• Etäisyys välyksettömien laakereiden välillä riippuu niiden tarkkuusluokasta ja asentotarkkuustavoitteesta joka annetaan alempana.
• Akselille on asennettava myös tarkka (paljon bittejä antava) akselin asentomittauslaite, esim. Virtual Absolute Gurney Precision Instruments:lta,
• tai sisä-/ulkopuoliseen uraan ERA 780C/880C inkrementti Heidenhain:lta..

• Kokeellinen määrittely kyllin pienellä taipumalla: Teräsputki: Ulkohaljaisija=323.9mm, seinämä=12.5mm, Fe 35, pituus noin 700-800 mm. Vaihtoehtoiset materiaalit ovat mahdollisia.
• Kuorma on noin puolet peili+vastapaino+elevaatiolänkien massasta (noin 16-20 tonnista)
• Tähän akseliin ei kohdistu vääntömomentia, ainoastaan taivutusta.
• Toinen elevaatiolänkipuolikas tarvitsee isoläpimittaisen hammaskehän ajomoottoreiden voiman välitykseen.
• Tämän kerän läpimitta on jotain 1.0 - 1.6 metriä ja akseli kääntyy hieman yli 90 astetta (ehkä 100 astetta ?)
• Ääritilanteissa tämä rakennelma saattaa olla voimakkaasti epätasapainossa aiheuttaen hampaistoon helposti luokkaa 100 kN olevan tangentiaalisen voiman.
• Systeemillä tulee olemaan lukitustapit, joilla elevaatiolänki saadaan lukittua ainakin 0 ja 90 asteen elevaatioihin ilman, että rattaita rasitetaan.
• Elevaation vaihteiston pitää antaa noin 1/6 rpm nopeus elevaatio- akselille moottorien pyöriessä 2000-4000 rpm. Kokonaisvälitys on tällöin luokkaa 1:12000 - 1:24000.
• Normaalissa käyttötilanteessa tasapainon oletetaan olevan hyvä ja tangentiaaliset voimat ovat alle 1kN.
• Moottoreiden vaihteistovälyksiä eliminoimaan tarkoitetut pitomomentit saattavat olla jopa suurempia, kuin itse kuorman momentti.

• Atsimuuttikääntökehän ei pitäisi muuttaa pyörimisasentoaan pelkästään siksi, että systeemin tasapaino siirtyy hieman eri kohtaan (vrt. Metsähovi). Jos sellaisia liikkeitä tapahtuu, niiden pitäisi olla alle yhden milliasteen (0.001 astetta) suuruisia.
  • Mikäili syynä on laakerikehän staattinen epätasaisuus, joka siis toistuu aina samassa kiertoasennossa, se ei välttämättä haittaa ollenkaan. (Ennustamattomat muutokset pyörimisakselin suunnassa eivät ole haluttuja.)
  • Mikäili syynä on laakerikuulien/-sylinterien läpimittojen vaihtelu, tilanne saattaa olla huonompi.
  • Näitä ongelmia voidaan kompensoida melko hyvin tarkalla kaltevuusmittarilla, joka mittaa atsimuuttihaarukan vaaka-asentoa suorakulmaisiin suuntiin. (Mistä saa ? Kuinka kalliita ? Tuleeko halvemmaksi käyttää kaltevuusmittausta, kuin ostaa huipputarkkoja laakereita atsimuuttiin ? Entä elevaatio ?)
• Hampaiston tarkkus ei ole kovin merkittävää. Epätasaisuudet hampaistossa ovat käytännössä merkityksettömiä koska moottoreiden ohjaus perustuu pääakselin kiertymään, jota mitataan suoraan, eikä moottorin nopeusanturin antamaan askelmäärään, tms. missä vaihteiston tasaisuus merkitsisi mitään.
• Laakereiden voitelussa ei saa käyttää aineita, joissa on yli n. 1µm hiukkasia, sillä sellaiset aiheuttavat havaittavaa satunnaista suunnanvaihtelua kun tällainen hiukkanen osuu laakerikuulan/sylinterin ja laakeripinnan väliin.

kurpitsa05.fig, kurpitsa05b.fig, kurpitsa05c.fig

Fig 6: Vaihtoehtoisia atsimuuttiakselin rakenteita:

kurpitsa06.fig, kurpitsa06b.fig

Fig 7: Metsähovin jalan atsimuuttilaakeri.

HUOM: Kaikki moottorit ovat atsimuuttihaarukassa!

Tämä rakenne on äärimmäisen herkkä alemman (rulla-)laakerin välyksille!

Vaihtoehtoisessa rakenteessa alempi laakeri on sekin kartio ja sitä kuormitetaan hallitulla esikuormituksella jotta välykset saadaan eliminoitua. Katso kuvaa Fig6.

kurpitsa07.fig

Fig 7B: Metsähovin jalan elevaatioakseli

Elevaatiovarressa oleva iso aukko on nähtävissä mm. tässä valokuvassa. (Oheinen piirros on päätelty sinipiirroksista ja valokuvista.)

Elevaatiovarsi on itsessään teräslevyistä rakennettu kotelorakenne poikkileikkausmitan ollessa noin 500x1800 mm.

Tämä elevaatioakselirakenne näyttää toimivan erittäin täsmällisesti.

kurpitsa07b.fig

Fig 10: Peilin kiinnityspisteiden geometria

Kiinnityspisteet ovat ympyrällä, jonka läpimitta on tasan 12 jalkaa (144 tuumaa.)

Varsinaiseen kiinnittämiseen käytetään läpimitaltaan 1.00 tuuman normaalia karkeakierteistä pulttia.

Pultin kiristysvoima on tuntematon.

kurpitsa10.fig

Fig 11: Draft idea of elevation-yoke dish-fixture grid.

This I-beam grid fixture connects the dish to the pedestal elevation mechanics with counterweights.

Problem: There are support trusses which are supposed to be attached into the elevation yoke, and those presume certain specified dimensions (specifically: width) for the elevation yoke...

To be equiped with torsion force sensors to see the amount of deformation as a function of tilt.

kurpitsa11.fig

Fig 11B: Some guestimates of forces at the fixing points

The values are more or less taken at random by guessing them. Real values will need good FEM model of the dish... :-/

The matrix shows how elevation change alters loading vectors at the dish fixing points.

kurpitsa11b.fig

Fig 12: Draft of what the original pedestal elevation arm looks like.

Notable detail is that the distance from elevation axle to dish fixture points is 1130 mm.

The big opening in the elevation arm can be seen at this photograph. (This is deduction from blueprints, and photographs.)

Also notable is that those elevation arms are massive construction.

kurpitsa12.fig

Fig 13: A draft of Az-bearing as done with a slewing-ring bearing

Problem: How will the orientation of the rotation axis change as a function of varying tilting moment ?

There is around 160-200 kN of axial fairly static load, and tilting moment can exist in range of 0 to 20 kNm (guestimated) in varying directions.

Desired limit in the amount of axis direction change is below 1 millidegrees! (0.001 degrees).

For various system construction time loads, the system must survive a lot larger tilting moments when wind blows to assembled mirror structure before protective radome has been installed. Guestimate: 200-400 kNm

The green marker shows roughly, which surfaces must be machined for smooth centered surfaces - centering of the ring to the Az-fork is highly important to within about 0.50 mm.

Centering is not quite that important in the base structure.

Exact placement of the ERA780C read-heads (in the Azimuth angle direction) is not important, they will be calibrated in software latter, when the systemwide calibration is done.

Placement of the read-heads on the scale tape is fairly high-precission thing:

• Permissible axial movement: ± 0.2 mm
  • This means the system must be flatter than this all way around!
  • This being at the azimuth bearing, there probably won't appear any (operation time) tilting forces to move the ring much at all.
• Maximum allowed Rotation centre excentricity for the scale tape is: 1.0 mm
  • The bearing and scale tape must be better centered than this!
• The scale tape length determines the diameter of the bottom of the scale tape installation slot
• Width of the scale tape slot is: 13.2 + 0.1 mm
• Depth of the scale tape slot is: 0.5 mm
• At one point there needs to be a small (ca. 2mm wide) slot to reach below the scale tape slot for removal of the scale tape.
• Slot diameter is given at UNSPECIFIED temperature (+20C ? Temp. range is given as -10C to +50C)
• The thermal expansion coefficient for the scale tape is 9-12 ppm/Kelvin.
• The thermal expansion coefficient for structural steel should be chosen to be as close to that as possible.
  • (The 60K temp range with 90000 line scale tape effects 0.17 mm radial differential change as compared with base structure made of 12 ppm/K material, which might not matter, after all.)

Add to the picture:

• Exact slewing-ring structure
• Pipes for grease distribution
• Exact mount companion ring structure details
• Extend the base-ring down and left, and make it a ring to be mated on top of some pilar/tower
• Extend the az-fork structure up and left (and around).
• Dust-cover fixed and rotating joints, and seals

The system has very large central hole in it, in order of 500 or 1000 mm in diameter of free space!

The dust-cover structure may need additional "touch-cover" structure to allow it to be fairly light-weight.

Various cables from the Az-fork are to be dropped down in neat controlled bundle near the center of that so that they can freely twist around while falling some 5-6 meters down. (For free rotation of about ± 2x360 degrees.)

THIS IS NOT IN ANY PARTICULAR SCALE!

kurpitsa13.fig

Fig 13B: A draft detail of El-bearing as done with a slewing-ring bearing

The rotation axis of this ring is horizontal!

Each bearing carries about half of the antenna + counterweight load, namely some 60-80 kN.

Problem: How will the orientation of the rotation axis change as a function of varying tilting moment ? Does it matter ?

Problem: What are the allowed tilting moments ? What are expected ?

There is definite forces applied at the gear, which is fixed into the El-arm part of the joint. (All drive motors are in the Az-fork!)

Desired limit in the amount of axis direction change is below 1 millidegrees! (0.001 degrees). (Or is it ?)

Absolute maximum for tilting and axial movement is 0.2 mm due to the high-precission angle encoder; see below.

For various system construction time loads, the system must survive a lot larger tilting moments when wind blows to assembled mirror structure before protective radome has been installed. Guestimate: 200-400 kNm

Also the gear teeth will receive possibly considerably large forces under wind conditions. However a locking pin system should alleviate, or hopefully eliminate that problem.

The green marker shows roughly, which surfaces must be machined for smooth centered surfaces - centering of the ring to the el-arm is highly important to within about 0.50 mm.

Centering is also quite important in the Az-fork structure, as these two disjoint bearings should have as accurately as possible the same rotation axis.

Exact placement of the ERA780C read-heads (in the elevation angle direction) is not important, they will be calibrated in software latter, when the systemwide calibration is done.

The read-heads allow

There will likely be several of those read-heads (2-3), and they are stationary in the az-fork reading rotating ring.

Placement of the read-heads on the scale tape is fairly high-precission thing:

• Permissible axial movement: ± 0.2 mm
  • This means the system must be straighter than this all way around!
  • This being at the elevation bearing, and there being considerable tilting moments present, this is yet unanswered problem.
• Maximum allowed Rotation centre excentricity for the scale tape is: 1.0 mm
  • The bearing and scale tape must be better centered than this!
• The scale tape length determines the diameter of the bottom of the scale tape installation slot
• Width of the scale tape slot is: 13.2 + 0.1 mm
• Depth of the scale tape slot is: 0.5 mm
• At one point there needs to be a small (ca. 2mm wide) slot to reach below the scale tape slot for removal of the scale tape.
• Slot diameter is given at UNSPECIFIED temperature (+20C ? Temp. range is given as -10C to +50C)
• The thermal expansion coefficient for the scale tape is 9-12 ppm/Kelvin.
• The thermal expansion coefficient for structural steel should be chosen to be as close to that as possible.
  • (The 60K temp range with 90000 line scale tape effects 0.6µm radial change, which might not matter, after all.)

Add to the picture:

• Exact slewing-ring structure
• Pipes for grease distribution (preferrably from Az-fork side!)
• Exact mount companion ring structure details
• Dust-proof encasing structure for the read scale tape, and the read-heads, of which the casing is stationary while the scale tape rotates
• Access to the slewing-ring bearing inside, thus the read-head base can't be solid ring around the system
• Dust-cover fixed and rotating joints, and seals

The system has very large central hole in it, in order of 500 or 1000 mm in diameter of free space!

The dust-cover structure may need additional "touch-cover" structure to allow it to be fairly light-weight.

Alternate design has the encoder scale tape in the Az-fork, and the read-heads are rotating. Could that be simpler to implement ?
(Picture of that is identical to Az-bearing; fig13, above)

THIS IS NOT IN ANY PARTICULAR SCALE!

kurpitsa13b.fig

(No figure) Random thoughts

• All bending structures be equiped with strain-gauges. (dish/el-yoke fixture, Az- and El- axles, support trusses ?)
• Measure tilting of Az-fork by inclinometers ?
• Az- and El- drive axles to be equiped with strain-gauges to measure the amount of unbalance in drive forces (twisting of the identical pinion drive axles)
• Motor positionable balance counterweights ?

Fig14: ERA780 asteikkonauhan tukikehä

Tämän rakenteen materiaalina käytetään ainetta, jonka lämpölaajenemiskerroin (alffa) on 10.5 ppm/K lämpötila-alueella 250-300K. Todennäköisimmin tämä aine on jokin muutoin seostamaton perusteräs, johon on lisätty 5-27% kromia.

kurpitsa14.fig

Lisää ajatusten keruuta:

Suomiversio on vaiheessa!

The system is a radio telescope with diameter of 13.7 meters, and it is enclosed in a wind/rain protective radome housing, thus we don't have wind forces to account in normal system operation.

For this system we are not looking absolute precission in the components per se, but what is foremost important is reliable repeatability of the axle orientations, and in their measurements.

Each axle's rotation will be measured with high-resolution incrementers made by Heidenhain (ERA 780 most likely). Those are installed as steel scale tape into a "large" diameter inside groove, and read from stationary encoders (encoders may also move, and scale tape be stationary); standard product model inner groove diameters are 1146.10 mm, and 573.20 mm, which are guiding diameters for our structure definitions, to have them somehow nicely in the bearing structure.

Present primary models are referred at following pictures:

fig7, fig7b, fig5, fig6, fig13, fig13b

We had recently an opportunity to study systems made in 1970es for this same purpose, bearings/gear structures used in those are pictured at "fig7" and at "fig7b".

At the "fig7/fig7b" pictures the "drive gears" are of fairly large diameter, most likely "60 inches a.k.a 2 yards" (the thing being american and inch/feet dimensioned.)

The bearings of elevation axles in the "fig7b" work very well having no practical backlash, and excellent axle and el-arm orientation control.

The lower bearing of the az-axle at "fig7" is way more problematic being effective cause for uncontrolled movements in order of 20µm/500mm; circa 8.25 arc seconds, which is 11 times larger than system tracking resolution goal. The problem has been countered at one site by purposefully unbalancing the system above the Az-bearings. Amount of this unbalance is roughly 1.5 kNm.

I have heard that British astronomers have used ball-bearing rings at some telescope, but how it works, that I don't know.

At figure "fig5" we have some rough draftings of how the loads are placed in normal operation at the Az-fork, and its associated bearing points. The moment nearest to the az-axle is for the bending of the structure, not tilting it.

In normal operation the amount of tilt-moment for Az-bearing will be well below about 10 kNm. Still it should not break causing the system to fall down if the tilt exceeds 100 kNm. Compare this to the mass gravity force (F_a) above the Az-ring: 150 - 200 kN.

Not even deformation should occur at 100 kNm, but returnable physical axle orientation changes are allowed, e.g. when tilt-moment exceeds the gravity force allowing one edge of the ring to raise..

Keeping the amount of Az-axle tilt-moment (M_k) in mind (±10kNm), the amount of the rotation axle tiling as a function of the tilt-moment should be as small as possible, preferrably zero.

Other earlier mentioned system mechanical reasons calls for inner diameters of about 1145-1250 mm. Preferrably 1146+60mm, or a bit more. (Giving some 30 mm room for the high resolution incremental encoder scale tape reader assembly.)

The gear at Az-ring can be at lower/outer ring, which is apparently normal for rings with outer gearing. Indeed all existing systems that I have seen have all drive motors, and gearboxes in the "az-fork" structure, which rotates, and the Az-gear itself is stationary.

To eliminate gear backlash there are two motors + their gearboxes to drive the Az-gear. The motors will always counter-rotate and keep small torque against each other (100 W DC motors via 1:18000 gearing ratio from motor axle to Az-axle.)

The elevation bearings/gears are their own story.

We do know that the existing el-axle constructions (fig7b) behave well, but we don't have a clue if it can also be done with slewing rings. (e.g. British astronomers are using ball-bearing rings at some telescope.)

Loading is primarily radial, but there exists some tilt-moment which orientation will always be towards earth, but as the elevation arm structure rotates from 0 to 90 degrees, forces caused by it will be varying. The el-arms are bound together by either HEB-beams, or equivalent size hollow beams, which will somewhat counteract the outwards tilting forces.

Here, again, the extremely accurately repeatable behaviour is the primarily wanted feature, Due to the construction symmetry, it is likely (no good FEM models have been made of this yet) that in essense the tilt moment present in el-bearings will be cross-compensated via the beams joining the el-arms. (The combined el-arms + joining beams are called: "el-yoke")

We expect the elevation arms, and the mirror + receivers attached into it to be slightly off-balance. Will this ever appear as direction changing torque moment at the elevation bearing is open. Most likely it will appear as changeing force depending on elevation.

Torques present at the el-axle in normal mode are aimed to be well below 1 kNm, A 2.0 Nm 3000 rpm DC motor via gear ratio of 1:18000 should be able to hold (and drive) the thing easily. In an overload a person is walking at the mirror surface (100 kg = 1000 N) some 10 meters from the gear -> 10 kNm torque at the gear. Similar loads may also occur during auxiliary mirror change operation, at which a 200 kg assembly is removed from 9m away of the el-azle -> 18 kNm torque.

The gear-backlash elimination with counter-torqueing motors may also produce gear teeth forces around 1-50 kNm... (must control that)

• 1.3 Nm / 275 rpm motor via 1:1650 gears -> 2.1 kNm minus frictions;
• 1.8 Nm / 3000 rpm motor via 1:18000 gears -> 32.4 kNm ...

SKF suggested using three identical cross-roller geared slewing bearings:

  RKS.221300101001  @ 17500 FIM/unit, (EUR 2617,-) ( +VAT )
  (offer dated 18/6/2001)

Cross-roller bearing
Raceway D =   980 mm
Outer D   =  1080 mm
Inner D   =   886 mm
Total width    82 mm
Outer ring w   72 mm
Inner ring w   53 mm
Gear module:  8
Gear teeths: 133

Bolts at both rings:  30 x M16

That ring is a bit small, though... and we are most uncertain about the effect of tilting moments on rotation axis orientation. More so when rotating at horizontal axle.

Hoest Rothe Erde (HRE) gave a suggestion only to the Az-ring:

EUR 5945,- freighted to Helsinki.

Four-point Ball-roller bearing (series RK600 ? (621 ?))
  Drawing:  061.25.1475.---.--.1203

Bearing height      =     75 mm
Bearing weight      ~    192 kg

Inner   d           =   1390 mm
Inner bolt circle d =   1420 mm
Raceway d           = ~ 1475 mm
Outer bolt circle d =   1530 mm
Gear midline d      =   1584 mm
Gear outer edge D   =   1600 mm

Gear module:  8
Gear teeths: 198

Bolts at both rings:  80 x M12,  Bolt strength grade 8.8,
Nominal preload 70%
Tightening factor Alpha-A: 1.60

It might well be that we use a larger diameter ring at Azimuth, and a smaller diameter ring at the Elevation!

Namely something like D_inner = 1145-1155mm for Az, and D_inner = 575-585 mm for the elevation!

Follow this link to: Building, radome data

Matti Aarnio <matti.aarnio@zmailer.org>; OH2MQK