strips. Then a zig-zagcut pattern parts the dish intwo equal parts. The zig-zagis arranged so every otherhole remains a part of onedish half. See Fig 5.


Figure 6 Double C section splitting method, proprietary to SCHULTZASSOCIATES

Reassembly is achieved by forcing shallowly tapered shank special bolts thru the holes in the splicestrips and the dish. The shank of these tapered bolts bring the two halves of the dish back veryclosely to where they were before the cut.

For the Double Csection method,again the splicingdetail is attached tothe dish shell beforeit is cut to preservesurface accuracy.See Fig 6. Theflanges are alignedby roll pins and/orbolt shank details toalign the shellh a l v e s i n t h edirection normal tot h e r e f l e c t i v esurface.

T h e a s s e m b l yprocess sequence is that two curved C channels which are doweled to each other are placed in thesame radial cut area and bonded to the doubly curved parabolic shell with iron oxide filled adhesivewhich fills the small gap between the flat flanges of the pair of C section members and the doublycurved dish shell.

Then the two shells are cut from the reflective side. Reassembly is accomplished by aligning thedowel holes as the thru bolts pull the flanges together.

There are two advantages to the double C section method. First, this method does not depend somuch on realignment of the shells by “peg in a hole” but by bolts pulling two flanges together. Pegsin holes tend to lose alignment due to Hertzian deflection and metal loss if bolts need to be forcedinto place to align shell edges as they were before splitting. This force will be needed when theedges relax away from the cut plane which will happen when the cut relieves the locked-in stressin the hydroformed shell. More degradation occurs if a second disassembly after the firstreassembly occurs.


Figure 7 Hat sections on pie panel

Figure 8 Support holds Gregorian sub reflector and swinging prime focus feed

Second, The double C section provides the beam sectionto form the truss member near the reflector.It is not immediately clear how to adapt the zig-zagmethod to provide this section property.

Curved radial truss members formed by the shell and areaenclosing sheet metal are either “hat sections” (See Fig 7)such as used for decades to rigidify pie panels or I sectionformed by back to back C sections used for the double Csection splitting method.

-center hub

The center hub is proportioned to connect the dish,Gregorian feed support structure and radial trusses to athree point attachment to the pedestals. A combination of


end castings and tubular formed sheet metal may prove to be economical for cost effective highvolume manufacturing.

-sub reflector support

Rectangular tubes minimize RF blockage while rigidifying the support of the sub reflector. See Fig8. Their deflection and impact on the gain and pointing error have not yet been studied.

-assembly

For decades dish antennas have been made up of many pie panels which were supported by acomplex back structure. The detail of the cost and complexity of this method, and economies to berealized by new methods, are detailed in my Experimental Astronomy article entitled “RadioAstronomy Antennas By the Thousands”.

The crux of the issue is whether at one extreme the antenna arrives at the site as hundred of partsneeding complex, labor-intensive alignment and careful assembly or whether a few parts arrive thatare simply bolted together and “plugged in”. USSKA designs are heavily directed to the latter,maybe at the expense of shipping volume costs. Bottom line costs will not be known until detailedcost/procedural shipping and assembly analysis, combined with the manufactured antenna cost,arrive at a minimum.

Again the ATA people are leading the way to low cost, high volume array antennas. They ship fewcomponents and carefully generate assembly procedures that involve little alignment and utilize sitehanding equipment to put a few big, already accurate, pieces together. We will do the same for theUSSKA.


Figure 9 Gravity deflection looking at the horizon

ANALYSIS

The intuitive reflector design was modeled in Solid Works in shell representation such that it wouldbe immediately available for analysis in Cosmos Works which operates in the same window as SolidWorks with a database common to modeling and FEA analysis. (Both companies are owned byDassault Systems)

Since Cosmos Works will only process all solid or all shell elements, only shells are practical sincesolid elements of thin objects like hydroformed reflectors are too numerous to be represented bysolids at appropriate aspect ratios. The views of the antenna shown above are of that shell model.

Cosmos calculates stress directly. For RMS deflection, individual mesh node deflections arecalculated by Cosmos Works, reflective surfaces are selected and initial coordinates and deflectionsare listed for those surfaces. The listings are reformatted for entry in a Levy formulation best fitroutine provided by Bill Imbriale, JPL Pasadena. This routine reports fitted and unfitted RMS anda listing of z errors after fitting. These residual errors are mapped by color error topography plotsgenerated by MathCAD seen below.

First deflection due to gravity were calculated for a dish looking at the horizon.

GRAVITY RESULTS

Fig 9 shows deflection. Topand bottom of dish droop down.Best fit error was calculated as0.0023" RMS. This error issmall compared to therequirements.

More complex calculationswhich yield an optimized“rigging angle” and associatedsurface corrections could beconsidered if needed in a latermore detailed design andanalysis effort


Radial delta Cp profile 15-165 deg. radial cut+R/d=15 deg. Down wind; -R/d=165 deg. Up wind

-2

-1.5

-1

-0.5

0

0.5

1

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

R/D

delta

Cp

solidrim porous3/4 solid dish75% porous rim

Figure 10 Extrapolation of surface differential coefficients for75% porosity in the outer 25% of dish radius

Second deflections due to windwere calculated for an orientationexpected to cause the most severewind deflection. That wind is whenthe look angle is at the horizon anda 15 MPH wind is applied 120o offthe antenna pointing.

Since there are no surface pressurecoefficients available for dishes with75% porosity in the outer 25% ofthe dish, coefficients wereextrapolated from data for smaller(12 meter) solid dishes, dishes with25% porosity in the outer 25% (16meter) and larger full size soliddishes tabulated in JPL CP-4. Thissequence brackets porosity fromzero to 100%. Fig 10 shows oneexample of the extrapolationp r o c e s s .


Figure 11 Iso pressure map superimposed on the CosmosWorks shells used to assign pressure toreflector face

Existing surface pressure coefficients are available for three radial locations across the dish face.Extrapolation plots were made for the other two orientations like Fig 10. Pressures were thenmapped to the facets of the 12-16 meter model by first using MathCAD to produce an iso pressureplot based on the extrapolated pressure tap locations, then superimposing that iso pressuretopography on the projection of the reflector facets. See Fig. 11. The center of each facet waslocated in this plot and an average pressure for that facet interpolated between the iso pressure lines.


Figure 12 15 MPH worst case surface error after best fit in inches

Figure 13 15 MPH deflection exaggerated

This pressure was thenapplied to the CosmosWorks model to apply theloading of 15 MPH windacross the dish at alpha =120o

The above extrapolationprocess is tenuous but theonly approach available.Clearly wind torque datamust be taken from aprototype antenna beforemany antennas are builtusing analysis based onsuch a poorly definedbasis.

WIND RESULTS

Result of this analysis arepictured in Fig 12 and Fig13. The best fit surfaceerror is 0.0018" RMS. Thereflector best fit pointingerror is 0.005o. Thisconsumes the whole

allowable specified error sothe structure will need to bei m p r o v e d o r s o m ecompensa t ion s t ra tegyemployed. This issue shouldbe resolved in the context ofthe analysis of the entireantenna including foundationand pedestal that are notdesigned at this point.

Third deflection due tothermal gradients werecalculated. Several challenges


arise when producing this analysis. First, assessment of realistic convective heat loss to the air inreal wind spectra. Second, acquiring solar heating weighted reflectance and IR re radiationemissivity. Third, grooming of the model to apply meaningful heat transfer parameters representingall significant elements of convection and radiation. Fourth, assessment of the solar heatingincidence on a statistical basis at all the geographic locations as yet unpicked and surveyed. Fifth,resolving the sun’s heating to the myriad surfaces of the model

Dynamic thermal analysis in time-varying environment is not provided in CosmosWorks. A steadystate analysis was utilized to assess the temperature distribution in the reflector. Convective heat transfer coefficients were first conservatively taken from text books listingformulation for dead calm air. Resulting temperature distributions contained differentials betweenthe hottest and coolest parts of the model were much higher than observed over many days in thetemperature survey “Thermal Behavior of the Leighton 10 meter Backup Structure” conducted byLamb and Woody and reported in NRAO / ALMA web site MMA memo 234 found at

www.ovro.caltech.edu/~lamb/ALMA/Antenna_memos.htm

The convective heat transfer coefficients were then adjusted upward to the point where the resultantpeak temperature difference was reduced to the least prevalent difference observed by Lamb andWoody, 9 deg. C, if the reflectance of their white paint was as good as high reflectance Trianglepaint. That paint is, at this time, unknown but certainly not as reflective as high reflectanceTriangle. When this paint solar heating reflectance is known, the convective coefficients can beraised to preserve the observed temperature difference. This will, in turn, reduce the calculatedRMS distortion.

Solar heating weighted reflectance and IR re radiation emissivity:Solar heating reflectance and IR emissivity for some reflector finishes

Surface Solar heating reflectance IR emissivity data source

Aged aluminum (no surface treatment) 71.3% 0.04 to 0.19 1, p9 & 2, p79Insil-tec white paint 77.8% 0.9 1, p5High reflectance Triangle white paint 85.0% 0.91 3, p10 ref. LBNLInorganic high reflectance coating 95.0% 0.4* 2, p256 reflectance only

*goal, notmeasured

data sources, title author publisher or url1 Laboratory Testing of the ReflectanceProperties of Roofing Materials

Florida Solar EnergyCenter

http://www.fsec.ucf.edu/bldg/pubs/cr670/

2 APPLIED SOLAR ENERGY Aden B. Meinel, MarjorieP. Meinel

ASSISON WESLEY, 1976

3 A Primer for Energy Efficient Buildingsand Construction

Solar San Antonio, Inc. www.solarsanantonio.org


Assess Solar flux for reflector heating:

Standard desert solar heating flux at the zenith is 980 watts.m^2 ref. p45. Meinel 2. At 60 deg. solar altitude, flux drops down to 925 watts.m^2. (reduction accounts for atmospheric attenuation)

Use 750 w/m^2 from Fig.2.4 p.47 Meinel 2 Urban (D+S) at 40 deg solar distance for 4' x 4' test. Use STANDARD (D) for Hat Creek gives 900 w/m^2 for 30 deg . solar altitude.

Finally discount flux by the cosine of the incident angle onto the absorbing surface. (Accounts for cosine loss when sun is at solar noon.)

Use solar heating reflectance value for Triangle white paint in "A Primer for Energy Efficient Buildings and Construction" by Solar San Antonio, Inc. ref. LBNL data. http://eetd.lbl.gov/CoolRoofs/ref_01htm

sh = solar heating w/m^2sd = solar desert heating straight up w/m^2

For SKA 12-16 dish when it is unpainted aged aluminum:

sh 900 100 85100

. cos 30 π.

180.

sh 116.913=

incidence angle, ia, deg:

ia

32.87

28.28

25.79

20.78

10.68

15.33

Facit average thermal heatring value, fsh, W/m^2:

fsh sh cos ia π

180..

fsh

98.196

102.959

105.268

109.308

114.888

112.754

=

evaluate heating for outer rows, fsh mesh, that are mesh of low crossection for solar intercept.p is fraction of intercept of the mesh. 25% for 12-16 mesh:

p .25

fshmesh p fsh. fshmesh

24.549

25.74

26.317

27.327

28.722

28.188

=

Figure 14 Calculation of solar heating at various cosines

Model groomingproved tedious. Fig.15 shows thecomplexity of themeshed shell model.T h e t e d i o u sgrooming involvesplacing numerous“split lines” whichdivide the surfacesin such a way thatthe automaticallygenerated meshnodes at joinededges behave in aconnec ted wayduring the analysis.This happens whennodes are co locatedparticularly at edgeswhere three shellsc o m e t o g e t h e redgewise.

Assessing the solarheating facet byfacet was calculatedin MathCAD. Fig14 shows thatca lcula t ion forT r i a n g l e h i g hreflectance paint.W o r s t c a s eassumptions forclear desert airi n c i d e n c e a r ed i scoun ted fo rlatitude and thecosine assuming thedish is face on to thesun. Angles, shownas “ia”, are takenfrom the Solid


Figure 16 Temperature gradients nearback structure detail

Figure 17 Calculated temperature distribution, IHRC

Figure 15 Mesh node connectivity at three way edgeintersections

Works model. Seven heating values arecalculated for both solid and mesh buto n l y s e v e n v a l u e s a r eactually used in the analysis.

Face on sun represents one of the extremethermal cases. It was calculated to berepresentative of thermal distortion.Other cases where sun incidence is off theRF axis are very much more complex toapply to the model. These can becalculated when more budget andschedule are available

THERMAL RESULTS

Fig 17 shows a representative temperaturedistribution, the one for an inorganic highreflectance coating (IHRC) fourth lineitem in table below, “Surface finish vs.RMS surface accuracy”. The highest temperature is 6.87 deg F(3.8 deg C) above ambient.

Fig 16 shows the temperature distribution near a radial hat section. Here we see that there is asmooth transition from the back structure cooling to the high temperature at the middle of thereflector shell between the supports.


Figure 18 Best fit errors for the IHRC coated reflector

Fig 18 shows theresidual error in thereflector surface afterbest fitting for IHRC. Itis clear from this plotthat the most significanterrors accrue due to thegradient shown in Fig.17. Ongoing designefforts will be directedat reducing this localphenomena.

Since thermal distortionis proving to be the mostchallenging issue for theUSSKA re f lec to r ,several combinations ofsolar heating weightedreflectance and reradiation IR emissivitywere analyzed tounderstand the overalli m p a c t o f t h e s eparameters. Some datap o i n t s r e p r e s e n tattainable combinations, others are included to complete the two emittance curves. See Fig.20, 2pgs.below. See also “Surface finish vs. RMS surface error”, a tabulation of candidate finishes and plot,Fig 19, of surface error and temperature difference for the table. Surface finish vs RMS surface error

solarheating

reflectance

re radiationIR emittance

t h e r m a ls u r f a c eerror in.RMS

M a x .temperaturedifferential,deg. F

Unfinished aluminum -aged 71.3% 0.05 0.104 101.6Insil-tec white paint 77.8% 0.9 0.03699 33Triangle high reflectance white paint 85.0% 0.91 0.0218 16.56Inorganic high reflectance coating IHRC 95.0% 0.4 0.00782 6.87


Temperature difference governs surface accuracy

0

20

40

60

80

100

120

0 0.02 0.04 0.06 0.08 0.1 0.12

surface accuracy, in. RMS

Tem

pera

ture

, deg

. F

Series1

Figure 19 Surface error vs. temperature differential, deg. F

The forming of the CADshell model for the analysishas yielded a designsuitable for analysis but notnecessarily effective forthe actual building of thereflector. Careful attentionshould be applied toshap ing the ac tua lfabrication details to makethem both structurallyeffective and cost effectiveafter the final optimizeddesign is established.Hasty building of thismodel would be no bettera prototype than the 6meter bread board that hasno production capable andsome structurally unstablejoints.


Figure 22 IHRC with doubled “egg crating”

Thermal Surface Accuracy, Natural Convection "3 sigma calm"USSKA Strawman 12-16 meter antenna

0.71

0.78

0.85

0.95

0.70.75

0.80.85

0.90.95

1

0 0.02 0.04 0.06 0.08 0.1

Surface accuracy, in. RMS

Ref

lect

ance

, sol

ar h

eatin

g w

eigh

ted

high em m itance ~.9

low em m itance ~.05

Triangle high reflectance paintInorganic coating (TBD)

USSKARequiredAccuracy

Insultec white paint

Aged Alum inum

Figure 20 Surface error vs. solar heating reflectance and IR emittance

Figure 21 IHRC with initial “egg crating”(Temperature values NOT from this study)

Some sensitivity analysis was performed to assess the variation of surface error when varying designparameters.

Two levels of “egg crating” were compared both with the same inorganic high reflectance coating(IHRC) assuming grey body IR emmitance (0.05). Figures 21 and 22 show the comparative “eggcrating”. Initial levels of “egg crating” produced best fit surface error of 0.0153 in. RMS while


USSKA SURFACE ACCURACYerror(in.) error sq. (in.^2)

Manufacturing 0.0080 0.0001Gravity 0.0023 0.0000Wind 0.0018 0.0000Thermal* 0.0078 0.0001 total 0.0001RSS (in.) 0.0115RSS (mm) 0.2933*developmental IHRC case used

doubled produced 0.0139 in. RMS, or a 9% reduction. Short dimension separation between “eggcrating” for initial design was 94” and 47" for doubled design.

Later the doubled “egg crated” design was analyzed scaled to half size such that the short dimensionspacing fell to 23.5" and the surface error was reduced by 66%. This change was run with a greaterIR emittance applied to both the 12 and 6 meter portion of the reflector making the heat sinks moreeffective. Also the material thicknesses were not scaled.

Both higher emittance and closer “egg crating” improve surface accuracy. It seems that much canbe done to improve surface error by better designs.

TOTAL SURFACE ERROR

All surface error sources are combined as the root of the sum of the squares, RSS’d. Thespecification is for 0.012 in. RMS. The strawman is then on track for meeting the specification.


Figure 24 von Mises stress induced by 100 MPH wind on stowedreflector

STRESS

With the reflector stowedat zenith pointing,stresses in the reflectorstructure are reasonableat 8 ksi peak. See Fig 23.

However buck l inganalysis may showfurther bracing isrequired for the longmembers to the bottom atthe “throat”.

Known reflector development issues to be studied in future work:

• Reflector thermal coating development optimization. Manufacturers will be contacted todetermine what can be achieved.

• Reflector heat sinking. Continued design work will show what the detail of added “eggcrating” should be prior to building a prototype in balance with reflectance development.Enough stiffening and heat sinking might find a solution with advanced titanium oxidecoatings as suggested by Aden Meinel.

• Material thickness considering stress and thermal, wind and gravity distortion. Variousthicknesses should be analyzed further to determine optimization suitable for the high


Figure 25 Typical azimuthbearing cross section

Figure 26 12-16 mantenna

Figure 27 Pedestal

quantity manufacturing anticipated. The potential savings and analytic costs should bemanaged in a strategic manner to attain the best overall cost.

PEDESTAL

-Azimuth bearing

The strawman design uses a turntable bearing withgear cut in the outer race of the bearing as the basisfor the azimuth axis. This arrangement has oftenproven to be economical. This bearing resides in thelower part of the housing just above the cylindricalpart of the pedestal.

The overall layout of reflector and pedestal,including throated reflector nested over an elevationaxis, was proportioned intuitively to give a resonant frequency that will allowsatisfactory statistically based wind gust response. This presumptionneeds to be analyzed and adjusted if need be in the future work. Thespace for this bearing allows a 45" pitch bearing with an outer race gearwith a 65” pitch diameter.

Loads for this bearing were assessed.

Again, extrapolation was required to assess coefficients that are used tocalculate the wind load reactions that must be resisted by the pedestalas it holds the reflector in the face of the survival and operating winds.No wind tunnel data was obtained in the 1960, CP-3 era. As above forthe reflective surface pressure differential extrapolation, coefficients forfull and outer radius porosity at 25% were used to extrapolate for a 75%porosity. Wind loads and estimated structural weight were resolved tothe azimuth bearing utilizing a computer program maintained bySCHULTZ ASSOCIATES that has its origin back to Blaw-Knox Co.and Philco-Ford more than 30 years ago. This program calculatedloading at all representative antenna elevation attitudes and azimuthwind angles. The peak azimuth bearing loads are noted for each windspeed. These peak loads were used to describe the loading for a 12-16meter USSKA turntable bearing specification used by a manufacturerto select the bearing cross section capable of resisting the loads andupdate the anticipated cost. See the specification that fallows.


USSKA 12-16 Meter Antenna Azimuth Bearing/Bull Gear Spec.

SIMILAR TO JPL-006 EXCEPT WITH LARGER SIZE AND HIGHER LOADING

PITCH DIAMETER: 45 in.

Max Rotation speed: .5 RPM

Life:

50,000 slow continuous revs with motion of .000002 rev oscillation at 1/6 hzsuperimposed for 250,000 hrs.

Loads:

Survival due to 100 MPH wind at stow (non operating)Axial 16,900 lbRadial 5,600 lbMoment 342,700 ft-lb

Operating up to 15 mph wind 80% of time

Axial 16,900 lbRadial 2,500 lbMoment 51,700 ft-lb

Operating up to 30 mph wind 19.5% of time


Operating up to 50 mph wind 0.5% of time


Stiffness:

Typical of a 45" dia. X roller bearing

Gearing:

4 Pitch 20 deg spur ~4" face 320 BHN AGMA CLASS 12


Figure 28 Pinion shrunk on output shaft forelevation drive on 30 meter AT&T commercialcommunications volume build antenna

-Azimuth Gear boxes

Maximum driving torque at 50 MPH worstorientation wind requires 25,000 lbstangential load on 4 pinion teeth (use 4 gearboxes). This load can be resisted by a 4pitch pinion tooth according to the R.W.Bertron gear tooth selection chart dated5-18-64. This chart has proven accuratewhen detailed gear analysis is laterperformed. That analysis will be done inthe next work segment

Gear ratios can be calculated then forestablishing gear box ratio and gear boxcontinuous torque rating. The bull gearspace allocation allows for a 5.5' or 65"pitch diameter. (Pitch means how manyteeth there are in the gear per inch of pitchdiameter.) Accordingly there are 65 x 4 =260 teeth in the bull gear. Antenna pinionsusually have 15 teeth. The bull gear and pinion gear ratio is then 260/15 = 17.333:1.

Specified slew rate is 1/2 revolution in a minute or 0.5 RPM. Many motors are built for 2500 RPMtop speed. Accordingly an overall ratio of 2500/0.5 = 5000:1 is a good starting point. The gear boxneeds to provide 5000/17.333 = 288 ratio to yield the overall ratio.

Gear box maximum driving torque is calculated using the pinion pitch radius times the toothtangential force. Half the pinion pitch diameter is 15/4 = 3.75" or 1.875". The torque is then 25000lbs x 1.875 = 47,875 in. lbs. Continuous rating for cyclo drives are consistently 1/3 the peak shorttime max torque for antenna applications or 47,875/3 = 15,625 in-lbs. From the Sumitomo cyclodrive catalog we find a model 6165 provides over 18,000 in. lbs. torque rating. Also the shaft size,1.875 inches will fit into a shrink fit hole in the pinion with a tooth height of clearance between boreand root of the pinion tooth roots.

COST ESTIMATE A table with a breakdown of a $131,103 cost estimate of the antenna described in this document follows with comments below: 1) The cost estimate is in 2005 dollars and escalation to construction years will be needed. 2) The conceptual design gives the weight of steel (18,316 lbs) and aluminum (5,800 lbs) required. A large portion of the cost estimate is based upon price per pound of steel fabrication ($3.27 per lb has been used) and aluminum fabrication ($6.33 per lb) and these costs can be updated and adjusted for country of manufacture. 3) The estimate does not include non-recurring engineering and tooling. The NRE will be of the order of $10M and must include: a) detailed structural design, analysis, and optimization. b) a hydroform mold for the reflector, c) manufacturing process design, d) an on-site hydroforming press and assembly building, e) two iterations of prototype antennas, 4) The estimates do not include: a) assembly and checkout: estimate 160 person hours at $60/hour = $9,600, b) servo electronics at $5,000, c) shipping at $5,000, d) thermal and environmental protection at $10,000, e) subreflector and prime focus flip assembly at $8,000, f) foundation and electrical service – this is site dependent and should be included in site costs. The total cost estimate including a) – e) is then $168,703. 5) The estimate assumes that an SKA construction organization with overhead costs included elsewhere in the cost estimate for management and purchasing. If a “turn key” job by an antenna manufacturer is desired then an additional 25% for management, purchasing, and profit must be included to bring the total to $200,879. 6) Prior to the NRE a contingency of 15% should be included; this could be reduced to 10% after the NRE with prototype antennas is complete. 7) The cost estimate is for quantities > 1000 with a 60% higher cost estimated for quantities < 10.

Cost Estimate for USSKA 12/16m Antenna July 19, 2005

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