Item 0859

DESIGN: UniCopter ~ Rotor - Hub - ARR - Bearings - Pitch - Roller, Ball and Needle

Outside Helicopter:

E-mail discussing the Sikorsky ABC:

One disadvantage that I remember was a short life on the spindle bearings. This was said to be caused by the large horizontal fin generating a large nose down pitching moment in descending flight such as a steep approach or an auto rotation, likely a very fixable problem.

UniCopter:

To be similar to the ABC one above, or use thrust bearings??

Axial and Radial Forces on Pitch Bearings:

From: DESIGN: UniCopter ~ Rotor - Disk - Blade Forces Currently 4-blade rotor only.

Ultimate radial load on a bearing sets = 65,057 lbf.-in / 3.5"[between brgs] = 18,588 lb. (82,683 N)

The bearing furthest from the mast will be subjected to the (slightly) higher radial load.

Note that the above loads include a 4.0 [LLF - limit load factor] x 1.5 [SF - safety factor].

Drawing:

Upper portion of drawing above.

The maximum axial loading is 5,611 [24,959] x (3.0 [LLF] x 1.5 [SF]) = 25,249 lb. (112,313 N)

The maximum radial loading is 10,837 [48,205] x (4 [LLF] x 1.5 [SF] = 65,022 lb.-in. / 3.5 = 18,578 lbs.

Therefore the worst case scenario on the inner bearing is a loading of 25,249 + 18,878 = 44,127 lbs. (196,286 N). Note that the LLF on the maximum axial loading has been reduced from 4 to 3 [173% RRPM] since I feel that the ability to experience maximum axial and maximum radial loads at the same time is probably impossible. Particularly with a rotor governor.

Lower portion of drawing above.

The minimum axial loading is 5,611 / 2 = 2,805 lbs top and bottom of bearing.

The maximum radial loading is 10,837 x (4 [LLF] x 1.5 [SF] = 65,022 lb.-in. / 3.4470 = 18,863 lbs.

Therefor the worst case scenario on the inner bearing is a point loading of 18,863 - 2,805 = 16,058 lbs ????

Upper portion of drawing above.

Copied from above: Ultimate radial moment on a blade = 65,022 lb.-in. (289,232 N) / 3.5"[between brgs] = 18,578 lb. (82,639 N)

Lower portion of drawing above.

Copied from above: Ultimate radial moment on a blade = 65,022 lb.-in. (289,232 N) / 3"[between brgs] = 21,674 lb. (96,410 N)

Would like to go with NU 2210 below because of OD (for greater hub to blade clearance) and ID (to suit spar), but the Life rating is very low. Are my calculations in accordance with conventional rotorcraft determining????

There will not be any shock loading on the bearings since thay are only subjected to aerodynamic forces and the blades will flex slightly..

FORM: Rotor - Hub - Pitch Bearings ~ UniCopter Not completed

 Inner Bearing: Bearing: SKF 29412 E NTN ET- 33013 - No SKF NTN 4T- 33113 - No SKF Quantity and Type: 1 - Spherical roller thrust 1 - Tapered roller 1 - Tapered roller Part number: 1048 1308 1308 Outer diameter: 5.1181" 3.9370" 4,3307" Inner diameter: 2.3622" 2.5590" 2.5590" Basic Dynamic Load Rating: [C] 345,000 N 97,500 144,000 Basic Static Load Rating: [Co] 915,000 N 156,000 211,000 Radial Load Factor for the Bearing: [X] 1.2 0.4 0.4 Axial Load Factor for the Bearing: [Y] 1.0 1.72 1.72 Actual Radial Bearing Load: [Fr] 73,398 N * 48,205 N (1) 48,205 N (1) Actual Axial Bearing Load: [Fa] 303,496 N * 24,959 N(1) 24,959 N(1) 391,574 N ** 62,211 N 62,211 N Basic Rating Life (in millions of revolutions): [L10] ? ?? 4 16 Rotor Revolutions per Minute: [nn] 10 RPM 500 RPM 500 RPM Basic Rating Life (in hours): [L10h] 1,093 hrs 149 hrs 547 hrs Reliability: [rr] 97 % 90 % 90 % Adjusted Rating Life (in hours): [Ln] 481 hrs 149 hrs 547 hrs Weight; 2.60 kg 0,73 kg 1.28 kg

NOTE (1) The actual loads do not included any LLF or SF.

_______________________

 Outer Bearing: Bearing: B-4420 NU 2210 NU 2212 7212 BE Quantity and Type: 1 - Full compliment needle 1 - Cylindrical roller 1 - Cylindrical roller 1 - Angular contact ball Part number: 0139 xx 1076 xx Outer diameter: xx" 3.5433" 4.3307" 4.3307" Inner diameter: xx" 1.9685" 2.3622" 2.3622" Basic Dynamic Load Rating: [C] xx N 78,100 128,000 57,200 *** Basic Static Load Rating: [Co] xx N 88,000 153,000 45,500 Radial Load Factor for the Bearing: [X] xx 1.0 1.0 1.0 Axial Load Factor for the Bearing: [Y] xx Actual Radial Bearing Load: [Fr] xx N * 48,205 N 73,398 N 73,398 N Actual Axial Bearing Load: [Fa] xx N * 0 0 0 xx N ** 48,205 N 73,398 N 73,398 N Basic Rating Life (in millions of revolutions): [L10] ? ?? 5 6 0 ??? Rotor Revolutions per Minute: [nn] 500 RPM 500 RPM 10 RPM 10 RPM Basic Rating Life (in hours): [L10h] xx hrs 166 hrs 10,640 hrs 789 hrs Reliability: [rr] xx % 90 % 97 % 97 % Adjusted Rating Life (in hours): [Ln] xx hrs 166 hrs 4,682 hrs 347 hrs Weight; xx kg 0,59 kg 1.10 kg 0.80 kg

* [Fr] must be less than 0.55 * [Fa]. This is OK.

* [P] = [Fa] + 1.2 * [Fr] = 303,496 + (1.2 * 73,398) = 391,574 N

** See SKF page 646.

*** This value looks like it can be increased by 5 to 20% by using a 30-deg bearing See Fafnir 2MM212WI

*** To reduce the OD to 3.74" 2 only NU1012's could be used for a total of 2 * 37,400 = 74,800 N, plus a reduction for the reduced moment arm length

Note that the weaker inner bearing has a much higher ratio of static to dynamic then either type of outer bearing and this application is very slow turning.

Note that the inner bearing will be under centrifugal loading constantly whereas the outer bearing will be under excessive loads occasionally.

Consider using the cylindrical roller thrust bearing and the Fafnir 3MM9114WI.

Friction:

General Information:

Ball bearings have a lower friction than tapered roller bearings. Consider tandem, or more, arraignment.

SKF spherical roller thrust bearings are recommended to be operated in oil not grease.

Algorithms for Friction at Pitch Bearings:

The force transmitted to the cyclic stick, by the friction in the teetering bearings and the seals:

Bearings:

Information and algorithms for bearings are from SKF General Catalogue, p 56.

Estimation of Frictional Moment:

M = 0.5 * μ * F * d

where:

M = frictional moment, [Nmm]

μ = coefficient of friction for the bearing;

Deep grove ball bearing = 0.0015 (unsealed bearing)

Angular contact ball bearing (single row) = 0.0020

Needle roller bearing = 0.0025

Spherical roller bearing = 0.0018

Needle roller thrust bearing = 0.0050

d = bearing bore diameter, [mm]

More Accurate Calculation of Frictional Moment:

M = M0 + M1

Remainder of information and algorithms can be found in SKF General Catalogue, p 58.

Seals:

Information and algorithms can be found in SKF General Catalogue, p 62.

M3 = ((d + D) / f3 )2 + f4

where:

M3 = frictional moment of 2 seals, [Nmm]

d = bearing bore diameter, [mm]

D = bearing outside diameter, [mm]

f3 = a factor [table 6]

f4 = a factor [table 6]

Estimate of Friction at Pitch Bearings:

1Nmm = 0.008857 in-lb (I think)

Consider ballscrew bearings for axial. 60° contact angle Fafnir p. 42

 Bearing: Static (N) Dynamic: (N) Dynamic Thrust (lbs) Weight: (lbs) 3MM9107WI 12900 20200 0.35 MM9311 WI 3H QUH 17000 2 for 2.16

9,357 pounds = 41,622 N

M0 = 0.5 * μ * F * d

M0 = 0.5 * 0.0020 * 41,622 * 35

M0 = 1,457 Nmm = 12.9 in-lbs

 Bearing: Static (N) Dynamic: (N) Weight: (lbs) 22206 CJ 13800 13100 0.64

4,107 pounds = 18,269 N

M2 = 0.5 * μ * F * d

M2 = 0.5 * 0.0018 * 18,269 * 30

M2 = 493 Nmm = 4.37 in-lbs

* locations = 8.74 in-lbs

Seals:

M3 = ((d + D) / f3 )2 + f4

M3 = ((30 + 72) / 20 )2 + 10

M3 = 36 Nmm = 0.32 in-lbs

Total Frictional Moment:

M = M0 + M2 + M3

M = 12.9 + 8.74 + 0.32 = 21.96 say 22 in-lbs

Note: Prouty says "most modern helicopters with a floor mounted cyclic stick have a longitudinal force gradiant of 1 to 4 lb/in, with the lateral system being somewhat less".

Lubrication:

Lubricate with oil, not grease, to minimize friction. Oil will require seals with higher friction. May need reservoir, sit gauge (or side fill hole). How does oil get to upper portion of bearings?

Note that this bearing set (the pitch bearings) should be an ideal candidate for elastomeric bearings. The friction of the bearings should be considerably less and there will not be any seals to add to the friction.

Consider: ~ March 13, 2003

• Consider 4-point ball bearing.
• Consider a Crossed Roller Bearing for the pitch bearing:

Consider: ~ February 24, 2004

2 larger angular contact ball bearings at the very root and a smaller full compliment ball (or roller) bearing outboard.

Consider: ~ November 24, 2006

The use of needle bearing for radial loads to keep the rotorhub's drag as low as possible. The control will be by power, therefor a higher friction should not be a problem. Consider a tension-torsion strap for the axial load, particularly if there are 4 blades per rotor.

Same Page ~ Different Craft: ~ SynchroLite (3-blade CVJ w/ HS) ~ SynchroLite (2-blade teetering) ~ Dragonfly

Last Revised: November 24, 2006